Evaluation of the Nusselt number for a fluid sphere in Stokes flow

Abstract

The Nusselt number Nu is evaluated for an isothermal fluid sphere immersed in a Stokes flow. The dimensionless convective-diffusive conservation equation is solved asymptotically for the case where the Peclet number based on the sphere radius, ε, is small relative to unity. The Nusselt number is evaluated by integrating the derivative of the asymptotic solution over the surface of the sphere. The conservation equation is also solved numerically. A comparison of the numerical and asymptotic solutions shows that the asymptotic expression for Nu is valid only for the Peclet number being small relative to unity. An alternative asymptotic expression for Nu is developed, and it is shown that this expression is valid for Peclet numbers of order unity.