Upper and lower bounds for the solution of a melting problem

Abstract

A slab, melting under an arbitrary heat input on one face and insulated on the other is studied. Variable material properties are taken into account. After preliminary general considerations, it is shown that the solution to the stated problem is unique. It is then proved that higher rates of melting and higher temperatures will result from higher heating rates; from this intuitively plausible result upper and lower bounds for the solution are easily constructed. An example is worked out in detail.