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A numerical study of double-diffusive flow in a long rotating porous channel

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Abstract

The problem of double-diffusive flow in a long rotating porous channel has been analysed numerically. The two opposite vertical walls of the channel are maintained at constant but different temperature and concentration, while both horizontal walls are kept insulated. The generalised model is used to mathematically simulate the momentum equations with employing the Boussinesq approximation for the density variation. Moreover, both the fluid and solid phases are assumed to be at a local thermal equilibrium. The Coriolis effect is considered to be the main effect of rotation, which is induced by means of the combined natural heat and mass transfer within the transverse plane. The governing equations are discretised according to the finite volume method with employing the hybrid differencing scheme to calculate the fluxes across the faces of each control volume. The problem of pressure–velocity coupling is sorted out by relying on PISO algorithm. Computations are performed for a wide range of dimensionless parameters such as Darcy–Rayleigh number (100 ≤ Ra* ≤ 10,000), Darcy number (10−6 ≤ Da ≤ 10−4), the buoyancy ratio (−10 ≤ N ≤ 8), and Ekman number (10−7 ≤ Ek ≤ 10−3), while the values of Prandtl and Schmidt numbers are maintained constant and equal to 1.0. The results reveal that the rotation seems to have a dominant role at high levels of porous medium permeability, where it reduces the strength of the secondary flow, and hence the rates of heat and mass transfer. However, this dominance decreases gradually with lessening the permeability for the same level of rotation, but does not completely vanish.

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Abbreviations

a :

Side length of the channel (m)

c :

Dimensional concentration (kg/m3)

c F :

Dimensionless form-drag constant

c p :

Specific heat of fluid phase (J/kg °K)

C :

Dimensionless concentration [C = (c − c c )/(c h  − c c )]

C 1, C 2, C 3 :

Coefficients of Eq. (17)

D :

The mass diffusivity of the solute into the solvent (m2/s)

D m :

The effective mass diffusivity (m2/s)

Da :

Darcy number (Da = K/a 2)

e :

Unit vector

Ek :

Ekman number (Ek = ν f /2ω a 2)

g :

Gravitational acceleration (m2 s−1)

K :

Permeability of the porous medium (m2)

k f :

Thermal conductivity of fluid phase (W m−1 °K−1)

k m :

Mean thermal conductivity (W m−1 °K−1)

k s :

Thermal conductivity of solid phase (W m−1 °K−1)

Le :

Lewis number (Le = Sc/Pr = α e /D m )

N :

Buoyancy ratio (N = β c Δc/β T ΔT)

Nu :

Average Nusselt number

p :

Dimensional pressure (Pa)

p r :

Dimensional reduced pressure (Pa)

P r :

Dimensionless reduced pressure

Pr :

Prandtl number (Pr = ν f /α e )

Ra :

Rayleigh number [Ra = g β T ΔT a 3/(ν α)]

Ra* :

Darcy–Rayleigh number [Ra* = Ra Da = g β T ΔT K a/(ν α)]

Sc :

Schmidt number (Sc = ν f /D m )

Sh :

Average Sherwood number

T :

Dimensional temperature (°K)

u, v, w :

Dimensional velocity components (m/s)

U, V, W :

Dimensionless velocity components

v:

Dimensional velocity vector (m/s)

x:

Dimensional position vector (m)

x, y, z :

Dimensional coordinates (m)

X, Y, Z :

Dimensionless coordinates

θ :

The dimensionless temperature

α e :

The effective thermal diffusivity (m2/s)

ρ f :

Fluid density (kg/m3)

μ f :

Dynamic viscosity (N s/m2)

ν f :

Kinematic viscosity (m2/s)

ε :

Porosity of the porous medium

β c :

Coefficient of concentration expansion (°K−1)

β T :

Coefficient of Thermal expansion (°K−1)

0:

Reference point

c :

Cold

e :

Effective

f :

Fluid phase

g :

Gravity

h :

Hot

m :

Mean

s :

Solid phase

ω :

Rotation

References

  1. Mojtabi A, Charrier-Mojtabi MC (2005) Double-diffusive convection in porous media. In: Vafai K (ed) Handbook of porous media, 2nd edn. Marcel Dekker, New York, pp 269–320

    Google Scholar 

  2. Nield DA, Bejan A (2013) Convection in porous media, 4th edn. Springer, New York

    Book  MATH  Google Scholar 

  3. Trevisan OV, Bejan A (1985) Natural convection with combined heat and mass transfer buoyancy effects in a porous medium. Int J Heat Mass Transf 28(8):1597–1611

    Article  Google Scholar 

  4. Goyeau B, Songbe JP, Gobin D (1996) Numerical study of double-diffusive natural convection in a porous cavity using the Darcy–Brinkman formulation. Int J Heat Mass Transf 39(7):1363–1378

    Article  MATH  Google Scholar 

  5. Nithiarasu P, Seetharamu KN, Sundararajan T (1996) Double-diffusive natural convection in an enclosure filled with fluid-saturated porous medium: a generalized non-Darcy approach. Numer Heat Transf Part A Appl 30(4):413–426

    Article  Google Scholar 

  6. Karimi-Fard M, Charrier-Mojtabi MC, Vafai K (1997) Non-darcian effects on double-diffusive convection within a porous medium. Numer Heat Transf Part A Appl 31(8):837–852

    Article  Google Scholar 

  7. Al-Farhany K, Turan A (2012) Numerical study of double diffusive natural convective heat and mass transfer in an inclined rectangular cavity filled with porous medium. Int Commun Heat Mass Transfer 39:174–181

    Article  Google Scholar 

  8. Vadasz P (1997) Flow in rotating porous media. In: du Plessis JP (ed) Fluid transport in porous media from the series advances in fluid mechanics 13. Computational Mechanics Publications, Southampton, pp 161–214

    Google Scholar 

  9. Vadasz P (1993) Fluid flow through heterogeneous porous media in a rotating square channel. Transp Porous Media 12:43–54

    Article  Google Scholar 

  10. Havstad MA, Vadasz P (1999) Numerical solution of the three-dimensional fluid flow in a rotating heterogeneous porous channel. Int J Numer Meth Fluids 31:411–429

    Article  MATH  Google Scholar 

  11. Vadasz P (1993) Three-dimensional free convection in a long rotating porous box. J Heat Transfer 115:639–644

    Article  Google Scholar 

  12. Vadasz P (1995) Coriolis effect on free convection in a long rotating porous box subject to uniform heat generation. Int J Heat Mass Transf 38(11):2011–2018

    Article  MATH  Google Scholar 

  13. Vadasz P (1994) Centrifugally generated free convection in a rotating porous box. Int J Heat Mass Transf 37(16):2399–2404

    Article  MATH  Google Scholar 

  14. Vadasz P (1996) Stability of free convection in a rotating porous layer distant from the axis of rotation. Transp Porous Media 23:153–173

    Article  Google Scholar 

  15. Vadasz P (1996) Convection and stability in a rotating porous layer with alternating direction of the centrifugal body force. Int J Heat Mass Transf 39(8):1639–1647

    Article  MATH  Google Scholar 

  16. Vadasz P, Govender S (1998) Two-dimensional convection induced by gravity and centrifugal forces in a rotating porous layer far away from the axis of rotation. Int J Rotating Mach 4(2):73–90

    Article  Google Scholar 

  17. Vadasz P (1998) Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J Fluid Mech 376:351–375

    Article  MATH  MathSciNet  Google Scholar 

  18. Straughan B (2001) A sharp nonlinear stability threshold in rotating porous convection. Proc R Soc Lond A 457:87–93

    Article  MATH  MathSciNet  Google Scholar 

  19. Malashetty MS, Swamy M, Kulkarni S (2007) Thermal convection in a rotating porous layer using a thermal non-equilibrium model. Phys Fluids 19(5):054102-1–054102-16

    Article  Google Scholar 

  20. Bhadauria BS, Hashim I, Kumar J, Srivastava A (2013) Cross diffusion convection in a newtonian fluid-saturated rotating porous medium. Transp Porous Med 98:683–697

    Article  MathSciNet  Google Scholar 

  21. Beckermann C, Viskanta R, Ramadhyani S (1986) A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium. Numer Heat Transf 10(6):557–570

    Article  Google Scholar 

  22. Vadasz P, Govender S (2001) Stability and stationary convection induced by gravity and centrifugal forces in a rotating porous layer distant from the axis of rotation. Int J Eng Sci 39:715–732

    Article  MATH  Google Scholar 

  23. Spalding DB (1972) A novel finite-difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng 4:551–559

    Article  Google Scholar 

  24. Issa RI (1986) Solution of the implicitly discretised fluid flow equations by operator-splitting. J Comput Phys 62:40–65

    Article  MATH  MathSciNet  Google Scholar 

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Alhusseny, A., Turan, A. A numerical study of double-diffusive flow in a long rotating porous channel. Heat Mass Transfer 51, 497–505 (2015). https://doi.org/10.1007/s00231-014-1426-x

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