Analytical and numerical solution of heat generation and conduction equation in relaxation mode: Laplace transforms approach

Abstract

In this article analytical solution of one-dimensional heat equation in relaxation mode of heat generation and conduction using Laplace transforms method is presented. The model adopted takes into account finite velocity of heat propagation, and relaxation of heat source capacity. The properties of heat source terms in four different cases are incorporated in the model and investigated. Temperature distributions and variations with conduction mode and relaxation time are analyzed. High relaxation time is observed to lowers the temperature profile, whereas enhanced temperature distribution changes at particular values of α, and for source capacity proportional to temperature. How the steady state solution is achieved for some selected values of coefficients is also discussed.