Effectiveness-N-tu relationship in perforated plate matrix heat exchangers

Perforated plate matrix heat exchangers (MHEs), invented nearly 40 years ago, are finding increasing use in small cryogenic liquefaction and refrigeration systems. There are two different approaches for analysis of the performance of MHEs: (i) to consider the MHE as a conventional exchanger with the plate acting as a fin; and (ii) to treat the MHE as a discrete set of plate-spacer pairs, with the number of plates being a very important parameter. The latter approach involves numerical solution of governing equations. In this paper a simple analytical approach is presented for analysis of the performance and design of MHEs. Closed-form expressions are presented for the effectiveness of the MHE in terms of different resistances and a finite number of plates. It is shown analytically that the first approach is only a special case of the second approach and that the solutions obtained with the present method are very close to those obtained with complex numerical models (in the second approach).