The asymptotic solution of a kind of Stefan problem (Q1060361)

We discuss the melting problem of an infinite solid slab with width L and arbitrary initial temperature distribution. The non-dimensional problem can be divided into three regions: liquid state region, solid state region and intersection surface between solid and liquid. By means of PLK method and like multi-scale method, the asymptotic solution of the problem can be derived. Next we analyse some phenomena as follows: 1) Temperature difference between the surface of the slab at the end of the phase change; 2) The time completing phase change; 3) Relation between phase change surface and time; 4) Distribution of temperature on solid state region; 5) Distribution of temperature on liquid state region. We discover that all conclusions coincide with experiment.