Numerical Simulation of Heat Transfer Problems in 3D Geometries

Abstract

A finite element procedure for transient three dimensional (3D) heat transfer problems was developed and implemented. The domain was divided into linear tetrahedral elements using a three dimensional mesh generator software. A pre-processing program was developed in order to the mesh information to be compatible with finite element program. All the numerical algorithms have been implemented using Matlab 6.5. Results were validated by comparing with analytical solutions of heat transfer in a finite cylinder and a sphere, and with the numerical solution generated by commercial software for heating an irregular piece of meat. A post-processing code was implemented in order to obtain further information from the results, such as the temperature prediction at an arbitrary point, and the average temperature. The code can also be used to determine concentration profiles in mass transfer problems (3D domains) and to simulate heat transfer problems in food processing with convective boundary conditions. The open source program can be easily applied with the important advantage that it can be coupled with macroscopic balances, microbial inactivation rates, or with different objective functions that optimize the process (e.g. quality attributes).