The slow, steady ascent of a hot solid sphere in a Newtonian fluid with strongly temperature-dependent viscosity

Abstract

In this paper, we revisit, both asymptotically and numerically, the problem of a hot buoyant spherical body with a no-slip surface ascending through a Newtonian fluid that has strongly temperature-dependent viscosity. Significant analytical progress is possible for four asymptotic regimes, in terms of two dimensionless parameters: the Péclet number, Pe, and a viscosity variation parameter, ∊. Severe viscosity variations lead to an involved asymptotic structure that was never previously adequately reconciled numerically; we achieve this with the help of a finite-element method. Both asymptotic and numerical results are also compared with those obtained recently for the case of a spherical body having a zero-traction surface.