This article investigates the entropy generation rate in shell and tube heat exchanger with porous medium inserted inside the tubes. Three different waste metal chips made of copper, aluminum, and mild steel are used as porous medium. There is a trade-off between the heat transfer and pressure drop in the design of enhanced heat exchangers. In porous flow if Reynolds number increases the rate of heat transfer will also increase at the expense of reasonable pressure drop. Due to turbulent energy dissipation at high Reynolds number, this pressure drop will increase further, resulting in high entropy generation. The empirical correlations are developed and used for the entropy generation minimization of the actual heat exchanger. The conclusions are derived on the basis of the behavior of the entropy generation number NS as a function of the Reynolds number. On the basis of the entropy generation minimization the upper limit of Reynolds number was found to be 1450, beyond which irreversibility increases.