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

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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.

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Abbreviations

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

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

c:

Cold surface

f:

Fluid phase

h:

Hot surface

s:

Solid phase

ref:

Reference value

′:

Derivative with respect to x

\({\hat{}}\) :

Dimensional

References

  • Banu N., Rees D.A.S.: The onset of Darcy–Bénard convection using a thermal nonequilibrium model. Int. J. Heat Mass Trans. 45, 2221–2228 (2002)

    Article  Google Scholar 

  • Gill A.E.: A proof that convection in a porous vertical slab is stable. J. Fluid Mech. 35, 545–547 (1969)

    Article  Google Scholar 

  • Kwok L.P., Chen C.F.: Stability of thermal convection in a vertical porous layer. ASME J. Heat Trans. 109, 889–893 (1987)

    Article  Google Scholar 

  • Lewis S., Bassom A.P., Rees D.A.S.: The stability of vertical thermal boundary layer flow in a porous medium. Eur. J. Mech. B 14, 395–408 (1995)

    Google Scholar 

  • Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)

    Google Scholar 

  • Qin Y., Kaloni P.N.: A nonlinear stability problem of convection in a porous vertical slab. Phys. Fluids A 5, 2067–2069 (2006)

    Article  Google Scholar 

  • Rees D.A.S.: The stability of Prandtl–Darcy convection in a vertical porous slot. Int. J. Heat Mass Trans. 31, 1529–1534 (1988)

    Article  Google Scholar 

  • Rees D.A.S., Bassom A.P.: Onset of Darcy–Bénard convection in an inclined porous layer heated from below. Acta Mech. 144, 103–118 (2000)

    Article  Google Scholar 

  • Straughan B.: A nonlinear analysis of convection in a porous vertical slab. Geophys. Astrophys. Fluid Dyn. 42, 269–275 (1988)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK

    D. Andrew S. Rees

Authors
  1. D. Andrew S. Rees
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Correspondence to D. Andrew S. Rees.

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Rees, D.A.S. The Effect of Local Thermal Nonequilibrium on the Stability of Convection in a Vertical Porous Channel. Transp Porous Med 87, 459–464 (2011). https://doi.org/10.1007/s11242-010-9694-5

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  • DOI: https://doi.org/10.1007/s11242-010-9694-5

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