In this paper, a particular heat exchanger is designed and analyzed by using second law of thermodynamics. The heat exchanger operates with the cross flow forced convection having cylindrical, square, and hexagonal pin fins (tubular router) placed in the rectangular duct. The pin fins are installed periodically at the top and bottom plates of the duct perpendicular to the flow direction, structured in-line, and staggered sheet layouts. The entropy generation in the flow domain of the channels is calculated to demonstrate the rate of irreversibilities. To obtain the efficiencies, irreversibility, thermal performance factor, and entropy generation number (EGN), the heat exchanger is operated at different temperatures and flow rates by using hot and cold fluids. Optimization of the design parameters and winglet geometry associated with the performance are determined by entropy generation minimization. The variation of the EGN with Reynolds number for various tubular routers is presented. The Reynolds number is determined according to the experimental plan and the performance is analyzed with the method of effectiveness-number of transfer unit (NTU). Based on particular designs, it was determined that the increment in fluid velocity enhances the heat transfer rate, which in turn decreases the heat transfer irreversibility.