A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

Abstract EN

A two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other.

In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature.

A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity.

The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity.

Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab.