ASYMPTOTIC BEHAVIOUR OF TEMPERATURE PROFILES OF A CLASS OF NON-LINEAR HEAT CONDUCTION PROBLEMS

Abstract

The conduction of heat into a semi-infinite homogeneous solid is investigated when the coefficient of thermal conductivity depends on the temperature and decreases with increasing temperature. It is assumed that initially, far from the face of the solid, the temperature tends to a value T<inf>0</inf>. At the face the temperature is held at a higher value T<inf>1</inf>. A similarity solution is shown to exist and it is demonstrated that for a large class of initial temperature distributions, the ensuing temperature profiles converge to this similarity profile as <it>t</it> tends to infinity.