Heat and Mass Transfer from Single Spheres in Stokes Flow

The classical problem of heat and mass transfer from single spheres at low values of the Reynolds number, where the velocity field is given by Stokes' formula, is considered. It is shown, by the use of a singular perturbation technique, how an expansion may be derived for the Nusselt number Nu in terms of the Péclet number Pe which yields an accurate expression for the rate of transfer of energy or matter in the range 0 ≦ Pe ≦ 1. It is also established, by studying both the Pe → 0 and Pe → ∞ asymptotes, that the functional relation between Nu and Pe as obtained with the Stokes velocity profile is less sensitive to an increase in the Reynolds number than the familiar Stokes law for the drag coefficient.