Approximate analytical solution for solidification of PCM in cylindrical geometry with temperature‑dependent thermal conductivity-perturbation method

Abstract

Abstract The Solidification process of Phase change materials inside cylindrical enclosures is analyzed and analytical solutions are derived to determine the positions of the interfaces at different time intervals. In this current investigation, we address the scenario involving temperature-dependent thermal conductivity. For the first time, we employ perturbation techniques to analytically derive the dimensional temperature for both phases. Our study specifically incorporates a linear model to account for the variation in thermal conductivity with temperature. The results show that the duration of complete solidification relies on the Stefan number. As these parameter is augmented, the total solidification time of the cylinder diminishes and escalates, respectively. Furthermore, it has been observed that an augmentation in the thermal conductivity of the phase change material (PCM) leads to a swifter solidification process.