Mixed convective cooling of a fin in a channel

Mixed convection heat transfer in an inclined parallel-plate channel with a transverse fin located at lower channel wall is investigated numerically. Employing the stream function vorticity transformation, solution of the transformed governing equations for the system is obtained by the control-volume method with non-uniform grid. The results indicate that the optimum aspect ratio of a fin corresponding to the fin with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed fin profile area. Also, the optimum aspect ratio increases with the inclination angle for Gr/Re2 = 10; whereas the effects of orientation on the optimum aspect ratio is not pronounced for Gr/Re2 < 1. In addition, the optimum aspect ratio of a fin with a smaller fin profile area and Re at Gr/Re2 = 0.1 approaches that of analytical solution having the assumption of constant heat-transfer-coefficient.