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Research Papers: Porous Media

Transverse Heterogeneity Effects in the Dissipation-Induced Instability of a Horizontal Porous Layer

[+] Author and Article Information
A. Barletta

 DIENCA, Alma Mater Studiorum-Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

M. Celli

 DIENCA, Alma Mater Studiorum-Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy;Department of Mechanical and Aerospace Engineering,  North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910

A. V. Kuznetsov1

Department of Mechanical and Aerospace Engineering,  North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910 e-mail: avkuznet@eos.ncsu.edu

1

Corresponding author.

J. Heat Transfer 133(12), 122601 (Oct 05, 2011) (8 pages) doi:10.1115/1.4004371 History: Received April 14, 2011; Accepted May 27, 2011; Published October 05, 2011; Online October 05, 2011

The linear stability of a parallel flow in a heterogeneous porous channel is analyzed by means of the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as, by the boundary conditions. A horizontal porous layer bounded by impermeable and infinitely wide walls is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against oblique rolls is studied. The eigenvalue problem is solved numerically.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Tb /Pe2 versus z for different values of ξp , with ξc  = −0.9,1

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Figure 4

Oblique-to-longitudinal stability ratio ROL versus P for different values of ξc , with ξp → −1

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Figure 5

Oblique-to-longitudinal stability ratio ROL versus P for different values of ξc , with ξp  = 1

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Figure 6

Oblique-to-longitudinal stability ratio ROL versus P for different values of ξc , with ξp  = 5

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Figure 7

Longitudinal rolls: plots of Λcr versus ξp (upper frame) and plots of acr versus ξp (lower frame), for different values of ξc

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Figure 1

Sketch of the porous layer and of the basic flow

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Figure 2

Tb /Pe2 versus z for different values of ξc , with ξp → −1 and ξp  = 1

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Figure 8

Longitudinal rolls: plots of Λcr versus ξc (upper frame) and plots of acr versus ξc (lower frame), for different values of ξp

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Figure 9

Longitudinal rolls: streamlines Ψ = constant (solid lines) and isotherms θ = constant (dashed lines) at critical conditions, a = acr and Λ =Λcr , for ξc  = −0.9 and ξp → −1 (a); ξc  = 5 and ξp → −1 (b); ξc  = −0.9 and ξp  = 10 (c); ξc  = 5 and ξp  = 10 (d)

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