Graetz Problem 2D Heat Transfer Solver

Repo containing a simple c++ script for solving the Graetz Heat-Transfer Problem.

Graetz Problem: Temperatur distribution in fully-developed fluid flow of uniform inlet temperature flowing into a pipe of circular cross-section where the pipe walls are held at a constant temperature.

A good description of the Graetz oroblem can be found in the paper "The Graetz Problem" by R. Shankar Subramanian included here in the repository as Graetz_Problem_Subramanian.pdf and available online here.

Some other mathematical setup notes can be found in the file Graetz_Problem_Setup_Zachary_Cotman.pdf

2 Versions of the program are available: one that solves the problem without including conduction, and one that includes conduction.

Exectution of the makefile and scripts require:

• make
• g++
• gnu scientific libraries

Files

• graetz_problem.cpp - main file for convection-only solution

• graetz_problem_conduct.cpp - main file for solution which includes conduction

• graetz_residual_functions.cpp - functions for calculating the residuals (errors)

• graetz_xy_functions.cpp - functions are used to build the right hand side(rhs), y, and initial guess, x, vectors used in the GSL sparse-matrix solver GMRES

• graetz_coeff_mat_functions.cpp - functions are used to build the coefficient matricies used in the GSL sparse-matrix solver GMRES

• input_parameters.h - boundary conditions and 2D mesh parameters, etc

• graetz_problem.dat - output temperature values

• graetz_problem_conduct.dat - output temperature values

• graetz_problem_residuals.dat - output residuals

• graetz_problem.info - some info from the simulation - useful primarily for debugging

• graetz_problem_conduct.info - some info from the simulation - useful primarily for debugging

• make_graetz_problem - makefile ( make -f make_graetz_problem )

• make_graetz_problem_conduct - makefile ( make -f make_graetz_problem_conduct )

Post Processing

Post-processing and plotting scripts originally made using Mathematica. I may re-write them in Jupytern Notebooks to make this accessible.

See the file 'Graetz_Problem_Zachary_Cotman.pdf' for the original report containing some plots from the post-processing scripts. Note that I actually made a mistake in a simple calculation in the setup. I may revisit, fix, and replcae this if I write some post-processing Jupyter Notebookes.