Thermal Conduction Equations For A Medium With An Inclusion Using Galerkin Method

Abstract

The Galerkin method is used to semi-analytically solve the heat conduction equation in non-homogeneous materials. The problem under deliberation is a square plate with a circular inclusion having different thermal conductivities. A generalized procedure that involves the Galerkin method and formulation of the final solution in terms of the procured base functions is adopted. The Galerkin method basically involves expressing the given boundary value problem in terms of a standard mathematical relation, generating a set of continuous base functions, formulating the matrix equation, and determining the solution.For the non-homogeneous material, a set of base functions for the plate and inclusion are determined separately, through which the solution is formulated for the entire domain. The Galerkin method involves tedious and time-consuming computations, which is facilitated with the aid of a computer algebra system, Mathematica.