The following study will examine the effect on overall thermal/fluid performance associated with different fin geometries, including, rectangular plate fins as well as square, circular, and elliptical pin fins. The use of entropy generation minimization, EGM, allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including base plate and applying the conservations equations for mass and energy with the entropy balance. The formulation for the dimensionless entropy generation rate is developed in terms of dimensionless variables, including the aspect ratio, Reynolds number, Nusselt number, and the drag coefficient. Selected fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate corresponding to different parameters including axis ratio, aspect ratio, and Reynolds number. The results clearly indicate that the preferred fin profile is very dependent on these parameters.