Convection in an internally cooled fluid layer heated from below

Abstract

Convection in a homogeneously cooled layer heated by a fixed temperature at the lower boundary is investigated numerically for various Rayleigh numbers $\mathit{Ra}$ and Prandtl numbers $\mathit{Pr}$. The upper boundary is kept insulating. Large aspect ratios up to 20 are used in order to study the large scale pattern of convection. The problem is mathematically identical with the problem of a homogeneously heated convection layer cooled from above. The mean temperature difference between the two boundaries decreases in proportion to ${\mathit{Ra}}^{-0.216}$.

Keywords:

• Convection
• internally cooled
• internally heated
• numerical simulations

Acknowledgements

This paper is a greatly extended version of an earlier report (Hartlep and Busse 2006) of work that was performed while F. H. Busse was visiting NASA Ames Research Center through the Senior Visiting Fellow Program of the NASA/Stanford University Center for Turbulence Research. More recent work by F. H. Busse has been supported by NASA grant NNX-09AJ85G.

Notes

No potential conflict of interest was reported by the authors.

Supplemental data for this article can be accessed at https://doi.org/10.1080/03091929.2017.1376324