Back to Search Start Over

Internal heating driven convection at infinite Prandtl number.

Internal heating driven convection at infinite Prandtl number.

Authors :
Whitehead, Jared P.
Doering, Charles R.
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