This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluidfrom entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at epsilon = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R = 0.9, the entropy generation number ratio is the same for all inlet temperature ratios at epsilon = 0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel-flow and counterflow heat exchangers. Copyright (C) 2010 John Wiley & Sons, Ltd.