Slow, steady ascent in a power-law fluid with temperature-dependent viscosity

► Complete asymptotic analysis (four regimes) for the ascent of a zero-traction sphere in a non-isothermal power law fluid (shear-thickening and shear-thinning). ► Closed-form expressions for the drag. ► Closed form expressions for the Nusselt number. ► Closed form expressions for the rise velocity. In this paper, we consider the problem of a hot buoyant spherical body with a zero-traction surface ascending through a power-law fluid that has 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, ϵ. For mild viscosity variations, Levich’s classical result for an isoviscous Newtonian fluid is generalized; more severe viscosity variations lead to an involved four-regime asymptotic structure that has similarities with that found for a Newtonian fluid with temperature-dependent viscosity.