LAUSR

The natural heat convection within a square enclosure filled with water–Al2O3 nanofluid has been studied numerically in the presence of a magnetic field. The effect of heat source geometry attached to the bottom wall on the Nusselt number was investigated by changing its nondimensional width and height, and side walls thickness of the enclosure ranging from 0.1 to 0.5, 0.1 to 0.8 and 0.05 to 0.2, respectively. A regression model has been obtained along with conducting a sensitivity analysis seeking an optimal heat transfer. Results, reveal that Nusselt number increases by enlarging the fin, and reaching a peak point before it declines. Thus, interestingly, the ever-increasing heat transfer by means of fin size does not retain and there is an optimal point wherein the maximum heat transfer occurs. Moreover, the thermal performance of the system largely depends on the fin size rather than the relative side walls thickness. However, its effect intensifies as the fin width increases. Results of optimization show that the maximum heat transfer occurs at $$W = 0.4615$$W=0.4615, $$H = 0.6467$$H=0.6467 and $$L_{\text{b}} = 0.2$$Lb=0.2.