1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Linear and nonlinear convection in porous media between coaxial cylinders
Rent:
Rent this article for
USD
10.1063/1.3637642
/content/aip/journal/pof2/23/9/10.1063/1.3637642
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/9/10.1063/1.3637642
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the annular cylindrical configuration.

Image of FIG. 2.
FIG. 2.

(Color online) Various simple mode patterns. The shading describes the vertical velocity at z = 0.5; lighter shades indicate larger, positive velocities, while darker shades indicate larger, negative velocities. The arrows are the radial and azimuthal velocities at z = 1 seen from above. (a) The mode (1,0) produced using Rw  = 0.01 and R = 0.6. (b) The mode (0,1) produced using Rw  = 0.1 and R = 1.2. (c) The mode (1,1) produced using Rw  = 0.2 and R = 1.6. (d) The mode (2,1) produced using Rw  = 0.5 and R = 2.

Image of FIG. 3.
FIG. 3.

(Color online) Contour plot of the critical Rayleigh number, Ra c , as a function of Rw and R when the sidewalls are insulated.

Image of FIG. 4.
FIG. 4.

(Color online) Contour plot of the critical Rayleigh number, Ra c , for conducting sidewalls.

Image of FIG. 5.
FIG. 5.

(Color online) Depiction of the mode maps for insulated sidewalls. (a) The values of m and (b) the values of p.

Image of FIG. 6.
FIG. 6.

Comparison between the mode map of Bau and Torrance, and that of the present analysis for insulating sidewalls. (a) The mode map made by Bau and Torrance and is a copy of Figure 3 in Ref. 14. (b) Our version of the Bau and Torrance mode map. Reprinted with permission from H. H. Bau and K. E. Torrance, Phys. Fluids 24(3), 382 (1981). Copyright 1981, American Institute of Physics.

Image of FIG. 7.
FIG. 7.

(Color online) Depiction of the mode maps for conducting sidewalls. (a) The values of m and (b) the values of p.

Image of FIG. 8.
FIG. 8.

Variation of Ra c with R for (i) circular cylinder with an insulated sidewall (Ref. 11, lowest curve), (ii) circular cylinder with a perfectly conducting sidewall (Ref. 13, middle curve), (iii) annular cylinder with perfectly conducting sidewalls and with Rw  = 10− 4. (The figure is adapted from Figure 1 in Ref. 13.)

Image of FIG. 9.
FIG. 9.

The variation of the amplitude of convection with Rayleigh number for modes (1,0) and (2,0) for Rw  = 0.1 and R = 0.7 and with insulated sidewalls. The dashed/dotted line is the amplitude of the basic mode (1,0). The continuous line is the amplitude of the stable part of the secondary mode (2,0) branch, while the dashed line is the unstable part.

Image of FIG. 10.
FIG. 10.

(Color online) A stable mixed mode convection pattern corresponding to modes (5,0) and (2,1). The sidewalls are insulated while Rw  = 0.7, R = 2.1, and Ra = 40. The pattern displays m = 2 characteristics near the inner radius and m = 5 characteristics near the outer radius. The perceived value of p is either 0 or 1 depending on the chosen azimuthal position.

Image of FIG. 11.
FIG. 11.

The variation of the amplitude of convection with Ra for the case, Rw  = 0.7 and R = 2.1, with insulated sidewalls. The continuous line corresponds to the stable part of basic mode (5,0) branch, which has the critical Rayleigh number 39.51, while the dashed line is the unstable region of this mode. The dashed/dotted line is the stable mixed mode branch.

Loading

Article metrics loading...

/content/aip/journal/pof2/23/9/10.1063/1.3637642
2011-09-16
2014-04-19
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Linear and nonlinear convection in porous media between coaxial cylinders
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/9/10.1063/1.3637642
10.1063/1.3637642
SEARCH_EXPAND_ITEM