Convection in a rotating cylinder with its sidewall having a finite thermal conductance |
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| Authors: | Jae Min Hyun |
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| Institution: | 1. Department of Mechanical Engineering , Clarkson University , Potsdam , New York , 13676 , U.S.A.;2. Department of Mechanical Engineering , Korea Advanced Institute of Science &3. Technology , P.O. Box 150, Chong Ryang, Seoul , Korea |
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| Abstract: | Abstract An investigation is made of steady thermal convection of a Boussinesq fluid confined in a vertically-mounted rotating cylinder. The top and bottom endwall disks are thermal conductors at temperatures Tt and Tb with δT = Tt ? Tb >0. The vertical sidewall has a finite thermal conductance. A Newtonian heat flux condition is adopted at the sidewall. The Rayleigh number of the fluid system is large to render a boundary layer-type flow. Finite-difference numerical solutions to the full Navier-Stokes equations are obtained. The vertical motions within the buoyancy layer along the sidewall induce weak meridional flows in the interior. Because of the Coriolis acceleration, the meridional flows give rise to azimuthal flows relative to the rotating container. Strong vertical gradients of azimuthal flows exist in the regions near the endwalls. As the stratification effect increases, concentration of flow gradients in thin endwall boundary layers becomes more pronounced. The azimuthal flow field exhibits considerable horizontal gradients. The temperature field develops horizontal variations superposed on the dominant vertical distribution. As either the sidewall thermal conductance or the stratification effect decreases, the temperature distribution tends to the profile varying linearly with height. Comparisons of the sizes of the dynamic effects demonstrate that, in the bulk of flow field, the vertical shear of azimuthal velocity is supported by the horizontal temperature gradient, resulting in a thermal-wind relation. |
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| Keywords: | Hysteresis Baroclinic instability annulus experiments numerical model |
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