Transport in Porous Media

, Volume 87, Issue 2, pp 459–464

The Effect of Local Thermal Nonequilibrium on the Stability of Convection in a Vertical Porous Channel

Article

Abstract

We consider the effect of local thermal nonequilibrium on the stability properties of convection in a vertical porous channel heated and cooled from the sides. On using an energy stability analysis of the linearised stability equations, we show that the system remains unconditionally stable to small-amplitude disturbances.

Keywords

Vertical porous layer Stability analysis Local thermal nonequilibrium 

List of Symbols

c

Specific heat

g

Gravity

h

Interfacial heat transfer coefficient

H

Nondimensional form of h

k

Disturbance wavenumber

L

Width of the layer

K

Permeability

p

Pressure

Ra

Darcy–Rayleigh number

t

Time

u

Horizontal velocity

v

Vertical velocity

x

Horizontal coordinate

y

Vertical coordinate

Greek Symbols

α

Diffusivity ratio

β

Thermal expansion coefficient

γ

Scaled conductivity ratio

θ

Fluid temperature

Θ

Disturbance fluid temperature

\({\overline{\Theta}}\)

Complex conjugate of Θ

λ

Exponential growth rate

μ

Dynamic viscosity

ρ

Density

\({\phi}\)

Solid temperature

Φ

Disturbance solid temperature

\({\overline{\Phi}}\)

Complex conjugate of Φ

ψ

Stream function

Ψ

Disturbance stream function

Subscripts and Superscripts

c

Cold surface

f

Fluid phase

h

Hot surface

s

Solid phase

ref

Reference value

Derivative with respect to x

\({\hat{}}\)

Dimensional

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References

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of BathBathUK

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