Abstract
When a long horizontal cylinder filled with fluid is differentially heated at the end walls at high Rayleigh number, A, the axial flow in the midsection consists of boundary layers at the top and bottom of the cylinder flowing in reverse directions, and the temperature is stably and linearly distributed in the vertical. Both the temperature is stably and linearly distributed in the vertical. Both the temperature and the flows are almost independent of the axial dimension. The adiabatic boundary condition on the cylinder requires temperature corrections which can induce cross-section boundary layers on the cylindrical wall and vertical internal boundary layers in the middle. Both types of boundary layers are O(A−¼) in width. Matching different boundary layers at the poles is achieved through additional A−⅙ and A−⅛ layers. The maximum boundary-layer velocity is calculated to be almost one-quarter of the axial velocity observed in experiments for A = 108.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
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