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Transport in Porous Media

, Volume 98, Issue 2, pp 443–450 | Cite as

Coriolis Effect on Convection in a Rotating Porous Layer Subjected to Variable Gravity

  • S. GovenderEmail author
Article

Abstract

We consider the effects of rotation in a porous layer heated from below and subjected to a variable gravity field. The study is presented for large Vadasz numbers where no oscillatory convection is possible. It is demonstrated that the Coriolis acceleration stabilizes the convection in a variable gravity field, whilst the effect of gravity parameter stabilses the convection when reduced and destabilizes the convection when increased.

Keywords

Rotation Porous layer Rayleigh number Variable gravity  Coriolis acceleration 

List of Symbols

Variables

\(H\)

The front aspect ratio of the porous layer, equals \({H_*}/{L_*}\).

\(W\)

The top aspect ratio of the porous layer, equals \({W_*}/{L_*}\).

\(\hat{{e}}_x \)

Unit vector in the \(x\)-direction.

\(\hat{{e}}_y \)

Unit vector in the \(y\)-direction.

\(\hat{{e}}_z \)

Unit vector in the \(z\)-direction.

\(H_*\)

The height of the porous layer.

\(k_*\)

Permeability of the porous matrix.

\(L_*\)

The length of the porous layer.

\(p\)

Dimensionless reduced pressure generalised to include the constant component of the centrifugal term.

\({\varvec{V}}\)

Dimensionless filtration velocity vector, equals \(u\hat{{e}}_x +v\hat{{e}}_y +w\hat{{e}}_z \).

\(Ra_{\mathrm{{g}}}\)

Porous media gravitational Rayleigh number equals, \({\beta _*\Delta T_{\mathrm{{C}}} g_*k_*}/{\nu _*\alpha _*}\).

\(R\)

Scaled centrifugal Rayleigh number, equals \({Ra_{\mathrm{{g}}} }/{\pi ^{2}}\).

\(T\)

Dimensionless temperature, equals \({({T_*-T_{\mathrm{{C}}} })}/{( {T_{\mathrm{{H}}} -T_{\mathrm{{C}}} })}\).

\(Ta\)

Taylor number, defined as \(({{2\varOmega _*k_*}/{\phi \nu _*}})^{2}\).

\(T_{\mathrm{{C}}}\)

Coldest wall temperature.

\(T_{\mathrm{{H}}}\)

Hottest wall temperature.

\(u\)

Horizontal \(x\) component of the filtration velocity.

\(v\)

Horizontal \(y\) component of the filtration velocity.

\(Va\)

Vadasz number, equals \({\phi Pr }/{Da}\).

\(w\)

Vertical \(z\) component of the filtration velocity.

\(W_*\)

The width of the layer.

\(x\)

Horizontal length coordinate.

\(y\)

Horizontal width coordinate.

\(z\)

Vertical coordinate.

Greek Symbols

\(\alpha \)

A parameter related to the wave number, equals \({\kappa ^{2}}/{\pi ^{2}}\).

\(\alpha _*\)

Effective thermal diffusivity.

\(\beta _*\)

Thermal expansion coefficient.

\(\eta \)

Variable gravity constant

\(\kappa \)

Wave number

\(\mu _*\)

Fluid dynamic viscosity.

\(\nu _*\)

Fluid kinematic viscosity.

\(\varOmega _*\)

Angular velocity of the rotating matrix.

\(\varDelta T_{\mathrm{{C}}}\)

Characteristic temperature difference.

\(\phi _*\)

Porosity

Subscripts

*

Dimensional values.

C

Related to coldest wall.

H

Related to hottest wall.

Notes

Acknowledgments

The author would like to dedicate this article to his wife Anusha Moodley and his daughters Sumithra Govender and Vinayia-Chrisinthi Govender.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Gas, Solar CSP and Wind Technology, Group TechnologyESKOM Holdings LtdJohannesburgSouth Africa
  2. 2.School of Mechanical EngineeringUniversity of KwaZulu-NatalDurbanSouth Africa

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