Approximate solutions for metallic regenerative heat exchangers

An analytical model to calculate the temperature profiles and the effectiveness of regenerative heat exchangers in counterflow is presented. It is limited to cases where the storage matrix has a small wall thickness so that no temperature variation in the matrix perpendicular to the flow direction has to be considered. This is usually the case for metallic matrices but can also be fulfilled for ceramic matrices in the form of a thin-walled monolith. Starting from a two-phase model for the gas and storage matrix an approximate solution is derived for the limiting case where the period of the hot and cold process stream becomes infinitesimally small. Using series expansions of this solution the equations to calculate the temperature profiles and the regenerator effectiveness are obtained. Contrary to already published correlations the presented analytical approach considers the heat conductivity in the storage matrix parallel to the flow direction. The range where these equations can be applied is shown by comparing the approximate solution with a numerical solution of the complete set of governing dynamic energy balance equations. The effect of important process parameters on the performance of a countercurrent regenerative heat exchanger is discussed.