• APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR REACTION-DIFFUSION EQUATION IN MICROWAVE HEATING MODEL IN A SLAB: HOMOTOPY ANALYSIS METHOD

Abstract

Mathematical modeling in microwave heating in an infinite slab with isothermal walls is discussed. In this paper , the approximate analytical solution of steady state non-linear reaction-diffusion equation is obtained using Homotopy analysis method (HAM). In particular, we consider the case where the source term decreases spatially and increases with temperature. A simple form of an approximate analytical expression of temperature profiles in terms of dimensionless parameter  and are also reported.  These approximate results are compared with the numerical results. A good agreement with simulation data is noted. The present approach is less computational and is applicable for solving other non-linear boundary value problem.