First-order nonlinear analysis of rapidly switched heat regenerators in counterflow

In this paper we derive closed-form expressions describing the first-order nonlinearities of the matrix temperature profile in rapidly switched heat regenerators in countercurrent where a slug of fluid oscillates within the matrix without exiting either end. The above derivation is based on the solution of the integral equation which describes heat transfer in the regenerator at periodic steady state through the series expansion method. The solution in a integral form of the gas energy conservation performed in an early and companion paper using a Lagrange formulation indicates that the matrix temperature distribution is the only unknown of the problem. For practical purposes, the regenerator effectiveness is also calculated and given in an algebraic form. It follows that in rapid oscillating and reversing flow circulations typical of Stirling cycle machines the effectiveness is underestimated by the conventional regenerator theory applicable only to slowly switched regenerators.