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Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder
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10.1063/1.4799253
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Affiliations:
1 Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
2 Department of Mathematics, University of Agder, Postboks 422, 4604 Kristiansand, Norway
Phys. Fluids 25, 044101 (2013)
/content/aip/journal/pof2/25/4/10.1063/1.4799253
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4799253

## Figures

FIG. 1.

A sketch of the fluid saturated porous cylinder.

FIG. 2.

Neutral stability: plots of versus for the most unstable modes, each frame is for a different value of . The horizontal dotted line is for = ; the vertical dotted lines bound the regions where each specified (, )-mode is preferred.

FIG. 3.

Neutral stability: plots of versus for the most unstable modes, each frame is for a different value of . The horizontal dotted line is for ; the vertical dotted lines bound the regions where each specified (, )-mode is preferred.

FIG. 4.

Selected modes, (, ), at onset of convection in the plane (, ); the solid lines bound the regions where each specified mode is preferred.

FIG. 5.

Qualitative plots of the time-independent normal modes Θ(, θ, ), given by Eq. , as functions of (, θ) at a fixed plane = constant, with 0 < < 1, for the pairs (, ) ordered according to Table .

## Tables

Table I.

Roots of Eq. , ζ ≡ λ , in increasing order.

/content/aip/journal/pof2/25/4/10.1063/1.4799253
2013-04-09
2014-04-17

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