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

作者：Vynnycky M^*; O' Brien M A

来源：Applied Mathematics and Computation, 2014, 231: 231-253.

DOI：10.1016/j.amc.2013.12.078

• Slow flow
• Temperature-dependent viscosity
• Asymptotics

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 Peclet number, Pe, and a viscosity variation parameter, epsilon. 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.

• 出版日期2014-3-15