Contact melting of a rectangular block with temperature-dependent properties

We consider a model for the contact melting of a block of phase change material on a flat, heated surface. The block and melt have linear temperature-dependent thermal conductivity and viscosity. The model consists of heat equations for the solid and liquid temperatures, the Navier–Stokes equations in the liquid melt layer, a Stefan condition at the solid–liquid interface and a force balance between the weight of the solid and the countering pressure in the liquid. The heat balance integral method is used to obtain an approximate solution for the solid temperature. We demonstrate that in the case of n-octadecane the inclusion of temperature-dependent effects slows down the melting process. Finally, we vary the parameters in the linear expressions for the conductivities and viscosities to understand the behaviour of the system.