Internal heating driven convection at infinite Prandtl number

Abstract

We derive an improved rigorous bound on the space and time averaged temperature $<T>$ 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 $<T>\ge 0.419[R\log (R){]}^{-1/4}$ where $R$ is the heat Rayleigh number. The analysis relies on a generalized Hardy-Rellich inequality that is proved in the appendix.

References in corpus (1)

• "Ultimate state" of two-dimensional Rayleigh-Benard convection between free-slip fixed temperature boundaries

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