On the flow, heat transfer, and stability of viscous fluids subject to body forces and heated from below in vertical channels
Closed-form solutions are presented for the fully-developed flow and heat transfer, neglecting frictional heating, of viscous fluids subject to a body force and heated from below in a vertical passage under various boundary conditions. The solutions are dependent on a dimensionless parameter, the Rayleigh Criterion, which had previously been shown to be the factor determining the stability and type of flow in horizontal layers of fluid heated from below. Similar stability characteristics are displayed in the present problem and the critical values of the Rayleigh Criterion are of the same order of magnitude as those for the horizontal layers. The whirling instability of a rotating shaft is shown to be a mechanical analogy to the flow problem under consideration herein. For large values of the Rayleigh Criterion it is demonstrated that the profiles become of the boundary layer type.
Comparisons are made with flows in an identical configuraton but where the heating is not from below and it is shown that in certain ranges of the parametric values the flow and heat transfer associated with heating from below is much greater and the heat transfer at the walls can be in opposite directions in the two problems.
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