Mixed convection about a rotating sphere

The paper presents a theoretical analysis of flow and heat transfer characteristics of the effects of buoyancy force on laminar boundary layer over a rotating sphere in forced flow under two kinds of heating conditions: uniform wall temperature and uniform surface heat flux. By applying appropriate coordinate transformations and using Merk's types of series, the governing momentum and energy equations are reduced to a set of coupled ordinary differential equations, which depend on wedge, rotation and buoyancy parameters. Numerical computations are carried out for Prandtl numbers 0.7,1.0 and for various values of buoyancy and rotation parameters. For aiding flow, it is found that both the friction factor and the local Nusselt number increase with increasing buoyancy force. The local free stream velocity increases with buoyancy which, in turn, affects the friction coefficient and Nusselt number. The coupling between rotation and buoyancy results in increased overshooting of the velocity profiles in the vicinity of the rotating sphere. For an equivalent buoyancy effect, heating by uniform surface heat flux yields larger local Nusselt number than heating by uniform wall temperature. The ratio Nu_UHF/Nu_UWT is higher for the rotating sphere (as compared to a nonrotating case) and further the ratio increases as the sphere spins faster. The effect of free stream, rotation and buoyancy on the eruption of flow is examined and also a suggestion for further investigation is made.