Based on the above model, the geometrical optimization analysis on a plate-fin heat exchanger is conducted by using the following examples. The fluid under study is air. The operating conditions for the case are obtained from the literature [21] . The geometric and operating parameters of the PFHE under study are given in Table 1. It should be noted that the mass flow rate ratio of cold-side fluid to hot-side fluid is set to be f ¼ _ m c= _ mh ¼ 1; 1:5; 2 for the analysis below. The main objective of this paper is to optimize the main geometrical parameters, i.e., the fin height and fin spacing of both side channels of the plate-fin heat exchanger, with minimizing the specific entropy generation rate for a specified heat transfer rate under the total heat transfer area constraint. Note that for specified heat transfer rate and given operating conditions, the outlet temperatures of fluids should be constant and the entropy generation due to heat transfer
is determined. As seen above, the entropy generation is related to both the heat transfer and fluid friction. Thus, the optimization actually aims at minimizing specific entropy generation rate due to pressure drop, which will lead to lowest pumping power on the premise of meeting a certain heat transfer requirement.