An analytical approach for transient thermal behavior of a packed-bed molten salt thermocline thermal storage with heat losses

This work presents the first comprehensive analytical solution for packed-bed thermocline storage systems that fully accounts for peripheral heat losses, offering a novel transient solution for local thermal non-equilibrium (LTNE) conditions and the first exact solution for the limiting case of local thermal equilibrium (LTE). Starting from a set of transient partial differential energy equations in cylindrical coordinates for the fluid and solid phases, the model was derived by integrating over the cross-section. The solution identifies six key dimensionless parameters that govern system performance. The model's accuracy was validated against experimental data, demonstrating excellent agreement and successfully capturing the characteristic temperature drop near the tank outlet. Crucially, this analysis is valid for any combination of heat transfer fluid and solid filler. The resulting analytical framework provides not only a valuable tool for efficient system design but also a reliable benchmark for validating complex numerical models.