This study investigates the mixed convection of Cu -water nanofluid in an open square cavity with an internal fin and a porous medium, using the two-phase mixture model. Though all the walls in the cavity are assumed to be insulated, the bottom wall, where the fin is attached, is evenly heated. The simulation examines the impact of varying Darcy numbers (Da=10( -1) , 10( -2) , 10( -3) , and 10( -4) ), porosity (epsilon=0.2, 0.4, 0.6, and 0.8), and solid volume fraction (0 <=phi <= 0.08) on Nusselt, entropy generation, and Bejan numbers. S-gen decreases as the Da increases, but Nu avg and Be increase - quite the opposite of expectations. Reducing material porosity increases heat transfer. Finally, incorporating nanofluid into heat transfer systems could lead to significant improvements in heat transfer efficiency. These findings provide practical guidance for optimizing material properties to achieve desired heat transfer characteristics.