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Finite-size effects on linear stability of pure-fluid convection

Chen, Yih-Yuh (1992) Finite-size effects on linear stability of pure-fluid convection. Physical Review A, 45 (6). pp. 3727-3731. ISSN 1050-2947. doi:10.1103/PhysRevA.45.3727.

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The linear stability of pure-fluid Rayleigh-Benard convection in a finite cell of arbitrary geometry can be formulated as a self-adjoint eigenvalue problem. This, when coupled with perturbation theory, allows one to deduce how the sidewalls affect its stability. In particular, it is shown that for almost all boundary conditions the difference between the onset Rayleigh number and its infinite-cell limit scales like L^-2 as the cell dimension L tends to infinity, and near the sidewall the temperature and velocity are of order L^-1 compared to their bulk values. The validity of replacing the true thermal boundary condition by a frequently used mathematically simpler homogeneous one is also demonstrated.

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Additional Information:©1992 The American Physical Society. Received 17 June 1991. Constant inspiration and encouragement from Professor M.C. Cross have made this work all the more enjoyable. I also thank Professor N.-C. Yeh and Professor H.B. Keller for useful discussions. This work is supported by NSF Grant No. DMR-9013984.
Issue or Number:6
Record Number:CaltechAUTHORS:CHEpra92
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3636
Deposited By: Tony Diaz
Deposited On:22 Jun 2006
Last Modified:08 Nov 2021 20:11

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