Direct contact melting process on cylindrical heating wall with an arbitrary temperature distribution

One of the important applications of the direct contact melting process is thermal storage systems. In such systems, a phase change material is stored in a small capsule that is heated from an outside heat source. A direct contact melting process takes place in the melting process of the thermal storage system. In this system, latent heat energy is used effectively. This paper presents a theoretical study of the direct contact melting process with a cylindrical heating wall that has arbitrary temperature distribution. The governing equations system with heat convection terms is solved analytically. It is shown that it can be transformed into an ordinary differential equations system by a similarity transformation. Temperature is solved using a perturbation technique. This solution is valid for almost all practical Stefan numbers. An analytical solution is obtained for a typical temperature distribution. It is shown that melting rate is enhanced by more than 10% by the effect of temperature distribution