Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field

Abstract

The problem of heat transfer at high Péclet number P_e from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for P_e → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of P_e results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.