The pillow-plate heat exchanger (PPHE) is a kind of heat exchanger constructed by a set of wavy surfaces like a pillow. In this study, the influence of pillow-plate geometrical parameters (including dimensionless channel height, dimension- less plate width, and pillow plates number) and flow specification (including Reynolds and Prandtl numbers) in terms of derived dimensionless parameters on their thermo-hydraulic performance is evaluated through a comprehensive parametric investigation. The fully developed regime in PPHE channel is assumed and fluid flow, heat transfer, and thermodynamics principles are combined in terms of the entropy generation minimization (EGM) approach. Afterwards, a multi-objective optimization method is applied by using the non-dominated sorting genetic algorithm (NSGA-II) to find the optimal design of PPHE. In this way, the maximization of performance evaluation criterion (PEC) against the minimum total entropy generation for PPHE is eventuated. The behavior of PPHE’s important evaluation criteria are illustrated for different Reyn- olds numbers from 1000 to 6000 by varying Prandtl number and the proposed dimensionless geometry parameters. Also, contrariness between two parts of non-dimensional entropy generation (NDEG), i.e., thermal and frictional, is concluded from the result for Pareto-optimal front. It indicates there is an optimum Re number that minimizes (NDEG)tot at any geo- metrical parameters. On the other hand, multi-objective optimization results show the conflict between two main objective functions namely PEC and (NDEG)tot that reveals any geometrical change to increase in the PEC of heat exchanger leads rising in total entropy generation and vice versa. The final optimum values of the objective functions are PECopt = 1.3712 and (NDEG)tot,opt = 0.0145 which occurs at Re = 3265

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