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On Thermal Convection in a Large Box
Author(s) -
Brown S. N.,
Stewartson K.
Publication year - 1977
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1977573187
Subject(s) - convection , bifurcation , thermal , mechanics , rayleigh number , amplitude , boundary value problem , natural convection , rayleigh–bénard convection , physics , boundary layer , mathematics , mathematical analysis , geometry , thermodynamics , nonlinear system , optics , quantum mechanics
Daniels [4] has shown that the presence of imperfectly insulating sidewalls transforms the onset of Bénard convection in a layer of fluid confined by one pair of lateral boundaries from a bifurcation to a continuous transition as the Rayleigh number increases through the critical value. In this paper these ideas are extended to accommodate rectangular containers with large, horizontal dimensions. The appropriate boundary conditions for the amplitude equations are derived, and a limited discussion of the properties of the solutions is undertaken. In particular it is shown that, in agreement with earlier theories and experiments, there is a preference for rolls parallel to the shorter side.