On the application of integral-methods to the solution of problems involving the solidification of liquids initially at fusion temperature

Abstract

Approximate integral-methods, similar to those used in the solution of the boundary layer equations in fluid dynamics, are developed for determining the location and time history of the unidimensional solid-liquid interface during the solidification of liquids initially at the fusion temperature. For isothermal wall condition the configurations treated are the inward solidification of the semiinfinite region, the circular cylinder and the sphere. Series solutions of the thermal equation giving the location of the solid-liquid interface, for small time, are derived for the latter two shapes and are used to estimate the accuracy of the approximate integral-methods. The approximate results for the circular cylinder are also compared with an existing numerical solution obtained by the relaxation method.