In recent decades, the second law of thermodynamics has been commonly applied in analyzing heat exchangers. Many researchers believe that the minimization of entropy generation or exergy losses can be considered as an objective function in designing heat exchangers. Some other researchers, however, not only reject the entropy generation minimization (EGM) philosophy, but also believe that entropy generation maximization is a real objective function in designing heat exchangers. Using driving forces and irreversibility relations, this study sought to get these two views closer to each other. Exergy loss relations were developed by sink–source modeling along the heat exchangers. In this case, two types of heat exchangers are introduced, known as “process” and “utility” heat exchangers. In order to propose an appropriate procedure, exergy losses were examined based on variables and degrees of freedom, and they were different in each category. The results showed that “EGM” philosophy could be applied only to utility heat exchangers. A mathematical model was also developed to calculate exergy losses and investigate the effects of various parameters. Moreover, the validity of the model was evaluated by some experimental data using a double-pipe heat exchanger. Both the process and utility heat exchangers were simulated during the experiments. After verifying the model, some case studies were conducted. The final results indicated that there was not a real minimum point for exergy losses (or entropy generation) with respect to the operational variables. However, a logic minimum point could be found for utility heat exchangers with regard to the constraints.