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Parmentier & Morgan 1982
Parmentier, E.M. and Morgan, J. (1982). Thermal convection in non-Newtonian fluids: Volumetric heating and boundary layer scaling. Journal of Geophysical Research 87: doi: 10.1029/JB087iB09p07757. issn: 0148-0227.

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.

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Journal of Geophysical Research
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