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
References
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)
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)
Christopher R.H., Middleman S.: Power law fluid flow through a packed tube. Ind. Eng. Chem. Fundam. 4, 422–426 (1965)
Dharmadhikari R.V., Kale D.D.: The flow of non-Newtonian fluids through porous media. Chem. Eng. Sci. 40, 527–529 (1985)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Nield D.A., Bejan A.: Convection in Porous Media. 3rd edn. Springer-Verlag, New York (2006)
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)
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)
Shenoy A.V.: Non-Newtonian fluid heat transfer in porous media. Adv. Heat Transf. 24, 101–190 (1994)
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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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DOI: https://doi.org/10.1007/s11242-008-9252-6