A note on the rate of heat or mass transfer from a small particle freely suspended in a linear shear field

Abstract

It is shown that for a small sphere freely suspended in a linear shear flow at small Reynolds numbers, the Nusselt number N is given by $N = \{1 - \alpha P^{\frac{1}{2}} + o(P^{\frac{3}{2}})\}^{-1}$, where P is the Péclet number. For any given type of shear flow, the numerical value of the constant α can be obtained from a general expression derived by Batchelor (1979). The corresponding result for a particle of arbitrary shape is N/N₀ = {1 − αN₀P^½ + O(P^3/2)}⁻¹, where N₀ is the Nusselt number for pure conduction.