In this paper the Boussinesq model is used to formulate the fluctuation term while the equations of conservation of mass, momentum and energy are formulated in terms of the vorticity and the stream functions. The dimensionless variables used lead to continuous fusion in the discretized control volumes while the boundary conditions at the moving liquid-solid interface are determined iteratively in terms of the enthalpy and the stream functions. In this study are presented the interface boundaries, heat flow through the walls of the inner cylinder and the heat stored. The results agree well with available theoretical and experimental results. Additionally the transient profiles of the stream function are presented to indicate the convective currents in the pcm. 7589