Analytical solution singlestep washocat.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as sy\n",
      "import matplotlib.pyplot as pl\n",
      "import numpy as np\n",
      "import cantera as ca\n",
      "import os\n",
      "import job_configurations as jc\n",
      "import simulation_brutus as sim_brutus\n",
      "import glob as gl\n",
      "\n",
      "%matplotlib inline\n",
      "sy.init_printing()\n",
      "import sys\n",
      "#sys.setrecursionlimit(1000)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "paraview version 4.1.0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/lib/pymodules/python2.7/matplotlib/__init__.py:758: UserWarning: Found matplotlib configuration in ~/.matplotlib/. To conform with the XDG base directory standard, this configuration location has been deprecated on Linux, and the new location is now '/home/vonrickenbach/.config'/matplotlib/. Please move your configuration there to ensure that matplotlib will continue to find it in the future.\n",
        "  _get_xdg_config_dir())\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ca.__file__"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sy.__version__"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "'0.7.5'"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%javascript\n",
      "IPython.load_extensions('toc');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "javascript": [
        "IPython.load_extensions('toc');"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.Javascript at 0x7fce49003cd0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D, D_b, h, rho, rho_b, wc_thickness, Y_b, L, Sh, A_V, surf_cov, Y_s, M_i,Y, x,RR,k_r,y, M_CO, k_r= sy.symbols(\"D D_b h rho rho_b  wc_thickness Y_b L Sh A_V, surf_cov Y_s M_i Y x RR k_r y M_CO, k_r\",positive=True,nonzero=True )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C1,C2,C3,C4= sy.symbols(\"C1 C2 C3 C4\" )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cond,T,Delta_H,T_s,T_b,y_temp,eps, tort, lambda_b = sy.symbols(\"cond T Delta_H T_s T_b y_temp epsilon tort lambda_b\",positive=True,nonzero=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y = sy.Function(\"Y\")(x)\n",
      "T = sy.Function(\"T\")(x)\n",
      "Y_b = sy.Function(\"Y_b\")(y)\n",
      "T_b = sy.Function(\"T_b\")(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq = sy.Eq(rho*D*sy.diff(sy.diff(Y,x),x)-M_i*RR*A_V,0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq=diffeq.subs({RR:k_r*(rho*Y/M_i)*(rho*k_r/M_CO)**2})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol=sy.dsolve(diffeq,Y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#homogeneous neumann\n",
      "neum_bc= sy.Eq(sy.diff(sol.rhs,x).subs({x:wc_thickness}),0)\n",
      "#neum_bc= sy.Eq(sol.rhs.subs({x:wc_thickness}),0)\n",
      "\n",
      "dir_bc = sy.Eq(sol.rhs.subs({x:0}),Y_s)\n",
      "\n",
      "bc_sol = sy.solve((dir_bc,neum_bc),C1,C2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "part_sol = sol.subs(bc_sol)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "part_sol"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Y{\\left (x \\right )} = \\frac{Y_{s} e^{\\frac{\\sqrt{A_{V}} k_{r}^{\\frac{3}{2}} \\rho x}{\\sqrt{D} M_{CO}}}}{e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + 1} + \\frac{Y_{s} - \\frac{Y_{s}}{e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + 1}}{e^{\\frac{\\sqrt{A_{V}} k_{r}^{\\frac{3}{2}} \\rho x}{\\sqrt{D} M_{CO}}}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 13,
       "text": [
        "                     _____   3/2                                              \n",
        "                   \u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5x                                          \n",
        "                   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                          \n",
        "                         ___                                                  \n",
        "                       \u2572\u2571 D \u22c5M_CO                                             \n",
        "              Y_s\u22c5\u212f                          \u239b                      Y_s       \n",
        "Y(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u239cY_s - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "            _____   3/2                      \u239c           _____   3/2          \n",
        "        2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness       \u239c       2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thic\n",
        "        \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500       \u239c       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                    ___                      \u239c                   ___          \n",
        "                  \u2572\u2571 D \u22c5M_CO                 \u239c                 \u2572\u2571 D \u22c5M_CO     \n",
        "       \u212f                               + 1   \u239d      \u212f                         \n",
        "\n",
        "                               \n",
        "               _____   3/2     \n",
        "            -\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5x \n",
        "            \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                   ___         \n",
        "         \u239e       \u2572\u2571 D \u22c5M_CO    \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f                   \n",
        "         \u239f                     \n",
        "kness    \u239f                     \n",
        "\u2500\u2500\u2500\u2500\u2500    \u239f                     \n",
        "         \u239f                     \n",
        "         \u239f                     \n",
        "      + 1\u23a0                     "
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ext_flux = sy.Eq(Sh * rho_b*D_b/L * (Y_b - Y_s),-rho * D* sy.diff(part_sol.rhs,x).subs({x:0}))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_s_sol=sy.solve(ext_flux,Y_s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "part_sol = part_sol.subs({Y_s:y_s_sol[0]})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "part_sol"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Y{\\left (x \\right )} = \\frac{\\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} \\operatorname{Y_{b}}{\\left (y \\right )} e^{\\frac{\\sqrt{A_{V}} k_{r}^{\\frac{3}{2}} \\rho x}{\\sqrt{D} M_{CO}}}}{\\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} - \\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b}} + \\frac{1}{e^{\\frac{\\sqrt{A_{V}} k_{r}^{\\frac{3}{2}} \\rho x}{\\sqrt{D} M_{CO}}}} \\left(\\frac{\\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} \\left(e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + 1\\right) \\operatorname{Y_{b}}{\\left (y \\right )}}{\\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} - \\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b}} - \\frac{\\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} \\operatorname{Y_{b}}{\\left (y \\right )}}{\\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} - \\sqrt{A_{V}} D L k_{r}^{\\frac{3}{2}} \\rho^{2} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b} e^{\\frac{2 \\sqrt{A_{V}} \\rho wc_{thickness}}{\\sqrt{D} M_{CO}} k_{r}^{\\frac{3}{2}}} + \\sqrt{D} D_{b} M_{CO} Sh \\rho_{b}}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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GaORYr9k+KVrfEH3fF1d1G+U0qspI2qC1kN7xRVlSEV5cUS3DYWPSfeRAbiAABJ6DQG6M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\nqMvh/a/7jk83FZ0/28sSzWv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       "prompt_number": 17,
       "text": [
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                               ___            \n",
        "                                                             \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5Sh\n",
        "Y(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                 _____   3/2                                  \n",
        "                             2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness                   \n",
        "                             \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                   \n",
        "                                         ___                                  \n",
        "         _____       3/2  2            \u2572\u2571 D \u22c5M_CO               _____       3/\n",
        "       \u2572\u2571 A_V \u22c5D\u22c5L\u22c5k\u1d63   \u22c5\u03c1 \u22c5\u212f                               - \u2572\u2571 A_V \u22c5D\u22c5L\u22c5k\u1d63  \n",
        "\n",
        "               _____   3/2                                                    \n",
        "             \u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5x                                                \n",
        "             \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                                \n",
        "                   ___                                                        \n",
        "                 \u2572\u2571 D \u22c5M_CO                                                   \n",
        "\u22c5\u03c1_b\u22c5Y_b(y)\u22c5\u212f                                                                 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                  _____   3/2                                 \n",
        "                              2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness                  \n",
        "                              \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                  \n",
        "                                          ___                                 \n",
        "2  2     ___                            \u2572\u2571 D \u22c5M_CO               ___          \n",
        " \u22c5\u03c1  + \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5Sh\u22c5\u03c1_b\u22c5\u212f                               + \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5\n",
        "\n",
        "         \u239b                                                                   \u239b\n",
        "         \u239c                                                                   \u239c\n",
        "         \u239c                                                                   \u239c\n",
        "         \u239c                                                                   \u239c\n",
        "         \u239c                                               ___                 \u239c\n",
        "         \u239c                                             \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5Sh\u22c5\u03c1_b\u22c5\u239d\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500 + \u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "         \u239c                          _____   3/2                               \n",
        "         \u239c                      2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness                \n",
        "         \u239c                      \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                \n",
        "         \u239c                                  ___                               \n",
        "         \u239c  _____       3/2  2            \u2572\u2571 D \u22c5M_CO               _____      \n",
        "Sh\u22c5\u03c1_b   \u239d\u2572\u2571 A_V \u22c5D\u22c5L\u22c5k\u1d63   \u22c5\u03c1 \u22c5\u212f                               - \u2572\u2571 A_V \u22c5D\u22c5L\u22c5k\n",
        "\n",
        "     _____   3/2                   \u239e                                          \n",
        " 2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness    \u239f                                          \n",
        " \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    \u239f                                          \n",
        "             ___                   \u239f                                          \n",
        "           \u2572\u2571 D \u22c5M_CO              \u239f                                          \n",
        "\u212f                               + 1\u23a0\u22c5Y_b(y)                                   \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                     _____   3/2                              \n",
        "                                 2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness               \n",
        "                                 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500               \n",
        "                                             ___                              \n",
        " 3/2  2     ___                            \u2572\u2571 D \u22c5M_CO               ___       \n",
        "\u1d63   \u22c5\u03c1  + \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5Sh\u22c5\u03c1_b\u22c5\u212f                               + \u2572\u2571 D \u22c5D_b\u22c5M_\n",
        "\n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                            \u2572\u2571\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                      _____   3/2                             \n",
        "                                  2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness              \n",
        "                                  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500              \n",
        "                                              ___                             \n",
        "              _____       3/2  2            \u2572\u2571 D \u22c5M_CO               _____    \n",
        "CO\u22c5Sh\u22c5\u03c1_b   \u2572\u2571 A_V \u22c5D\u22c5L\u22c5k\u1d63   \u22c5\u03c1 \u22c5\u212f                               - \u2572\u2571 A_V \u22c5D\u22c5L\n",
        "\n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "___                                                                           \n",
        " D \u22c5D_b\u22c5M_CO\u22c5Sh\u22c5\u03c1_b\u22c5Y_b(y)                                                    \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                       _____   3/2                            \n",
        "                                   2\u22c5\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5wc_thickness             \n",
        "                                   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500             \n",
        "                                               ___                            \n",
        "   3/2  2     ___                            \u2572\u2571 D \u22c5M_CO               ___     \n",
        "\u22c5k\u1d63   \u22c5\u03c1  + \u2572\u2571 D \u22c5D_b\u22c5M_CO\u22c5Sh\u22c5\u03c1_b\u22c5\u212f                               + \u2572\u2571 D \u22c5D_b\u22c5\n",
        "\n",
        "           \u239e                     \n",
        "           \u239f     _____   3/2     \n",
        "           \u239f  -\u2572\u2571 A_V \u22c5k\u1d63   \u22c5\u03c1\u22c5x \n",
        "           \u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           \u239f         ___         \n",
        "           \u239f       \u2572\u2571 D \u22c5M_CO    \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f                   \n",
        "           \u239f                     \n",
        "           \u239f                     \n",
        "           \u239f                     \n",
        "           \u239f                     \n",
        "           \u239f                     \n",
        "M_CO\u22c5Sh\u22c5\u03c1_b\u23a0                     "
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "cantera_file = \"/home/vonrickenbach/contrib_git/cantera_tests/washcoat_model/cantera_input.cti\"\n",
      "gas = ca.import_phases(cantera_file,[\"gas\"])[0]\n",
      "interface = ca.Interface(cantera_file,\"pt_surf\",[gas])\n",
      "interface.TPX = (1000,1E5,[1])\n",
      "massfrac = np.array([0.0001,0.0,0.1,0.8999])\n",
      "\n",
      "porosity = 0.3\n",
      "\n",
      "gas.TPY = (1000,1E5,massfrac)\n",
      "wc_thick = 1E-4\n",
      "val_dict = {}\n",
      "\n",
      "cont_diff = gas.mix_diff_coeffs[0]*porosity/2\n",
      "knuds_diff = 1E-7/3.0*np.sqrt(8*ca.gas_constant /(np.pi*0.032))*porosity/2\n",
      "val_dict[D] = 1./(1./knuds_diff+1./cont_diff)\n",
      "val_dict[D_b] = gas.mix_diff_coeffs[0]\n",
      "val_dict[rho] = gas.density\n",
      "val_dict[rho_b] = gas.density\n",
      "val_dict[A_V] = 5.0/wc_thick\n",
      "val_dict[wc_thickness] = wc_thick\n",
      "val_dict[Sh] = 400.0\n",
      "#val_dict[Y_b] = 0.0001\n",
      "val_dict[L] = 100*wc_thick\n",
      "val_dict[k_r] = 1\n",
      "val_dict[M_i] = 0.032\n",
      "val_dict[Delta_H] = interface.delta_enthalpy[0]/1000\n",
      "val_dict[cond] = (gas.thermal_conductivity*porosity+(1.-porosity)*0.05)\n",
      "val_dict[lambda_b] = gas.thermal_conductivity\n",
      "#val_dict[T_b] = 1000\n",
      "sol_simple = part_sol.subs(val_dict)\n",
      "#ext_flux.subs({Y_s:y_s_sol[0]}).rhs.subs(val_dict)\n",
      "#sol_simple = part_sol\n",
      "\n",
      "#ext_flux_T.subs({T_s:T_s_sol[0]}).rhs.subs(val_dict)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq_T = sy.Eq(sy.diff(cond *sy.diff(T,x),x)-RR*A_V*Delta_H,0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple.subs({y:0.005,x:0.0})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Y{\\left (0.0 \\right )} = \\frac{4.1530307772742 \\cdot 10^{-5} M_{CO} \\left(e^{\\frac{8.06242418535907}{M_{CO}}} + 1\\right) \\operatorname{Y_{b}}{\\left (0.005 \\right )}}{4.1530307772742 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.1530307772742 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 20,
       "text": [
        "                                                                     \u239b 8.06242\n",
        "                                                                     \u239c \u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                     \u239c       M\n",
        "                                             4.1530307772742e-5\u22c5M_CO\u22c5\u239d\u212f       \n",
        "Y(0.0) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                  8.06242418535907                            \n",
        "                                  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                            \n",
        "                                        M_CO                                  \n",
        "         4.1530307772742e-5\u22c5M_CO\u22c5\u212f                 + 4.1530307772742e-5\u22c5M_CO +\n",
        "\n",
        "418535907    \u239e                                              \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    \u239f                                              \n",
        "_CO          \u239f                                              \n",
        "          + 1\u23a0\u22c5Y_b(0.005)                                   \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                      8.06242418535907                      \n",
        "                      \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      \n",
        "                            M_CO                            \n",
        " 8.86579864118988e-7\u22c5\u212f                 - 8.86579864118988e-7"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "adsfaf"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq_T=diffeq_T.subs({RR:k_r*(rho*y_temp/M_i)*(rho*k_r/M_CO)**2}).subs({y_temp:sol_simple.rhs})\n",
      "sol_T=sy.dsolve(diffeq_T,T)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "DomainError",
       "evalue": "there is no ring associated with RR",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mDomainError\u001b[0m                               Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-21-c4e07d89d767>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mdiffeq_T\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdiffeq_T\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m{\u001b[0m\u001b[0mRR\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mk_r\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrho\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0my_temp\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mM_i\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrho\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mk_r\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mM_CO\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m{\u001b[0m\u001b[0my_temp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0msol_simple\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrhs\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0msol_T\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdsolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdiffeq_T\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/ode.py\u001b[0m in \u001b[0;36mdsolve\u001b[1;34m(eq, func, hint, simplify, ics, xi, eta, x0, n, **kwargs)\u001b[0m\n\u001b[0;32m    557\u001b[0m         \u001b[1;31m# The key 'hint' stores the hint needed to be solved for.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    558\u001b[0m         \u001b[0mhint\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'hint'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 559\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_helper_simplify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msimplify\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    560\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    561\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_helper_simplify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmatch\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msimplify\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/ode.py\u001b[0m in \u001b[0;36m_helper_simplify\u001b[1;34m(eq, hint, match, simplify, **kwargs)\u001b[0m\n\u001b[0;32m    579\u001b[0m         \u001b[1;31m# attempt to solve for func, and apply any other hint specific\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    580\u001b[0m         \u001b[1;31m# simplifications\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 581\u001b[1;33m         \u001b[0mrv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0modesimp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msolvefunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmatch\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhint\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    582\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mrv\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    583\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/multidimensional.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m    135\u001b[0m                     \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mapply_on_element\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwrapper\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    136\u001b[0m                     \u001b[1;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 137\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    138\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/ode.py\u001b[0m in \u001b[0;36modesimp\u001b[1;34m(eq, func, order, hint)\u001b[0m\n\u001b[0;32m   1226\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1227\u001b[0m     \u001b[1;31m# First, integrate if the hint allows it.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1228\u001b[1;33m     \u001b[0meq\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_handle_Integral\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhint\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1229\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mEquality\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1230\u001b[0m         \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"eq should be an instance of Equality\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/ode.py\u001b[0m in \u001b[0;36m_handle_Integral\u001b[1;34m(expr, func, order, hint)\u001b[0m\n\u001b[0;32m   2036\u001b[0m         \u001b[0msol\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexpr\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2037\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mhint\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mendswith\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"_Integral\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2038\u001b[1;33m         \u001b[0msol\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdoit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2039\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2040\u001b[0m         \u001b[0msol\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexpr\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/relational.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m     97\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'deep'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     98\u001b[0m             \u001b[0mlhs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlhs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdoit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 99\u001b[1;33m             \u001b[0mrhs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrhs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdoit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mhints\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    100\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_eval_relation_doit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlhs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrhs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    101\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m   1598\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'deep'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1599\u001b[0m             terms = [ term.doit(**hints) if isinstance(term, Basic) else term\n\u001b[1;32m-> 1600\u001b[1;33m                                          for term in self.args ]\n\u001b[0m\u001b[0;32m   1601\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mterms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1602\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m   1598\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'deep'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1599\u001b[0m             terms = [ term.doit(**hints) if isinstance(term, Basic) else term\n\u001b[1;32m-> 1600\u001b[1;33m                                          for term in self.args ]\n\u001b[0m\u001b[0;32m   1601\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mterms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1602\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m   1598\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'deep'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1599\u001b[0m             terms = [ term.doit(**hints) if isinstance(term, Basic) else term\n\u001b[1;32m-> 1600\u001b[1;33m                                          for term in self.args ]\n\u001b[0m\u001b[0;32m   1601\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mterms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1602\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m   1598\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhints\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'deep'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1599\u001b[0m             terms = [ term.doit(**hints) if isinstance(term, Basic) else term\n\u001b[1;32m-> 1600\u001b[1;33m                                          for term in self.args ]\n\u001b[0m\u001b[0;32m   1601\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mterms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1602\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py\u001b[0m in \u001b[0;36mdoit\u001b[1;34m(self, **hints)\u001b[0m\n\u001b[0;32m    553\u001b[0m                     \u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxab\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    554\u001b[0m                     \u001b[0mmeijerg\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmeijerg1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrisch\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrisch\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmanual\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmanual\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 555\u001b[1;33m                     conds=conds)\n\u001b[0m\u001b[0;32m    556\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mantideriv\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mmeijerg1\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    557\u001b[0m                     \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtry_meijerg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mxab\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/integrals.py\u001b[0m in \u001b[0;36m_eval_integral\u001b[1;34m(self, f, x, meijerg, risch, manual, conds)\u001b[0m\n\u001b[0;32m    809\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mrisch\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mFalse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    810\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 811\u001b[1;33m                 \u001b[0mresult\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrisch_integrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mseparate_integral\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mconds\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mconds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    812\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    813\u001b[0m                 \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/risch.py\u001b[0m in \u001b[0;36mrisch_integrate\u001b[1;34m(f, x, extension, handle_first, separate_integral, rewrite_complex, conds)\u001b[0m\n\u001b[0;32m   1663\u001b[0m     \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1664\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1665\u001b[1;33m     \u001b[0mDE\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mextension\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mDifferentialExtension\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mhandle_first\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mhandle_first\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrewrite_complex\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrewrite_complex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1666\u001b[0m     \u001b[0mfa\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDE\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfa\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mDE\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfd\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1667\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/risch.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, f, x, handle_first, dummy, extension, rewrite_complex)\u001b[0m\n\u001b[0;32m    381\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    382\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mhandle_first\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'exp'\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mlog_new_extension\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 383\u001b[1;33m                 \u001b[0mexp_new_extension\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_exp_part\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mexps\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdummy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdummy\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    384\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mexp_new_extension\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m                     \u001b[1;31m# reset and restart\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/risch.py\u001b[0m in \u001b[0;36m_exp_part\u001b[1;34m(self, exps, dummy)\u001b[0m\n\u001b[0;32m    440\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    441\u001b[0m             \u001b[0marga\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfrac_in\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 442\u001b[1;33m             \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mis_log_deriv_k_t_radical\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marga\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margd\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    443\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    444\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mA\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/integrals/prde.py\u001b[0m in \u001b[0;36mis_log_deriv_k_t_radical\u001b[1;34m(fa, fd, DE, Df)\u001b[0m\n\u001b[0;32m    734\u001b[0m     \u001b[0mH\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    735\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mDf\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 736\u001b[1;33m         dfa, dfd = (fd*derivation(fa, DE) - fa*derivation(fd, DE)).cancel(fd**2,\n\u001b[0m\u001b[0;32m    737\u001b[0m             include=True)\n\u001b[0;32m    738\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/decorators.py\u001b[0m in \u001b[0;36m__sympifyit_wrapper\u001b[1;34m(a, b)\u001b[0m\n\u001b[0;32m     75\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'_op_priority'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     76\u001b[0m                     \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msympify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstrict\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 77\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     78\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mSympifyError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     79\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mretval\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36m__mul__\u001b[1;34m(f, g)\u001b[0m\n\u001b[0;32m   3842\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mas_expr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3843\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3844\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3845\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3846\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0m_sympifyit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'g'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36mmul\u001b[1;34m(f, g)\u001b[0m\n\u001b[0;32m   1347\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmul_ground\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1348\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1349\u001b[1;33m         \u001b[0m_\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mper\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mF\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mG\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_unify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1350\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1351\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'mul'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36m_unify\u001b[1;34m(f, g)\u001b[0m\n\u001b[0;32m    355\u001b[0m             \u001b[0mgens\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_unify_gens\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgens\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgens\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    356\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 357\u001b[1;33m             \u001b[0mdom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlev\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgens\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgens\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    358\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    359\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgens\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mgens\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/domains/domain.py\u001b[0m in \u001b[0;36munify\u001b[1;34m(K0, K1, symbols)\u001b[0m\n\u001b[0;32m    248\u001b[0m         \"\"\"\n\u001b[0;32m    249\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0msymbols\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 250\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mK0\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munify_with_symbols\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mK1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    251\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    252\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mK0\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mK1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/domains/domain.py\u001b[0m in \u001b[0;36munify_with_symbols\u001b[1;34m(K0, K1, symbols)\u001b[0m\n\u001b[0;32m    228\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mUnificationFailed\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"can't unify %s with %s, given %s generators\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mK0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    229\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 230\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mK0\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mK1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    231\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    232\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0munify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mK0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/domains/domain.py\u001b[0m in \u001b[0;36munify\u001b[1;34m(K0, K1, symbols)\u001b[0m\n\u001b[0;32m    272\u001b[0m                  K1.is_FractionField and K0.is_PolynomialRing) and\n\u001b[0;32m    273\u001b[0m                  (not K0_ground.has_Field or not K1_ground.has_Field) and domain.has_Field):\n\u001b[1;32m--> 274\u001b[1;33m                 \u001b[0mdomain\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdomain\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_ring\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    275\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    276\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mK0\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Composite\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;32mnot\u001b[0m \u001b[0mK1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Composite\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mK0\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_FractionField\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mK1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_PolynomialRing\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/domains/realfield.pyc\u001b[0m in \u001b[0;36mget_ring\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    104\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mget_ring\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    105\u001b[0m         \u001b[1;34m\"\"\"Returns a ring associated with ``self``. \"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 106\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mDomainError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'there is no ring associated with %s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    107\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    108\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mget_exact\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mDomainError\u001b[0m: there is no ring associated with RR"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_T\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#homogeneous neumann\n",
      "neum_bc_T= sy.Eq(sy.diff(sol_T.rhs,x).subs({x:wc_thickness}),0)\n",
      "\n",
      "dir_bc_T = sy.Eq(sol_T.rhs.subs({x:0}),T_s)\n",
      "\n",
      "bc_sol_T = sy.solve([dir_bc_T,neum_bc_T],C1,C2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bc_sol_T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "part_sol_T = sol_T.subs(bc_sol_T)\n",
      "ext_flux_T = sy.Eq(Sh * lambda_b/L * (T_b - T_s),-cond* sy.diff(part_sol_T.rhs,x).subs({x:0}))\n",
      "T_s_sol=sy.solve(ext_flux_T,T_s)\n",
      "part_sol_T = part_sol_T.subs({T_s:T_s_sol[0]})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple_T = part_sol_T.subs(val_dict)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple_T.subs({x:0})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y_s = sol_simple.subs({x:0})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T_s = sol_simple_T.subs({x:0})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A_V = 1000\n",
      "u   = 2.5\n",
      "rho = gas.density\n",
      "h = val_dict[Sh]*val_dict[D_b]/val_dict[L]\n",
      "\n",
      "diffeq_y_b = sy.Eq(rho * u * sy.diff(Y_b,y)+rho* h* A_V* (Y_b-Y_s.rhs),0)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_b_sol = sy.dsolve(diffeq_y_b,Y_b,simplify=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_b_sol = sy.solve(y_b_sol,Y_b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "KeyboardInterrupt",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-35-8d0f72e6d270>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0my_b_sol\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my_b_sol\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mY_b\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/solvers.py\u001b[0m in \u001b[0;36msolve\u001b[1;34m(f, *symbols, **flags)\u001b[0m\n\u001b[0;32m    899\u001b[0m     \u001b[1;31m###########################################################################\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    900\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mbare_f\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 901\u001b[1;33m         \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_solve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mflags\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    902\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    903\u001b[0m         \u001b[0msolution\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_solve_system\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mflags\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/solvers.py\u001b[0m in \u001b[0;36m_solve\u001b[1;34m(f, *symbols, **flags)\u001b[0m\n\u001b[0;32m   1207\u001b[0m             \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1208\u001b[0m                 \u001b[1;31m# try remove all...\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1209\u001b[1;33m                 \u001b[0mu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0munrad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf_num\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1210\u001b[0m             \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1211\u001b[0m                 \u001b[1;31m# ...else hope for the best while letting some remain\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/solvers/solvers.py\u001b[0m in \u001b[0;36munrad\u001b[1;34m(eq, *syms, **flags)\u001b[0m\n\u001b[0;32m   2764\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0meq\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcov\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdens\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2765\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2766\u001b[1;33m     \u001b[0mpoly\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0meq\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mas_poly\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2767\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2768\u001b[0m     \u001b[1;31m# if all the bases are the same or all the radicals are in one\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/basic.py\u001b[0m in \u001b[0;36mas_poly\u001b[1;34m(self, *gens, **args)\u001b[0m\n\u001b[0;32m    775\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    776\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 777\u001b[1;33m             \u001b[0mpoly\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mPoly\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mgens\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    778\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    779\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mpoly\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Poly\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, rep, *gens, **args)\u001b[0m\n\u001b[0;32m     85\u001b[0m                 \u001b[1;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_from_poly\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     86\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 87\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_from_expr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     88\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     89\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36m_from_expr\u001b[1;34m(cls, rep, opt)\u001b[0m\n\u001b[0;32m    196\u001b[0m         \u001b[1;34m\"\"\"Construct a polynomial from an expression. \"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    197\u001b[0m         \u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_dict_from_expr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 198\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mopt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    199\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    200\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_hashable_content\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.py\u001b[0m in \u001b[0;36m_from_dict\u001b[1;34m(cls, rep, opt)\u001b[0m\n\u001b[0;32m    145\u001b[0m                 \u001b[0mrep\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmonom\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdomain\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mconvert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    146\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 147\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnew\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mDMP\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfrom_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlevel\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdomain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mgens\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    148\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    149\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/polyclasses.py\u001b[0m in \u001b[0;36mfrom_dict\u001b[1;34m(cls, rep, lev, dom)\u001b[0m\n\u001b[0;32m    257\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mfrom_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlev\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    258\u001b[0m         \u001b[1;34m\"\"\"Construct and instance of ``cls`` from a ``dict`` representation. \"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 259\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlev\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlev\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    260\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    261\u001b[0m     \u001b[1;33m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/densebasic.py\u001b[0m in \u001b[0;36mdmp_from_dict\u001b[1;34m(f, u, K)\u001b[0m\n\u001b[0;32m   1013\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1014\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcoeff\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1015\u001b[1;33m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1016\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1017\u001b[0m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_zero\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/densebasic.py\u001b[0m in \u001b[0;36mdmp_from_dict\u001b[1;34m(f, u, K)\u001b[0m\n\u001b[0;32m   1013\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1014\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcoeff\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1015\u001b[1;33m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1016\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1017\u001b[0m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_zero\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/densebasic.py\u001b[0m in \u001b[0;36mdmp_from_dict\u001b[1;34m(f, u, K)\u001b[0m\n\u001b[0;32m   1013\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1014\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcoeff\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1015\u001b[1;33m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1016\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1017\u001b[0m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_zero\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/polys/densebasic.py\u001b[0m in \u001b[0;36mdmp_from_dict\u001b[1;34m(f, u, K)\u001b[0m\n\u001b[0;32m   1015\u001b[0m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_from_dict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcoeff\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mK\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1016\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1017\u001b[1;33m             \u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdmp_zero\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1018\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1019\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mdmp_strip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mh\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "inflow_bc= sy.Eq(y_b_sol.rhs.subs({y:0}),0.0001)\n",
      "y_b_part_sol = y_b_sol.subs({C1:sy.solve(inflow_bc,C1)[0]})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_b_sol"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$0.842313084290166 \\log{\\left (\\operatorname{Y_{b}}{\\left (y \\right )} \\right )} = C_{1} - \\frac{1803.0 y \\left(1.09270868277246 \\cdot 10^{-6} e^{\\frac{8.06242418535907}{M_{CO}}} - 1.09270868277246 \\cdot 10^{-6}\\right)}{4.15303088193764 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.15303088193764 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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91a7EFbzj4eH+lNRMEi7R5ccT3gXI3DiGlqEdV8w4N41HK4ju40XwJxTGkTLn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\nAABJRU5ErkJggg==\n",
       "prompt_number": 34,
       "text": [
        "                                                                             \u239b\n",
        "                                                                             \u239c\n",
        "                                                                             \u239c\n",
        "                                                                    1803.0\u22c5y\u22c5\u239d\n",
        "0.842313084290166\u22c5log(Y_b(y)) = C\u2081 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                               8.0624241853590\n",
        "                                                               \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                                     M_CO     \n",
        "                                     4.15303088193764e-5\u22c5M_CO\u22c5\u212f               \n",
        "\n",
        "                     8.06242418535907                      \u239e                  \n",
        "                     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      \u239f                  \n",
        "                           M_CO                            \u239f                  \n",
        "1.09270868277246e-6\u22c5\u212f                 - 1.09270868277246e-6\u23a0                  \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "7                                                   8.06242418535907          \n",
        "\u2500                                                   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500          \n",
        "                                                          M_CO                \n",
        "  + 4.15303088193764e-5\u22c5M_CO + 8.86579864118988e-7\u22c5\u212f                 - 8.86579\n",
        "\n",
        "            \n",
        "            \n",
        "            \n",
        "            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "            \n",
        "            \n",
        "            \n",
        "864118988e-7"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple = sol_simple.subs({Y_b:y_b_part_sol.rhs})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Y{\\left (x \\right )} = \\frac{4.1530307772742 \\cdot 10^{-5} M_{CO} \\left(- \\frac{1803.0 y \\left(1.09270868277246 \\cdot 10^{-6} e^{\\frac{8.06242418535907}{M_{CO}}} - 1.09270868277246 \\cdot 10^{-6}\\right)}{4.15303088193764 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.15303088193764 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}} + 0.0001\\right) e^{\\frac{40312.1209267953 x}{M_{CO}}}}{4.1530307772742 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.1530307772742 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}} + \\frac{1}{e^{\\frac{40312.1209267953 x}{M_{CO}}}} \\left(\\frac{4.1530307772742 \\cdot 10^{-5} M_{CO} \\left(- \\frac{1803.0 y \\left(1.09270868277246 \\cdot 10^{-6} e^{\\frac{8.06242418535907}{M_{CO}}} - 1.09270868277246 \\cdot 10^{-6}\\right)}{4.15303088193764 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.15303088193764 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}} + 0.0001\\right) \\left(e^{\\frac{8.06242418535907}{M_{CO}}} + 1\\right)}{4.1530307772742 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.1530307772742 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}} - \\frac{4.1530307772742 \\cdot 10^{-5} M_{CO} \\left(- \\frac{1803.0 y \\left(1.09270868277246 \\cdot 10^{-6} e^{\\frac{8.06242418535907}{M_{CO}}} - 1.09270868277246 \\cdot 10^{-6}\\right)}{4.15303088193764 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.15303088193764 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}} + 0.0001\\right)}{4.1530307772742 \\cdot 10^{-5} M_{CO} e^{\\frac{8.06242418535907}{M_{CO}}} + 4.1530307772742 \\cdot 10^{-5} M_{CO} + 8.86579864118988 \\cdot 10^{-7} e^{\\frac{8.06242418535907}{M_{CO}}} - 8.86579864118988 \\cdot 10^{-7}}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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Ott3mWm7RzPZttF2nzqGqLuVjyCIaupiggmIaqKuWnN5xV8s1kLyGdEogdcJ3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\n86e//B8q34jG4bsTcAAAAABJRU5ErkJggg==\n",
       "prompt_number": 28,
       "text": [
        "                               \u239b                                          \u239b   \n",
        "                               \u239c                                          \u239c   \n",
        "                               \u239c                                          \u239c   \n",
        "                               \u239c                                 1803.0\u22c5y\u22c5\u239d1.0\n",
        "       4.1530307772742e-5\u22c5M_CO\u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                               \u239c                            8.06242418535907  \n",
        "                               \u239c                            \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \n",
        "                               \u239c                                  M_CO        \n",
        "                               \u239d  4.15303088193764e-5\u22c5M_CO\u22c5\u212f                 +\n",
        "Y(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                             8.06242418535907 \n",
        "                                                             \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \n",
        "                                                                   M_CO       \n",
        "                                    4.1530307772742e-5\u22c5M_CO\u22c5\u212f                 \n",
        "\n",
        "                  8.06242418535907                      \u239e                     \n",
        "                  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      \u239f                     \n",
        "                        M_CO                            \u239f                     \n",
        "9270868277246e-6\u22c5\u212f                 - 1.09270868277246e-6\u23a0                     \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                 8.06242418535907             \n",
        "                                                 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500             \n",
        "                                                       M_CO                   \n",
        " 4.15303088193764e-5\u22c5M_CO + 8.86579864118988e-7\u22c5\u212f                 - 8.86579864\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                 8.06242418535907             \n",
        "                                                 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500             \n",
        "                                                       M_CO                   \n",
        "+ 4.1530307772742e-5\u22c5M_CO + 8.86579864118988e-7\u22c5\u212f                 - 8.86579864\n",
        "\n",
        "                  \u239e                       \u239b                        \u239b          \n",
        "                  \u239f  40312.1209267953\u22c5x   \u239c                        \u239c          \n",
        "                  \u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500   \u239c                        \u239c          \n",
        "                  \u239f         M_CO          \u239c                        \u239c          \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + 0.0001\u239f\u22c5\u212f                     \u239c4.1530307772742e-5\u22c5M_CO\u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                  \u239f                       \u239c                        \u239c          \n",
        "                  \u239f                       \u239c                        \u239c          \n",
        "                  \u239f                       \u239c                        \u239c          \n",
        "118988e-7         \u23a0                       \u239c                        \u239d  4.153030\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                          \u239c                                   \n",
        "                                          \u239c                                   \n",
        "                                          \u239c                                   \n",
        "118988e-7                                 \u239d                               4.15\n",
        "\n",
        "                                \u239b                     8.06242418535907        \n",
        "                                \u239c                     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500        \n",
        "                                \u239c                           M_CO              \n",
        "                       1803.0\u22c5y\u22c5\u239d1.09270868277246e-6\u22c5\u212f                 - 1.092\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                  8.06242418535907                                            \n",
        "                  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                            \n",
        "                        M_CO                                                  \n",
        "88193764e-5\u22c5M_CO\u22c5\u212f                 + 4.15303088193764e-5\u22c5M_CO + 8.865798641189\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                     8.06242418535907                                         \n",
        "                     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                         \n",
        "                           M_CO                                               \n",
        "30307772742e-5\u22c5M_CO\u22c5\u212f                 + 4.1530307772742e-5\u22c5M_CO + 8.8657986411\n",
        "\n",
        "              \u239e                                       \u239e                       \n",
        "              \u239f                                       \u239f \u239b 8.06242418535907    \n",
        "              \u239f                                       \u239f \u239c \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    \n",
        "70868277246e-6\u23a0                                       \u239f \u239c       M_CO          \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + 0.0001\u239f\u22c5\u239d\u212f                 + 1\n",
        "       8.06242418535907                               \u239f                       \n",
        "       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                               \u239f                       \n",
        "             M_CO                                     \u239f                       \n",
        "88e-7\u22c5\u212f                 - 8.86579864118988e-7         \u23a0                       \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "         8.06242418535907                                                     \n",
        "         \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                                                     \n",
        "               M_CO                                                           \n",
        "8988e-7\u22c5\u212f                 - 8.86579864118988e-7                               \n",
        "\n",
        "                            \u239b                                          \u239b      \n",
        "\u239e                           \u239c                                          \u239c      \n",
        "\u239f                           \u239c                                          \u239c      \n",
        "\u239f                           \u239c                                 1803.0\u22c5y\u22c5\u239d1.0927\n",
        "\u23a0   4.1530307772742e-5\u22c5M_CO\u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                            \u239c                            8.06242418535907     \n",
        "                            \u239c                            \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \n",
        "                            \u239c                                  M_CO           \n",
        "                            \u239d  4.15303088193764e-5\u22c5M_CO\u22c5\u212f                 + 4.\n",
        "\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                8.06242418535907              \n",
        "                                                \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500              \n",
        "                                                      M_CO                    \n",
        "                       4.1530307772742e-5\u22c5M_CO\u22c5\u212f                 + 4.153030777\n",
        "\n",
        "               8.06242418535907                      \u239e                        \n",
        "               \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      \u239f                        \n",
        "                     M_CO                            \u239f                        \n",
        "0868277246e-6\u22c5\u212f                 - 1.09270868277246e-6\u23a0                        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                              8.06242418535907                \n",
        "                                              \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                \n",
        "                                                    M_CO                      \n",
        "15303088193764e-5\u22c5M_CO + 8.86579864118988e-7\u22c5\u212f                 - 8.86579864118\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                    8.06242418535907                          \n",
        "                                    \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                          \n",
        "                                          M_CO                                \n",
        "2742e-5\u22c5M_CO + 8.86579864118988e-7\u22c5\u212f                 - 8.86579864118988e-7    \n",
        "\n",
        "               \u239e\u239e                      \n",
        "               \u239f\u239f                      \n",
        "               \u239f\u239f                      \n",
        "               \u239f\u239f                      \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500 + 0.0001\u239f\u239f                      \n",
        "               \u239f\u239f                      \n",
        "               \u239f\u239f  -40312.1209267953\u22c5x \n",
        "               \u239f\u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "988e-7         \u23a0\u239f          M_CO        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f                    \n",
        "                \u239f                      \n",
        "                \u239f                      \n",
        "                \u239f                      \n",
        "                \u23a0                      "
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T_s = T_s.subs({Y_b:y_b_part_sol.rhs})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cp = gas.cp_mass\n",
      "\n",
      "h_t = val_dict[Sh]*gas.thermal_conductivity/(rho*cp)/val_dict[L]\n",
      "\n",
      "\n",
      "diffeq_T_b = sy.Eq(u * sy.diff(T_b,y)+h_t* A_V* (T_b-T_s.rhs),0)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T_b_sol = sy.dsolve(diffeq_T_b,T_b,simplify=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_c1_tb = sy.solve(sy.Eq(T_b_sol.subs({y:0}).rhs,1000),C1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T_b_part_sol = T_b_sol.subs({C1:sol_c1_tb[0]})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple_T = sol_simple_T.subs({Y_b:y_b_part_sol.rhs,T_b:T_b_part_sol.rhs})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple = sol_simple.subs({M_CO:0.028})\n",
      "sol_simple_fun=sy.lambdify((x,y),sol_simple.rhs)\n",
      "#sol_simple_fun_T=sy.lambdify((x,y),sol_simple_T.rhs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple.rhs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$5.02945961701987 \\cdot 10^{-126} \\left(- 961.318603896209 y + 0.0001\\right) e^{1439718.60452841 x} + \\frac{1}{e^{1439718.60452841 x}} \\left(- 545.453534778406 y + 5.67401413608029 \\cdot 10^{-5}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 30,
       "text": [
        "                                                      1439718.60452841\u22c5x      \n",
        "5.02945961701987e-126\u22c5(-961.318603896209\u22c5y + 0.0001)\u22c5\u212f                   + (-5\n",
        "\n",
        "                                          -1439718.60452841\u22c5x\n",
        "45.453534778406\u22c5y + 5.67401413608029e-5)\u22c5\u212f                   "
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_grid(ratio=1.1,wc_thickness=1E-4,nx=32):\n",
      "    dx_c = wc_thickness*(1-ratio)/(1-ratio**nx)\n",
      "    dx = []\n",
      "    for x_c in range(nx):\n",
      "        dx.append(dx_c)\n",
      "        dx_c *= ratio\n",
      "    return np.cumsum(dx) -0.5*np.array(dx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = pl.figure()\n",
      "fig1 = pl.figure()\n",
      "fig3 = pl.figure()\n",
      "\n",
      "\n",
      "\n",
      "ax = fig.add_subplot(1,1,1)\n",
      "ax1 = fig1.add_subplot(1,1,1)\n",
      "ax3 = fig3.add_subplot(1,1,1)\n",
      "\n",
      "data_folder = \"/home/vonrickenbach/contrib_git/cantera_tests/washcoat_model/\"\n",
      "err_T = []\n",
      "err_Y = []\n",
      "grids = [32]\n",
      "#grids = [32,64]\n",
      "\n",
      "index = 7\n",
      "\n",
      "x_ind = 0.0001\n",
      "\n",
      "for nx in grids:\n",
      "    x_val = get_grid(nx=nx)\n",
      "\n",
      "    y_val =[sol_simple_fun(item,x_ind) for item in x_val]\n",
      "    ax.plot(x_val*1E6,np.array(y_val),'k')\n",
      "\n",
      " #   T_val = np.array([sol_simple_fun_T(item,x_ind) for item in x_val])\n",
      " #   ax1.plot(x_val,T_val-1000)\n",
      "    data= np.genfromtxt(os.path.join(data_folder,\"grid_\"+str(31)+\"_0.dat\"))\n",
      "#    ax1.plot(x_val,data[5,1:]-1000,'o')\n",
      "\n",
      "    ax.set_xlabel(\"x-xoordinate ($\\mu m$)\")\n",
      "    ax.set_ylabel(\"$O_2$ mass-fraction\")\n",
      "\n",
      "    ax.plot(x_val*1E6,data[0,1:],'ko')\n",
      "#    err_T.append(np.amax(np.abs(data[5,1:])-T_val+1000))\n",
      "    err_Y.append(np.amax(np.abs(data[0,1:])-y_val))\n",
      "    ax.legend([\"Analytical solution\",\"Numerical solution\"])\n",
      "\n",
      "fig.tight_layout()\n",
      "fig.savefig(\"wc.png\")\n",
      "#ax3.loglog(grids,err_T/err_T[-3])\n",
      "#ax3.loglog(grids,err_Y/err_Y[-3])\n",
      "#ax3.loglog(grids,(1./np.array(grids)*16)**2)\n",
      "\n",
      "\n",
      "fluxes_data = np.genfromtxt(os.path.join(data_folder,\"fluxes_\"+str(0)+\"_0.dat\"))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T_val"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fluxes_data[0,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "- gas.density * val_dict[D]*sy.diff(sol_simple.rhs,x).subs({y:0,x:0.000})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sy.diff(sol_simple.rhs,y).subs({y:0,x:0})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = []\n",
      "\n",
      "nx = 32\n",
      "\n",
      "for g_idx in range(nx):\n",
      "    data.append(np.genfromtxt(os.path.join(data_folder,\"grid_\"+str(g_idx)+\"_1000.dat\")))\n",
      "\n",
      "data = np.array(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import matplotlib as ml\n",
      "\n",
      "species_data = data[:,5,:]\n",
      "\n",
      "fig = pl.figure()\n",
      "ax = fig.add_subplot(111, projection='3d')\n",
      "\n",
      "x,y = np.meshgrid(np.linspace(0,0.005,32),get_grid())\n",
      "ax.plot_surface(x,y,species_data[:,1:],cmap=ml.cm.coolwarm)\n",
      "ax.plot_surface(x,y,sol_simple_fun(x,y),cmap=ml.cm.coolwarm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple_fun(np.array([1E-5,1E-5]),np.array([0.005,0.005]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mult2(a,b):\n",
      "    return a*b * 2\n",
      "\n",
      "sol_simple_fun(x,y)\n",
      "mult2(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import matplotlib as ml\n",
      "\n",
      "species_data = data[:,5,:]\n",
      "\n",
      "fig = pl.figure()\n",
      "ax = fig.add_subplot(111, projection='3d')\n",
      "\n",
      "x,y = np.meshgrid(np.linspace(0,0.005,32),get_grid())\n",
      "\n",
      "z = y * 1.0\n",
      "\n",
      "for (x_ind,y_ind),val in np.ndenumerate(x):\n",
      "\n",
      "    print(x_ind,y_ind,val,y[x_ind,y_ind])\n",
      "    z[x_ind,y_ind] = sol_simple_fun(val,y[x_ind,y_ind])\n",
      "    \n",
      "ax.plot_surface(x,y,species_data[:,1:],cmap=ml.cm.coolwarm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_simple_fun(0.005,1E-4)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Analytical solution unsteady"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t,rhocp,T_bulk,h_temp,T_0= sy.symbols(\"t rhocp T_bulk h_temp T_0\",positive=True )\n",
      "C1,C2 = sy.symbols(\"C1 C2\")\n",
      "\n",
      "Ts = sy.Function(\"Ts\")(t)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq_T_t = sy.Eq(sy.diff(Ts,t),h_temp/rhocp*(-Ts+T_bulk))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diffeq_T_t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} \\operatorname{Ts}{\\left (t \\right )} = \\frac{h_{temp}}{rhocp} \\left(T_{bulk} - \\operatorname{Ts}{\\left (t \\right )}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAASgAAAAvBAMAAACiW0omAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
       "prompt_number": 5,
       "text": [
        "d           h_temp\u22c5(T_bulk - Ts(t))\n",
        "\u2500\u2500(Ts(t)) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "dt                   rhocp         "
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_Ts = sy.dsolve(diffeq_T_t,Ts)\n",
      "sol_Ts"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\operatorname{Ts}{\\left (t \\right )} = \\frac{C_{1}}{e^{\\frac{h_{temp} t}{rhocp}}} + T_{bulk}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAA0BAMAAAAaiOsnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 6,
       "text": [
        "            -h_temp\u22c5t          \n",
        "            \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500         \n",
        "              rhocp            \n",
        "Ts(t) = C\u2081\u22c5\u212f           + T_bulk"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C1_sol = sy.solve(sy.Eq(sol_Ts.subs({t:0}).rhs,T_0),C1)[0]\n",
      "sy.Eq(sol_Ts.subs({t:0}).rhs,T_0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$C_{1} + T_{bulk} = T_{0}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAI0AAAARBAMAAAAS1DKuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nI8haiS49fcx/7jOJHTLy+WsAAAAASUVORK5CYII=\n",
       "prompt_number": 7,
       "text": [
        "C\u2081 + T_bulk = T\u2080"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'sol' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-8-56717d999058>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0msol\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mNameError\u001b[0m: name 'sol' is not defined"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_Ts = sol_Ts.subs({C1:C1_sol})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_Ts = sol_Ts.subs({h_temp:0.026,T_0:300,rhocp:1,T_bulk:310}).rhs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_time(name):\n",
      "    name = os.path.basename(name)\n",
      "    try:\n",
      "        return int(\"\".join([char for char in name[6:] if char.isdigit() or char == \"-\"]))\n",
      "    except:\n",
      "        print(name)\n",
      "    \n",
      "get_time(\"grid_0_-1.dat \")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$-1$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAPBAMAAAAMihLoAAAAJ1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAilU6eAAAADHRSTlMAEM3dMiK7mat272a9noTYAAAALklE\nQVQIHWNggANFOIuBIewggiNWgcRh4CSTI2QMAioMZBsAcxB71+FuGBtMAwDSnw2AS5zPhQAAAABJ\nRU5ErkJggg==\n",
       "prompt_number": 11,
       "text": [
        "-1"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def apply_array(func):\n",
      "    def apply_arr(array): \n",
      "        vals = np.array(np.zeros(len(time)))\n",
      "        for idx,ti in enumerate(array):\n",
      "            vals[idx] = func(ti)\n",
      "        return vals\n",
      "    \n",
      "    return apply_arr\n",
      "\n",
      "\n",
      "num_Ts = apply_array(sy.lambdify(t,sol_Ts))\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "num_Ts(time)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([ 300.        ,  300.5167805 ,  301.00685479,  301.47160299,\n",
        "        301.91233392,  302.33028873,  302.72664445,  303.10251728,\n",
        "        303.45896574,  303.79699363,  304.1175529 ,  304.4215463 ,\n",
        "        304.70982991,  304.98321558,  305.24247322,  305.48833292,\n",
        "        305.72148708,  305.94259228,  306.1522712 ,  306.35111432,\n",
        "        306.53968162,  306.71850412,  306.88808543,  307.04890311,\n",
        "        307.20141004,  307.34603571,  307.48318741,  307.61325138,\n",
        "        307.73659389,  307.8535623 ,  307.96448602,  308.06967741,\n",
        "        308.16943272,  308.26403286,  308.35374426,  308.43881955,\n",
        "        308.51949831,  308.59600775,  308.66856333,  308.73736938,\n",
        "        308.80261967,  308.86449795,  308.92317848,  308.97882652,\n",
        "        309.03159877,  309.08164386,  309.12910271,  309.17410899,\n",
        "        309.21678942,  309.25726422])"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time = np.linspace(0,100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def load_wc_ani(sim):\n",
      "\n",
      "    filelist = gl.glob(os.path.join(sim.info.local[\"sim_folder\"],\"grid_0_*\"))\n",
      "    \n",
      "    \n",
      "    filelist = [filename for filename in filelist if get_time(filename) >  0]\n",
      "    time_data = np.genfromtxt(os.path.join(sim.info.local[\"sim_folder\"],\"time_file.dat\"))\n",
      "\n",
      "    \n",
      "    sorted_list = sorted(filelist,key=lambda name :get_time(name))\n",
      "    wc_data = []\n",
      "    for filename in sorted_list:\n",
      "        wc_data.append([time_data[get_time(filename)-1,1],np.genfromtxt(filename)])\n",
      "    \n",
      "    sim.all_data = wc_data  \n",
      "    return time_data\n",
      "\n",
      "\n",
      "\n",
      "def create_simulation_python(input_dict,folder,root_folder=\".\",ref_folder=None):\n",
      "     \n",
      "\n",
      "    config_sim = jc.configuration_mb_local\n",
      "    config_sim[\"transat_version\"] = \"wc_python\"\n",
      "\n",
      "    config_sim[\"jobname\"] = inputs[\"folder\"]\n",
      "    config_sim[\"root_folder\"] = root_folder\n",
      "    simulation = sim_brutus.job(**config_sim)\n",
      "\n",
      "    simulation.sim_info = input_dict.copy()\n",
      "    simulation.sim_info[\"converged\"] = False\n",
      "\n",
      "\n",
      "    return simulation\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim_list_val  = []\n",
      "root_folder= \"/home/vonrickenbach/contrib_git/cantera_tests/\"\n",
      "\n",
      "folder = \"washcoat_model\"\n",
      "temperatures = np.array([300])\n",
      "temp_array= temperatures\n",
      "\n",
      "\n",
      "for temperature in temperatures:\n",
      "        inputs = {}\n",
      "        inputs[\"wc_thickness\"] = 20\n",
      "        inputs[\"temperature\"] = temperature\n",
      "        inputs[\"cov_CO\"] = 1\n",
      "        inputs[\"folder\"] = folder\n",
      "        inputs[\"res\"] = 20\n",
      "        inputs[\"nx\"]  = 32\n",
      "        inputs[\"t_fac\"]  = 1\n",
      "        inputs[\"x_cells\"]  = 20\n",
      "        inputs[\"velocity\"] = 25000/3600.*0.07\n",
      "        \n",
      "        inputs[\"sh_number\"] = 4000\n",
      "        inputs[\"a_v\"] = 4000\n",
      "\n",
      "        inputs[\"mf\"] = 1E3\n",
      "\n",
      "        sim_list_val.append(create_simulation_python(inputs,folder,root_folder=root_folder))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Warning Initial conditions with single block code not supported\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim = sim_list_val[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time_val = load_wc_ani(sim)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print_wc_time(sim,time_val)\n",
      "pl.plot(time,num_Ts(time))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7fd49d2ba250>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BqFFcbtyMH3+EOaPgm2+yFrtwcDDLvA0ZYtZC1ioWIiIFT2FZRMQekpJMi8XU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\nANwgLAMAAABuEJYBAAAAN/4HOlLseE+XlUYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd49d2ba2d0>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time_val"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([[    0.     ,     0.     ],\n",
        "       [    2.     ,     5.03766],\n",
        "       [    3.     ,    67.8332 ],\n",
        "       [    4.     ,   135.371  ],\n",
        "       [    5.     ,   208.025  ],\n",
        "       [    6.     ,   287.012  ],\n",
        "       [    7.     ,   315.811  ],\n",
        "       [    8.     ,   371.016  ],\n",
        "       [    9.     ,   408.778  ],\n",
        "       [   10.     ,   655.483  ],\n",
        "       [   11.     ,   801.204  ],\n",
        "       [   12.     ,   895.027  ],\n",
        "       [   13.     ,   925.811  ],\n",
        "       [   14.     ,   974.649  ],\n",
        "       [   15.     ,  1000.     ]])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def print_wc_time(sim,sp=4,sli=1,time=3.6E-5):\n",
      "\n",
      "    nplots = 1\n",
      "    figs = [pl.figure(figsize=(12,6)) for item in range(1)]\n",
      "    axs = [figs[0].add_subplot(1,nplots,item+1) for item in range(nplots)]\n",
      "    data = np.array([item[1] for item in sim.all_data])\n",
      "    time_val = np.array([item[0] for item in sim.all_data])\n",
      "    axs[0].plot(time_val,data[:,-1,sli],'r')\n",
      "\n",
      "\n",
      "    st_idx = 0\n",
      "    axs[0].set_title(\"T at first cell over time\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gas.TPX = (310.0,1E5,[0.1,0,0.9,0.0])\n",
      "\n",
      "gas.thermal_conductivity"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'gas' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-32-cbbd8da86911>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mgas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mTPX\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m310.0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1E5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0.1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.9\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mgas\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mthermal_conductivity\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mNameError\u001b[0m: name 'gas' is not defined"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "0.003/(1+100*0.028)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$0.000789473684211$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKkAAAAPBAMAAABtvvLvAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ncpf1Vv67SKcUBL+BHU/GfA0M+//jD4keCMsb4XucAAAAAElFTkSuQmCC\n",
       "prompt_number": 22,
       "text": [
        "0.000789473684211"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}