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

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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.

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Abbreviations

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

Ra d :

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

μ*:

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

ρ ∞ :

Density at some reference point

α :

Thermal diffusivity

α d :

Dispersion diffusivity

α e :

Effective diffusivity

β T :

Coefficient of thermal expansion

β c :

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

θ w :

 = T w − T ∞

φ w :

 = C w − C ∞

w, ∞:

Conditions on the wall and the ambient medium

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, 721 302, India

    R. R. Kairi, P. A. L. Narayana & P. V. S. N. Murthy

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  1. R. R. Kairi
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  2. P. A. L. Narayana
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  3. P. V. S. N. Murthy
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Correspondence to P. V. S. N. Murthy.

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Kairi, R.R., Narayana, P.A.L. & Murthy, P.V.S.N. The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium. Transp Porous Med 76, 377–390 (2009). https://doi.org/10.1007/s11242-008-9252-6

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