On the ADI scheme for a two-dimensional transient heat conduction problem with phase change

In this study, the Alternative-Direction-Implicit (ADI) scheme was used to solve a two-dimensional transient heat conduction problem with phase change. In order to solve this problem, the phase change latent heat effect was approximated in the neighborhood of the phase change by a large heat capacity within a small temperature range. This treatment makes it possible to transform the moving boundary phase change heat transfer problem to one involving a single phase transient heat transfer problem with variable specific heat and thermal conductivity. To illustrate this numerical scheme, an example is presented, using water as the working medium. The effects of specific heat and thermal conductivity within the layer of phase change and temperature range across the layer, as well as grid point and time step on the numerical results are presented. Also, the results are compared to those obtained analytically, as well as those obtained using a three-time level implicit numerical scheme.