Finite Difference Method Applied in Two-Dimensional Heat Conduction Problem in the Permanent Regime in Rectangular Coordinates

Abstract

The solution of many conduction heat transfer problems is found by two-dimensional simplification using the analytical method since different points have different initial temperatures. The temperature at each point of a given element can be analyzed through the Heat Equation that, in some cases, converges to analytical solutions without precision and is far from the real. However, with the application of the Finite Difference Method (FDM), it is possible to solve it numerically in a relatively fast way, providing satisfactory results for the most varied boundary conditions and diverse geometries, characteristics of heat transfer problems by conduction. This study solved two problems inside a plate with and without heat generation involved in temperature distribution. Algorithms were built with the aid of the Matlab programming language, and applied to obtain a numerical solution using the FDM numerical method. The computational and analytical solutions were then compared. Under certain conditions of the parameters involved in the phenomenon of each problem, the numerical method was very efficient for presenting errors less than or equal to 0.003 and 0.03, respectively, for cases without and with heat generation.