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Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection

Chen, Yih-Yuh (1992) Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection. Journal of Fluid Mechanics, 241 . pp. 549-585. ISSN 0022-1120. doi:10.1017/S0022112092002155.

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The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.

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Additional Information:Copyright © 1992 Cambridge University Press. Reprinted with permission. (Received 18 January 1991 and in revised form 24 January 1992) I would like to thank Professor M.C. Cross for the many stimulating and helpful discussions.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10885
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Deposited On:15 Jun 2008
Last Modified:08 Nov 2021 21:11

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