Study of heat and fluid flow during melting of PCM inside vertical cylindrical tube

This paper presents numerical investigation to study the melting of Phase Change Material (PCM) partially filled in a vertical cylindrical tube. The top space of tube was filled with air to take into account the volumetric expansion of PCM. The natural convection inside PCM liquid phase was considered via the temperature dependency of density and gravitational force. The finite-volume method was adopted to discretize the conservation equations of mass, momentum, and energy. The enthalpy porosity formulation was employed to solve the energy equation in both regions of PCM, liquid and solid. In this multiphase system, the Air-PCM interactions have been treated using the Volume of Fluid model (VOF). The mathematical model is based on conjugate heat transfer in PCM subjected to a constant temperature at the external surface of cylindrical shell. The obtained results have been analyzed and compared with literature, and a good agreement was showed. Then, a parametric study was carried out to establish correlations for the liquid fraction and time of complete melting as a function of all dimensionless parameters that governing this problem, such as Fourier number, Grashof number, Stefan number, wall to PCM thermal diffusivity ratio, tube aspect ratio, shell-to-tube diameter ratio and dimensionless initial temperature. The results show that all parameters of the problem can really affect the phase change phenomena and consequently, affect the melting time.