Numerical solution of the heat conduction equation with the electro-thermal analogy and the code PSPICE

摘要

The central objective of this paper is to provide numerical analysts with a new procedure named the network simulation method (NSM) for solving the heat conduction equation in bodies of regular shape. In principle, NSM rests on the electro-thermal analogy (loosely called the resistance–capacitance analogy or the RC analogy) that exists between the unsteady, unidirectional conduction of heat and the unsteady flow of electric current. Once the electric network model has been set up for the heat conduction equation, the numerical treatment of the analog electric circuit equation can be easily done with the computer code PSPICE. As a conceptual example, the allied numerical solution of the heat conduction equation for a large plate with symmetric surface temperatures has been carried out, demonstrating that the temperature–time histories and the heat flux–time histories can be obtained simultaneously, quickly, and accurately for the entire time domain.