Evaluation of conductive, radiative, chemical, and convective heat transfer in complex systems using a fast-running, implicit, lumped-capacitance formulation

摘要

Accurate finite-element simulation of 3-D nonlinear heat transfer in complex systems may require meshes composed of tens of thousands of finite elements and hours of CPU time on today's fastest computers. To treat applications in which thousands of calculations may be necessary such as for risk assessment or design of high-temperature manufacturing processes, methods are needed which can solve these problems far more efficiently and maintain an acceptably high degree of accuracy. For this purpose, we developed the Thermal Evaluation and Matching Program for Risk Applications (TEMPRA). The primary differentiator between TEMPRA and comparable codes is its numerical formulation, which is designed to be unconditionally stable even with very large time steps, to afford good accuracy even with relatively coarse meshing, and to facilitate benchmarking/calibration through the use of adjustable parameters. Analysis for a sample problem shows that TEMPRA can obtain temperature response solutions with errors of less than 10% using approximately 1/1000 of the computer time required by a typical finite element code.