Perfect Contact - Laplace Transform and their Links

Abstract

In this paper, we consider a slab represented by the interval 0 < x < 1, at the initial temperature uo(x) = M > 0 having a positive constant heat flux q on the left face and the contact perfect condition, ux(1, t) + yut(1,t) = 0 on the right face
x = 1. We consider the corresponding heat conduction problem and we assume that the phase-change temperature is OºC. We compare estimations of the time of the occurrence of the phase-change obtained by means of Laplace Transform and Method of Lines.