The long standing issue of increased heat transfer, always accompanied by increased pressure drop using metal foams, is addressed in the present work. Heat transfer and pressure drop, both of various magnitudes, can be observed in respect to various flow and heat transfer influencing aspects of considered metal foams. In this regard, for the first time, orderly varying pore density (characterized by visible pores per inch, i.e., PPI) and porosity (characterized by ratio of void volume to total volume) along with varied thickness are considered to comprehensively analyze variation in the trade-off scenario between flow resistance minimization and heat transfer augmentation behavior of metal foams with the help of numerical simulations and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) which is a multi-criteria decision-making tool to address the considered multi-objective problem. A numerical domain of vertical channel is modelled with zone of metal foam porous media at the channel center by invoking LTNE and Darcy–Forchheimer models. Metal foams of four thickness ratios are considered (1, 0.75, 0.5 and 0.25), along with varied pore density (5, 10, 15, 20 and 25 PPI), each at various porosity conditions of 0.8, 0.85, 0.9 and 0.95 porosity. Numerically obtained pressure and temperature field data are critically analyzed for various trade-off scenarios exhibited under the abovementioned variable conditions. A type of metal foam based on its morphological (pore density and porosity) and configurational (thickness) aspects, which can participate in a desired trade-off scenario between flow resistance and heat transfer, is illustrated.