From the second law of thermodynamics, the concepts of irreversibility, entropy generation, and availability are applied to counterflow parallel-flow and cross-flow heat exchangers. In the case of the cross-flow configuration, there are four types of heat exchangers: 1) both fluids unmixed, 2) both fluids mixed 3) fluid of maximum heat capacity rate mixed and the other unmixed, 4) fluid of minimum heat capacity rate mixed and the other unmixed In the analysis, the heat exchangers are assumed to have a negligible pressure drop irreversibility. The counterflow heat exchanger is compared with the other five heat exchanger types and the comparison will indicate which one has the minimum irreversibility rate. In this comparison, only the exit temperatures and the heat transfer rates of the heat exchangers are different The other conditions (inlet temperatures, mass flow rates, number of transfer units) and the working fluids are the same in the heat exchangers.