OPTIMAL HEATING OF A SLAB WITH A PLANE HEAT SOURCE OF TIMEWISE VARYING STRENGTH

Abstract

The optimal heating rate is sought for a plate with temperature-dependent thermal conductivity and an internally located continuous plane heat source. At the final specified time t_f, the final temperature distribution T_f(x) should approximate as closely as possible a specified uniform temperature T_d, and a minimum amount of energy should be used for the heating. We determine the location and the timewise variation of the strength of the plane heat source that satisfy such requirements.