Heat conduction across interface between two materials. Part I: perfectly conducting interface

Abstract

This report presents a mathematical model for steady, two-dimensional heat conduction in rectangular coordinates. The model is developed using the Fourier heat conduction equation and accounts for the effects of thermal conductivity and boundary conditions. The numerical solution is obtained by expanding the Fourier heat conduction equation with the separation of variables and the trigonometric Fourier series, and the results are presented in the form of contour plots and heat maps depicting the temperature distribution. The model is validated by comparing the numerical results with analytical solutions for simple geometries. The limitations of the model, including the lack of inclusion of convection and radiation and the assumption of steady-state conditions, are discussed. This model is an attempt to produce a useful tool for predicting temperature distributions in complex geometries and can be used for designing and optimizing heat transfer systems.