Heat or mass transfer from a moving drop - Some approximate relations for the Nusselt number

The external problem of heat/mass transfer for a steadily moving surfactant-free spherical drop is considered. Simple approximate relations for the maximum velocity at the surface of the drop and the Nusselt (Sherwood) number are derived on the basis of the boundary-layer-type estimates. The relations contain adjustable 0(1) numerical factors, which are chosen so as to give the best fit to the results of the previously obtained accurate numerical solutions of the Navier-Stokes and convective-diffusion equations for Re ≤ 200 and Pe ≤ 1000. It is also indicated how the knowledge of the maximum surface velocity allows one to reduce the internal problem to the well-documented case or low Reynolds number.