Transport in Porous Media

, 79:255

Modulated Centrifugal Convection in a Vertical Rotating Porous Layer Distant from the Axis of Rotation

Article

Abstract

The effect of rotation speed modulation on the onset of centrifugally driven convection has been studied using linear stability analysis. Darcy flow model with zero-gravity is used to describe the flow. The perturbation method is applied to find the correction in the critical Rayleigh number. It is found that by applying modulation of proper frequency to the rotation speed, it is possible to delay or advance the onset of centrifugal convection.

Keywords

Centrifugal convection Rotation speed modulation Rayleigh number Coriolis force Rotating porous layer 

Nomenclature

Latin symbols

a

Wave number

az

Vertical component of wave number

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

Unit vector in the x-direction

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

Unit vector in the y-direction

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

Unit vector in the z-direction

Da

Darcy number, equals \({k_\ast /L_\ast ^2 }\)

L*

The length of the porous layer

H*

The height of the porous layer

H

The front aspect ratio of the porous layer, equals H*/L*

k*

The permeability of the porous medium

p

Dimensionless reduced pressure generalized to include the constant component of the centrifugal term

Pr

Prandtl number, equals υ*/α*

Raω

Porous media centrifugal Rayleigh number related to the contribution of the horizontal location within the porous layer to the centrifugal acceleration equals, \({\beta_\ast \Delta T\omega_\ast ^2 L_\ast ^2 k_\ast /\upsilon_\ast \alpha_\ast}\)

Raω0

Porous media centrifugal Rayleigh number related to the contribution of the offset distance from the rotation center to the centrifugal acceleration equals, \({\beta_\ast \Delta T\omega_\ast ^2 L_\ast x_{0\ast } k_\ast /\upsilon_\ast \alpha_\ast }\)

T*

Dimensional temperature

T

Dimensionless temperature, equals (T* − TR)/ΔT

Ta

Taylor number, defined as (2ω*k*/δυ*)2

u

Horizontal x-component of the filtration velocity

v

Horizontal y-component of the filtration velocity

w

Vertical z-component of the filtration velocity.

V

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

Va

Vadasz number, defined as δ Pr /Da

W

The top aspect ratio of the porous layer, equals W*/L*

W*

The width of the porous layer

x0

The dimensionless offset distance from rotation center, equals x0*/L*

x

Horizontal lengths coordinate

y

Horizontal widths coordinate

z

Vertical coordinate

Greek symbols

α*

Effective thermal diffusivity

β*

Thermal expansion coefficient

ΔT

Characteristic temperature difference

δ

Porosity

ω

Modulation frequency

ζ

Vorticity vector

ζx

x-component of the vorticity vector

υ*

Fluid kinematic viscosity

Ω

Rotation speed of the porous layer

Subscripts

*

Dimensional values

c

Critical values

z

Related to the quantities in the vertical direction

b

Related to basic state

References

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of SciencesJai Narain Vyas UniversityJodhpurIndia
  2. 2.Department of Mathematics, Faculty of ScienceBanaras Hindu UniversityVaranasiIndia

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