Melting of Thin Cylindrical Tubes

Abstract

It has been shown that the use of a polynomial profile for the temperature distribution in the case of thin cylindrical tubes is justified in the Goodman's technique of heat balance integral. The above technique has been used to obtain an approximate solution to the problem of melting (solidification) in a tube which is subjected to a constant heat flux at the inner surface while its outer surface is kept insulated. The temperature history and the melting rate are studied for the time during which the melting proceeds. Lighthill's technique for rendering approximate solution uniformly valid has been used and the first three terms of the series solution have been expressed in terms of an intrinsically small parameter.