SOLVING OF TWO-DIMENSIONAL STABLE THERMAL CONDUCTION PROBLEM WITHOUT AN INTERNAL HEAT SOURCE USING FINITE DIFFERENCE METHOD

Abstract

This article presents the steps to establish the formula for calculating temperatures at any of the nodal points within the network of two-dimensional perpendicular lines x, y. Consider in the case of stable heat conduction without an internal heat source, the temperature field is described by the Laplace operator in the two-dimensional Cartesian coordinate system. Finite difference method (FDM) is adopted to calculate the temperature value of four nodes in the x, y grid on a two-dimensional plate. The nodal equations are written and the Gauss method is also used to solve these systems of equations and their results are the temperatures at the various nodes.