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.
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Rajagopal, K.R., Saccomandi, G. & Vergori, L. Stability analysis of the Rayleigh–Bénard convection for a fluid with temperature and pressure dependent viscosity. Z. Angew. Math. Phys. 60, 739–755 (2009). https://doi.org/10.1007/s00033-008-8062-6
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DOI: https://doi.org/10.1007/s00033-008-8062-6