A novel hybrid method based cubic B-spline for one-dimensional Stefan problem with moving PCM, size-dependent thermal conductivity and periodic boundary condition

Phase change materials (PCM) are substances that release and absorb sufficient energy at phase transition to provide useful heat or cooling. Stefan problems including PCM have many applications in science and engineering. Since an exact solution for this type of Stefan problem does not exist, tracking the moving boundary and obtaining accurate temperature distribution are still challenging issues in mathematical aspects. Therefore, in this paper, a new approach based on combining the cubic B-spline and a fourth-order compact finite difference scheme is developed to capture the behavior of the one-dimensional Stefan problem including moving PCM, variable thermal conductivity and periodic boundary condition. The proposed combined method in space and the Crank-Nicolson method in time are applied to the model after the moving domain is transformed into the fixed domain by the boundary immobilization method. The comparative results have seen a good agreement for a particular case. Besides, the stability of the scheme and the effect of the model parameters on the numerical solution are analyzed. The computations reveal that the new combined method is seen to pull up the accuracy of the model solutions and presents an efficient alternative solution to the model.