An Algorithm based on Predicting the Interface in Phase Change Materials


1 Department of Mechanical Engineering, Semnan University, Semnan, Iran

2 Department of Mechanical Engineering, Griffith University, Australia


Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its velocity and the temperature distribution within the domain are important for these applications. Well known numerical techniques have difficulties with time-dependent boundary conditions. Therefore, fine mesh and small time steps are needed to obtain accurate solutions. There are two main approaches to solve the Stefan problem: front-tacking and variable grid method. The most existing methods are not applicable to all situations and they cannot be easily implemeted in two-dimensional or three-dimensional geometries and all boundary conditions. In this paper, we proposed an algorithm to solve one-dimensional Stefan problem in all kind of boundary condition; also it can be easily extended for 2D and 3D Stephan problems using finite difference method. For validation, the results are compared with exact solution of constant boundary condition. Afterward, periodic boundary condition is considered. The results showed significant relationship between numerical and exact solution, and the maximum error was approximately  0.4%.


1.     Crank, J., "Free and moving boundary problems" (oxford science publications)", Clarendon Press, Oxford, UK, 1984, (1987).
2.     Gupta, S., Laitinen, E. and Valtteri, T., "Moving grid scheme for multiple moving boundaries", Computer Methods in Applied Mechanics and Engineering,  Vol. 167, No. 3-4, (1998), 345-353.
3.     Mackenzie, J. and Robertson, M., "The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method", Journal of Computational Physics,  Vol. 161, No. 2, (2000), 537-557.
4.     Adami, M., "Transient two-dimensional (RZ) cyclic charging analysis of space thermal energy storage systems (research note)", International Journal of Engineering, 15 (2002), 205-210.
5.     Bakhshipour, S., Valipour, M. and Pahamli, Y., "Parametric analysis of domestic refrigerators using pcm heat exchanger", International Journal of Refrigeration,  Vol. 83, (2017), 1-13.
6.     Costa, M., Buddhi, D. and Oliva, A., "Numerical simulation of a latent heat thermal energy storage system with enhanced heat conduction", Energy Conversion and Management,  Vol. 39, No. 3-4, (1998), 319-330.
7.     Lamberg, P., Lehtiniemi, R. and Henell, A.-M., "Numerical and experimental investigation of melting and freezing processes in phase change material storage", International Journal of Thermal Sciences,  Vol. 43, No. 3, (2004), 277-287.
8.     Kushwaha, M. and Singh, A.K., "A study of a stefan problem governed with space–time fractional derivatives", Journal of Heat and Mass Transfer Research (JHMTR),  Vol. 3, No. 2, (2016), 145-151.
9.     Savović, S. and Caldwell, J., "Finite difference solution of one-dimensional stefan problem with periodic boundary conditions", International Journal of Heat and Mass Transfer,  Vol. 46, No. 15, (2003), 2911-2916.
10.   Marshall, G., "A front tracking method for one-dimensional moving boundary problems", SIAM journal on scientific and Statistical Computing,  Vol. 7, No. 1, (1986), 252-263.
11.   Furzeland, R., "A comparative study of numerical methods for moving boundary problems", IMA Journal of Applied Mathematics,  Vol. 26, No. 4, (1980), 411-429.
12.   Wu, Z., Luo, J. and Feng, J., "A novel algorithm for solving the classical stefan problem", Thermal Science,  Vol. 15, No. suppl. 1, (2011), 39-44.
13.   Moghadam, A.J. and Hosseinzadeh, H., "Thermal simulation of solidification process in continuous casting", International Journal of Engineering-Transactions B: Applications,  Vol. 28, No. 5, (2015), 812-821.