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Non-parallel plane Rayleigh-Bénard convection in cylindrical geometry. (English) Zbl 0827.76084

Summary: This paper considers the effect of a perturbed wall in regard to the classical Bénard convection problem in which the lower rigid surface is of the form \(z= \varepsilon^2 g(s)\), \(s= \varepsilon r\), in axisymmetric cylindrical polar coordinates \((r, \phi, z)\). The boundary conditions at \(s= 0\) for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem representing the distribution of convection cells near the center.

MSC:

76R05 Forced convection
76E15 Absolute and convective instability and stability in hydrodynamic stability
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