In the present work, a thermal modeling is conducted for optimal design of compact heat exchangers in order to minimize cost and entropy generation. In this regard, an $ε−NTU$ method is applied for estimation of the heat exchanger pressure drop, as well as effectiveness. Fin pitch, fin height, fin offset length, cold stream flow length, no-flow length, and hot stream flow length are considered as six decision variables. Fast and elitist nondominated sorting genetic algorithm (i.e., nondominated sorting genetic algorithm II) is applied to minimize the entropy generation units and the total annual cost (sum of initial investment and operating and maintenance costs) simultaneously. The results for Pareto-optimal front clearly reveal the conflict between two objective functions, the number of entropy generation units and the total annual cost. It reveals that any geometrical changes, which decrease the number of entropy generation units, lead to an increase in the total annual cost and vice versa. Moreover, for prediction of the optimal design of the plate fin heat exchanger, an equation for the number of entropy generation units versus the total annual cost is derived for the Pareto curve. In addition, optimization of heat exchangers based on considering exergy destruction revealed that irreversibilities, such as pressure drop and high temperature difference between cold and hot streams, play a key issue in exergy destruction. Thus, more efficient heat exchanger leads to have a heat exchanger with higher total cost rate. Finally, the sensitivity analysis of change in the optimum number of entropy generation units and the total annual cost with change in the decision variables of the plate fin heat exchanger is also performed, and the results are reported.

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