Analytical and numerical analysis of PCM solidification inside a rectangular finned container with time-dependent boundary condition

This work presents an approximate analytical model to evaluate the temperature distribution and position of the solid-liquid interface during the solidification of the phase change material inside a two-dimensional finned container with time-dependent boundary condition. Locating a fin inside the container will increase the rate of heat transfer and compensates for the low thermal conductivity of the phase change material. This leads to the two-dimensionalization of the freezing problem, which impedes the presentation of the analytical solution to predict the freezing process. Considering rational simplifying assumptions, such as negligible natural convection, one-directional heat transfer and constant thermo-physical properties, permits to obtain a general solution. After, two special cases of linear and sinusoidal time-dependent boundary conditions are discussed. Analytical results for non-dimensional temperature distribution and position of the solidification front are compared with those of the lattice Boltzmann method with respect to the Fourier number at Stefan number of 0.218. The numerical and analytical solutions exhibit an acceptable level of agreement, justifying the use of the current analytical model. In the end, the effect of the container aspect ratio on the complete freezing time and performance of the finned container has been evaluated.