Contact melting process on an arbitrary shape wall coated by porous layer

This paper presents a theoretical study of direct contact melting process in a capsule with an arbitrary two-dimensional heating wall. One of the important applications of this system is that of thermal energy storage systems. Latent heat energy is used in this system effectively. The phase change material (PCM) is stored in a small capsule. The heating wall shape of the capsule in this system is not simple. Sometimes it is complicated. In recent research, this process was only solved for several limited simple wall shapes. Governing equations were solved using approximated methods or numerical methods. In this paper, the authors analytically solve governing equations systems with heat convection terms. It is shown that the governing equations systems can be transformed into ordinary differential equations systems by a similarity transformation. It is also shown that there exists an exact solution that is obtained without using any approximate method. This solution is valid for the whole range of Stefan number