Compact heat exchangers have drawn considerable attention in the recent years due to unprecedented growth of information and process technology and the resulting demand of highly efficient and compact heat removal devices. Until now the performance evaluation of such heat exchangers are made by and large in a substantative way without caring for the thermodynamic potential that the heat transfer device can utilise. The ＇Second Law analysis＇ is a technique which can remove this deficiency. The exergy analysis presented in this paper has also got the unique feature of linking heat transfer to pressure drop encountered. To carryout the analysis a novel approach is suggested here. Firstly, the pressure drop data for unknown heat exchanger surface is predicted by analysing similar data with the help of Artificial Neural Network (ANN). Subsequently the heat transfer data for the same surface has been predicted by using a rediscovered analogy known as Leveque analogy in its modified form. Finally these two fold data are combined in the ＇Second Law analysis＇ which indicates the possibility of optimizing the design of the heat exchanger for minimum irreversibility. In the whole exercise a compact regenerator bed consisting of crossed rod bundles has been used to demonstrate the methodology developed.