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

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 - α P1/2 + o(P3/2)\⁻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 − αN0P½ + O(P3/2)}−1, where N0 is the Nusselt number for pure conduction.