Anharmonic analysis of a time-dependent packed bed thermocline

A vectorized separation of variables approach is applied to a coupled pair of parabolic partial differential equations describing the degradation of a thermocline in a packed bed thermal storage tank. The time-dependent quasi-one-dimensional model includes the effects of finite tank length, thermal conduction in the direction parallel to the tank walls, and heat transfer between the fluid and solid components of the bed. For certain classes of boundary conditions, the analysis leads to an eigenvalue problem for the spatial dependence of the fluid and solid temperatures in the bed. The eigenvalues and corresponding eigenfunctions are readily calculated, and completeness of the eigenfunctions follows from a transformation to an integral equation by the construction of a Green’s tensor function. The method is illustrated by an example which arises in the analysis of the thermal storage subsystem of a central solar receiver power plant.