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Transport in Porous Media

, Volume 76, Issue 3, pp 377–390 | Cite as

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

  • R. R. Kairi
  • P. A. L. Narayana
  • P. V. S. N. MurthyEmail author
Article

Abstract

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.

Keywords

Natural convection Thermal dispersion Solutal dispersion Non-Newtonian fluids Non-Darcy porous medium 

Nomenclature

b

Coefficient in the Forchheimer term

d

Pore diameter

\({\varepsilon }\)

Porosity of the saturated porous medium

f

Dimensionless stream function

g

Acceleration due to gravity

c

Forchheimer coefficient

k*

Intrinsic permeability of the porous medium for flow of power law fluid

Gr*

Non-Darcian (inertia) parameter or Grashof number based on permeability for power law fluid

n

Power law index

N

Buoyancy ratio

Nu

Nusselt number

Sh

Sherwood number

Le

Lewis number

Rad

Pore diameter dependent Rayleigh number

T

Temperature

C

Concentration

x, y

Axial and normal co-ordinates

u, v

Velocity components in x and y directions

Greek Symbols

μ*

Fluid consistency of the inelastic non-Newtonian power-law fluid

ρ

Density at some reference point

α

Thermal diffusivity

αd

Dispersion diffusivity

αe

Effective diffusivity

βT

Coefficient of thermal expansion

βc

Coefficient of solutal expansion

ψ

Dimensionless stream function

η

Similarity variable

θ

Dimensionless temperature

φ

Dimensionless concentration

γ

Coefficient of thermal dispersion

ξ

Coefficient of solutal dispersion

θw

 = T w − T

φw

 = C w − C

Subscripts

w, ∞

Conditions on the wall and the ambient medium

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References

  1. Chen H.T., Chen C.K.: Natural convection of a non-Newtonian fluid about a horizontal cylinder and sphere in a porous medium. Int. Commun. Heat Mass. Transf. 15, 605–614 (1988a)CrossRefGoogle Scholar
  2. Chen H.T., Chen C.K.: Natural convection of non-Newtonian fluids along a vertical plate embedded in a porous medium. ASME J. Heat Transf. 110, 257–260 (1988b)CrossRefGoogle Scholar
  3. Christopher R.H., Middleman S.: Power law fluid flow through a packed tube. Ind. Eng. Chem. Fundam. 4, 422–426 (1965)CrossRefGoogle Scholar
  4. Dharmadhikari R.V., Kale D.D.: The flow of non-Newtonian fluids through porous media. Chem. Eng. Sci. 40, 527–529 (1985)CrossRefGoogle Scholar
  5. El-Amin M.F.: Double dispersion effects on natural convection heat and mass transfer in non-Darcy porous medium. Appl. Math. Comput. 156, 1–17 (2004)CrossRefGoogle Scholar
  6. El-Hakiem M.A.: Thermal dispersion effects on combined convection in non-Newtonian fluids along a non-isothermal vertical plate in a porous medium. Transp. Porous Media 45, 29–40 (2001)CrossRefGoogle Scholar
  7. Gorla R.S.R., Kumari M.: Mixed convection in non-Newtonian fluids along vertical plate in a porous medium. Acta Mechanica 118, 55–64 (1996)CrossRefGoogle Scholar
  8. Jumah R.Y., Mujumdar A.S.: Free convection heat and mass transfer of non-Newtonian power law fluids with yield stress from a vertical plate in a saturated porous media. Int. Commun. Heat Mass Transf. 27, 485–494 (2000)CrossRefGoogle Scholar
  9. Mehta K.N., Rao K.N.: Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal horizontal plate embedded in a porous medium. Int. J. Eng. Sci. 32, 521–525 (1994a)CrossRefGoogle Scholar
  10. Mehta K.N., Rao K.N.: Buoyancy-induced flow of non-Newtonian fluids in a porous medium past a vertical plate with non-uniform surface heat flux. Int. J. Eng. Sci. 32, 297–302 (1994b)CrossRefGoogle Scholar
  11. Mohammadien A.A., El-Amin M.F.: Thermal dispersion radiation effects on non-Darcy natural convection in a fluid saturated porous medium. Transp. Porous Media 40, 153–163 (2000)CrossRefGoogle Scholar
  12. Murthy P.V.S.N.: Effect of double dispersion on Mixed convection heat and mass transfer in non-Darcy porous medium. Trans. ASME J. Heat Transf. 122, 476–484 (2000)CrossRefGoogle Scholar
  13. Murthy P.V.S.N., Singh P.: Thermal dispersion effect on non-Darcy natural convection with lateral mass flux. Heat Mass Transf. 33, 1–5 (1997)CrossRefGoogle Scholar
  14. Nakayama A., Koyama H.: Buoyancy induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium. Appl. Sci. Res. 48, 55–70 (1991)CrossRefGoogle Scholar
  15. Nield D.A., Bejan A.: Convection in Porous Media. 3rd edn. Springer-Verlag, New York (2006)Google Scholar
  16. Rastogi S.K., Poulikakos D.: Double-diffusion from a vertical surface in a porous region saturated with a non-Newtonian fluid. Int. J. Heat Mass Transf. 38, 935–946 (1995)CrossRefGoogle Scholar
  17. Shenoy A.V.: Darcy-Forchheimer natural, forced and mixed convection heat transfer in non-Newtonian power-law fluid-saturated porous media. Transp. Porous Media 11, 219–241 (1993)CrossRefGoogle Scholar
  18. Shenoy A.V.: Non-Newtonian fluid heat transfer in porous media. Adv. Heat Transf. 24, 101–190 (1994)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • R. R. Kairi
    • 1
  • P. A. L. Narayana
    • 1
  • P. V. S. N. Murthy
    • 1
    Email author
  1. 1.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

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