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Thermal dispersion effects on forced convection in a parallel plate porous channel

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Abstract

Thermal dispersion effects on fully developed forced convection inside a porous-saturated parallel plates duct with uniform heat flux at the wall are investigated on the basis of the Brinkman model. Having known the velocity distribution, the energy equation is solved using asymptotic techniques for the limiting case when thermal conductivity, as a result of thermal dispersion, weakly changes with the Péclet number. A numerical solution, valid for the entire range of thermal dispersion conductivity, is also presented. This latter solution is performed to check the accuracy of the former one. It was seen that in the limiting regions the results of both methods are in close agreement with each other and also with those previously reported in the literature. Validity range for the presented closed form solution is also discussed as a function of the Péclet number.

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Abbreviations

C:

Dispersion coefficient

c P :

Specific heat at constant pressure

D1 :

Integration constant

Da:

Darcy number

G :

Applied pressure gradient

k :

Thermal conductivity

K :

Permeability

M :

μ eff/ μ

Nu:

Nusselt number

Pe:

Péclet number, Pe = RePr

Pr:

Prandtl number, \( \Pr = \frac{{\mu c_{p} }}{{k_{e} }} \)

Re:

Reynolds number, \( \text{Re} = \frac{\rho U\sqrt K }{\mu } \)

q″:

Wall heat flux

s :

\( \left( {M\,{\text{Da}}} \right)^{ - 1/2} \)

T* :

Temperature

T m :

Bulk mean temperature

T w :

Downstream wall temperature

u :

μu*/GH 2

u* :

Filtration velocity

\( \hat{u} \) :

u */U

U :

Mean velocity

(x * ,y *):

Cartesian coordinate

y :

y */H

θ :

(T * − T w )/(T m  − T w )

μ :

Fluid viscosity

μ eff :

Effective viscosity in the Brinkman term

ρ :

Fluid density

0, 1:

Term sequence in asymptotic expansion

d:

Dispersion

e:

Effective

f:

Fluid

s:

Solid

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Acknowledgments

Support from High Impact Research Grant UM.C/HIR/MOHE/ENG/23 and University of Malaya, Malaysia are acknowledged.

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Authors and Affiliations

  1. School of Mechanical and Mining Engineering, University of Queensland, Brisbane, QLD, 4072, Australia

    K. Hooman

  2. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

    M. Dahari

Authors
  1. K. Hooman
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  2. M. Dahari
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Correspondence to K. Hooman.

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Hooman, K., Dahari, M. Thermal dispersion effects on forced convection in a parallel plate porous channel. Meccanica 50, 1971–1976 (2015). https://doi.org/10.1007/s11012-015-0149-5

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  • DOI: https://doi.org/10.1007/s11012-015-0149-5

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