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Research Papers: Fundamental Issues and Canonical Flows

Stability of Dean Flow Between Two Porous Concentric Cylinders With Radial Flow and a Constant Heat Flux at the Inner Cylinder

[+] Author and Article Information
R. K. Deka

Department of Mathematics,
Gauhati University,
Guwahati 781014, India
e-mail: rkdgu@yahoo.com

A. Paul

Department of Basic Sciences,
Assam Don Bosco University,
Guwahati 781017, India
e-mail: ashpaul85@gmail.com

1Corresponding author.

Manuscript received May 8, 2012; final manuscript received February 7, 2013; published online March 21, 2013. Assoc. Editor: Ye Zhou.

J. Fluids Eng 135(4), 041203 (Mar 21, 2013) (8 pages) Paper No: FE-12-1231; doi: 10.1115/1.4023661 History: Received May 08, 2012; Revised February 07, 2013

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.

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Figures

Grahic Jump Location
Fig. 1

Horizontal stationary concentric cylinder system driven by a constant azimuthal pressure gradient (∂p/∂θ)0  <  0. A constant heat flux (CHF) (dT¯=-q/K) is applied at the inner cylinder and the outer cylinder is kept at a constant temperature T¯=T2 with a radial flow U = U0 through the permeable walls of the cylinders. Point B denotes the delivery side, while point A denotes the suction side of the pump.

Grahic Jump Location
Fig. 2

Variation of the critical Dean number Rec(d/R2)1/2 with N for β = −1, 1 with η = 0.95 and 0.8

Grahic Jump Location
Fig. 3

Variation of the critical Dean number Rec(d/R2)1/2 with N for β = −1, 1 with η = 0.7 and 0.5

Grahic Jump Location
Fig. 4

Variation of the critical Dean number Rec(d/R2)1/2 with η for N = 0, 1 and β = 1 and −10

Grahic Jump Location
Fig. 5

Variation of the critical Dean number Rec(d/R2)1/2 with β for N = 0, 1 with η = 0.95 and 0.8

Grahic Jump Location
Fig. 6

Variation of the critical Dean number Rec(d/R2)1/2 with β for N = 0, 1 with η = 0.7 and 0.5

Grahic Jump Location
Fig. 7

Variation of the critical wave number ac with β for N = 0, 1 with η = 0.95 and 0.8

Grahic Jump Location
Fig. 8

Variation of the critical wave number ac with β for N = 0, 1 with η = 0.7 and 0.5

Grahic Jump Location
Fig. 9

Variation of the critical radial Reynolds number (βc) at which instability first sets in

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