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Internal heating driven convection at infinite Prandtl number.
Internal heating driven convection at infinite Prandtl number.
- Source :
-
Journal of Mathematical Physics . Sep2011, Vol. 52 Issue 9, p093101. 11p. - Publication Year :
- 2011
-
Abstract
- We derive an improved rigorous lower bound on the space and time averaged temperature <T> of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries driven by uniform internal heating. A singular stable stratification is introduced as a perturbation to a non-singular background profile yielding <T> >= 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 52
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 66184911
- Full Text :
- https://doi.org/10.1063/1.3637032