A simplified solution of the regenerator periodic problem: the case for air conditioning

This work presents an analytical solution for the periodic heat transfer problem of regenerators used in air conditioning, which are operating at low regeneration temperatures and mass flow rates. These types of regenerators are characterized by NTU/Cr ^?<1. The partial differential equations for hot and cold airflows as well as the regenerator matrix were solved using a successive transformation of variables. They were reduced to the ordinary Bessel differential equation of the type xf″+f′?xf=0. The conventional initial and reversal boundary conditions were used in this work. The solution gives a correlation for the prediction of the regenerator effectiveness. Besides the effectiveness, the solution facilitates the calculation of the matrix temperature distribution and exit airflow temperatures. The result is compared with the available numerical and analytical solutions from literature. The result of this analysis reveals that the consideration of a non-linear matrix temperature distribution as in some previous work for low temperature regenerators just complicates the solution procedure with no significant improvement in the accuracy within the parameter space typical for air conditioning applications.