Rajagopal, K.R., Saccomandi, G. and Vergori, L. (2009) Stability analysis of the Rayleigh–Bénard convection for a fluid with temperature and pressure dependent viscosity. Zeitschrift für Angewandte Mathematik und Physik, 60(4), pp. 739-755. (doi: 10.1007/s00033-008-8062-6)
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Abstract
The classical problem of thermal-convection involving the classical Navier–Stokes fluid with a constant or temperature dependent viscosity, within the context of the Oberbeck–Boussinesq approximation, is one of the most intensely studied problems in fluid mechanics. In this paper, we study thermal-convection in a fluid with a viscosity that depends on both the temperature and pressure, within the context of a generalization of the Oberbeck–Boussinesq approximation. Assuming that the viscosity is an analytic function of the temperature and pressure we study the linear as well as the non-linear stability of the problem of Rayleigh–Bénard convection. We show that the principle of exchange of stability holds and the Rayleigh numbers for the linear and non-linear stability coincide.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Vergori, Dr Luigi |
| Authors: | Rajagopal, K.R., Saccomandi, G., and Vergori, L. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Zeitschrift für Angewandte Mathematik und Physik |
| Publisher: | Springer |
| ISSN: | 0044-2275 |
| ISSN (Online): | 1420-9039 |
| Published Online: | 04 March 2009 |
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