TIME ESTIMATES FOR THE PHASE-CHANGE PROCESS IN A MATERIAL WITH A PERFECT THERMAL CONTACT BOUNDARY CONDITION

In this paper, we consider a slab represented by the interval 0 < y < `, at the initial temperature v0(y) = M> 0 having a positive constant heat flux q0 on the left face and a contact perfect condition, kvy(`, τ) +Mfcfvτ (`, τ) = 0, on the right face y = `. We consider the corresponding heat conduction problem and we assume that the phase-change temperature is 00C. We obtain time estimates for the occurrence of a phase-change by means of Laplace Transform and Method of Lines. Introduction an preliminaries We consider a one-dimensional slab [0, `] with its face y = ` in perfect thermal contact with mass Mf per unit area of a well-stirred fluid (or a perfect conductor) of specific heat cf. We consider the following heat conduction problem