Internal heating driven convection at infinite Prandtl number

Details Internal heating driven convection at infinite Prandtl number Internal heating driven convection at infinite Prandtl number

2011-04-14

arxiv.org/abs/1104.2792v1

Physics

Fluid Dynamics

Scientific paper

We derive an improved rigorous bound on the space and time averaged temperature $$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel approach is used wherein a singular stable stratification is introduced as a perturbation to a non-singular background profile, yielding the estimate $\geq 0.419[R\log(R)]^{-1/4}$ where $R$ is the heat Rayleigh number. The analysis relies on a generalized Hardy-Rellich inequality that is proved in the appendix.

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