Abstract Heat exchange by forced fluid flow between two coupled fixed beds containing solids can be used to recover heat from hot products to cool input in many industrial processes. The heat exchange between the fixed beds is studied. Analytical solutions for the transient fluid and solid temperature distributions and heat recovery effectiveness are derived. The intra-particle transient temperature distributions are accounted for in the more accurate analysis and the results are compared to lumped analysis. It is shown that the heat recovery effectiveness reaches maximum at certain optimum time instant at which the fluid circulation should be stopped. Damping of cyclic oscillations in fluid temperature or concentration is considered and analytical solution for the damper is presented.