Numerical simulation of moving boundary problem with moving phase change material and size-dependent thermal conductivity

The Keller box method is applied to the one-phase moving boundary problem with moving phase change material, size-dependent thermal conductivity, and periodic boundary conditions. The phase transition process is allowed to occur when the material is forced to move in one direction or the other at a constant speed. The boundary immobilization method is applied to immobilize the moving boundary, and for the numerical approximation of moving boundary problem, we proposed Keller box method. Keller box method also accommodates the non-linearity in thermal conductivity and Stefan condition. Using the convergence analysis, the proposed scheme obtains stability, as well as second-order accuracy for both spatial and temporal directions, under reasonable conditions. To validate the proposed numerical scheme, we have considered a particular case of this problem having a similarity solution. It is found that the numerical results obtained by the Keller box method have good agreement with the similarity solution and also verified that the computational rate of convergence of our scheme is two. The effects of various parameters and size-dependent thermal conductivity on the position of moving boundary are also investigated.