Natural convection heat transfer from a finned sphere

Natural convection heat transfer from a finned sphere has been studied numerically in both laminar (105 ⩽ Ra ⩽ 108) and turbulent (1010 ⩽ Ra ⩽ 1012) regimes. Computations are done for the Nusselt number (Nu) by varying the fin-height-to-sphere-diameter ratio (H/D) and the fin-pitch-to-sphere-diameter ratio (P/D) in the range of 0.017-0.200 and 0.131-0.393 respectively. Five different turbulence models have been used to compute the mean Nusselt number for some cases and for the purpose of developing a general correlation for the Nu from our computed results we have used the k-ε model. The numerical procedure has been verified first by comparing the numerically obtained Nusselt number for a simple sphere (without fins) with that of the given correlations from the literature. For the sphere having conductive (Al) fins, with increasing number of fins, Nu decreases for laminar heat transfer and increases for turbulent heat transfer. For the sphere having non-conductive fins, Nu decreases with increasing number of fins in both laminar and turbulent heat transfer. Also, Nu increases with increasing fin height for conductive fins over the sphere and decreases for non-conductive fins. Finally, correlations of Nusselt number for natural convective heat transfer from a finned sphere are developed with the pertinent input parameters like Ra, P/D and H/D in the range stated above.