Analytical Solution of the Thermal Behavior of a Circulating Porous Heat Exchanger

The transient thermal behavior of a two-dimensionalcirculating porous bed is analyt- ically investigated. A one-energy equationmodel, representing both the gas and solid phases via a unified temperature, is employed to describe the thermal behaviorof the circulatingbed. The latter isessentiallya tubeand shellheatexchanger com- monly used in technologically important applica- tions. The model equation is transformed into a simpler set of partial differential equations using an analytical procedure. The analytical solution, based on the method of separation of variables and the principle of superposition, is formulated for the calculation of the temperature distribution in the radial and axial directions of the bed. The temperature distribution can be determined under different process parameters and conditions. Con- vergence criteria of the solution are derived for typicalprocess conditions. Thedeveloped closed- form solutionofthetransientone-equationenergy model provides a simple and convenient means for estimating the thermal behavior of the circu- lating bed.