The problem of instability of diabatic flow between rotating, concentric cylinders has been studied analytically. The basic equations were reduced to a form identical to that of a similar instability fluid flow problem, namely, the instability of a horizontal layer of fluid heated from below. The latter problem has been solved by Pellew and Southwell, and their solution was used to calculate and predict the instability of diabatic flow in the annulus. The results of the analysis show that heating of the inner rotating cylinder stabilizes the flow, while heating of the outer stationary cylinder destabilizes the flow.
The Influence of a Radial Temperature Gradient on the Instability of Fluid Flow in an Annulus With an Inner Rotating Cylinder
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Becker, K. M., and Kaye, J. (May 1, 1962). "The Influence of a Radial Temperature Gradient on the Instability of Fluid Flow in an Annulus With an Inner Rotating Cylinder." ASME. J. Heat Transfer. May 1962; 84(2): 106–110. https://doi.org/10.1115/1.3684306
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