SEMI-ANALYTICAL SOLUTION OF THE HEAT CONDUCTION IN A PLATE WITH HEAT GENERATION

Abstract

In the present work, a formulation for the solution of the two-dimensional steady state heat conduction with heat generation is presented. The classical integral transform technique (CITT) is used to solve the problem in a semi- analytical manner. CITT deals with expansions of the sought solution in terms of infinite orthogonal basis of eigenfunctions, keeping the solution process always within a continuous domain. For the particular problem, the resulting system is composed of a set of uncoupled differential equations which can be solved analytically. However, a truncation error is involved since the infinite series must be truncated to obtain numerical results. For comparison and validation purposes, the second order central finite difference method (FDM) is also implemented. The convergence analysis showed that CITT has a greater performance having no difficulties to obtain accurate results with very few terms in the solution summation. The FDM had convergence troubles specially for the positions near the center and for high concentration of heat generation in the center of the plate.