Conjugate Mathematical Model of Heat and Mass Transfer in the Thermal Energy Storage Module with a “Solid Body–Liquid” Phase Transition

Computer modeling results of heat and mass transfer processes in a thermal energy storage module with a “solid body–liquid” phase transition are presented. A cylindrical element filled with heat storage material was studied. A channel with the moving heat transfer fluid is located inside the cylindrical element as a “double pipe.” A coupled non-stationary non-linear 3D mathematical model was developed, which consists of the energy equations for phase change materials and heat transfer fluid. Latent heat in phase change material was taken into account by the effective heat capacity method. Natural convection at melting is calculated together with forced convection of heat transfer fluid through introduction of the effective heat transfer coefficient. The finite volume method with splitting by physical processes and space coordinates is used during the creation of the numerical algorithm. A conducted numerical parametric study allowed us to determine the temperature distribution in the phase change material and heat transfer fluid, the moving interface velocity, full time of charging of the thermal energy storage module, and the influence this process had on the heat transfer fluid temperature and velocity. The results were verified through comparison of an analytical solution of a test problem and with experimental data. The presented method can be used during the design of the latent thermal energy storage module, which functions in wide temperature range, with different phase change materials types and different heat transfer fluids types.