Thermal convection in non‐Newtonian fluids: Volumetric heating and boundary layer scaling

Abstract

Thermal convection in a volumetrically heated fluid layer, in which strain rate is proportional to stress with a power law exponent n, is studied by using finite difference approximations. As in earlier studies of convection in a layer heated from below, convection cell structure is found to be relatively independent of n for n ≤ 3. The rate of heat transfer, expressed in terms of an effective Rayleigh number based on a dissipation rate averaged viscosity, is also relatively independent of n. A relationship between effective Rayleigh number and the Rayleigh number based on the viscosity at a reference strain rate is derived on the basis of boundary layer scaling. This relationship agrees with finite difference solutions for both a volumetrically heated layer and a layer heated from below. Applied to planetary interiors, the power law exponent n is shown to influence the time scale of thermal evolution.