A linear analysis for the instability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure gradient is presented when a radial flow through the permeable walls of the cylinders is present. In addition, a constant heat flux at the inner cylinder is applied. The linearized stability equations form an eigenvalue problem, which is solved by using the classical Runge–Kutta–Fehlberg scheme combined with a shooting method, which is termed the unit disturbance method. It is found that for a given value of the constant heat flux parameter N, even for a radially weak outward flow, there is a strong stabilizing effect and the stabilization is greater as the gap between the cylinders increases. However, in the presence of a weak inward flow for a wider gap, the constant heat flux has no role on the onset.
Stability of Dean Flow Between Two Porous Concentric Cylinders With Radial Flow and a Constant Heat Flux at the Inner Cylinder
Manuscript received May 8, 2012; final manuscript received February 7, 2013; published online March 21, 2013. Assoc. Editor: Ye Zhou.
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Deka, R. K., and Paul, A. (March 21, 2013). "Stability of Dean Flow Between Two Porous Concentric Cylinders With Radial Flow and a Constant Heat Flux at the Inner Cylinder." ASME. J. Fluids Eng. April 2013; 135(4): 041203. https://doi.org/10.1115/1.4023661
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