Advertisement

Heat and Mass Transfer

, 47:1525 | Cite as

MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

  • D. Nikodijevic
  • D. Milenkovic
  • Z. StamenkovicEmail author
Original

Abstract

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.

Keywords

Viscous Dissipation Joule Heating Hartmann Number Micropolar Fluid Immiscible Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

B

Magnetic field vector

B0

Applied magnetic field strength

Bx

Strength of induced magnetic field

b

Dimensionless ratio of magnetic fields

C

Constant

cp

Specific heat capacity

Di

Coefficients

E

Electric field vector

F

Constant

Ha

Hartmann number

hi

Height of the region i

J

Current density

K

Loading parameter

k

Fluid thermal conductivity

p

Pressure

Q

Constant

Rm

Magnetic Reynolds number

S

Constant

T

Temperature

t

Time

U0

Upper plate velocity

u

Velocity in x-direction

v

Velocity vector

x

Longitudinal coordinate

y

Transversal coordinate

Greek symbols

α

Fluid viscosities ratio

β

Ratio of heights of two regions

Φ

Dissipative function

λ

Cosine of inclination angle

μ

Dynamic viscosity

μe

Magnetic permeability

ν

Kinematic viscosity

θ

Applied magnetic field inclination angle

Θ

Dimensionless temperature

ρ

Fluid density

σ

Electrical conductivity

ξ

Ratio of thermal conductivities

Subscripts

1

Fluid in region I

2

Fluid in region II

w

Plate

*

Dimensionless quantities

References

  1. 1.
    Blum EL, Zaks MV, Ivanov UI, Mikhailov YA (1967) Heat exchange and mass exchange in magnetic field. Zinatne, Riga 223Google Scholar
  2. 2.
    Barletta A, Celli M, Magyari E, Zanchini E (2008) Buoyant MHD flows in a vertical channel: the levitation regime. Heat Mass Transf 44:1005–1013CrossRefGoogle Scholar
  3. 3.
    Xu H, Liao SJ, Pop I (2007) Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Eur J Mech B Fluids 26:15–27MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Mukhopadhyay S, Layek GC, Samad SkA (2008) Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int J Heat Mass Transf 48:4460–4466CrossRefGoogle Scholar
  5. 5.
    Abel MS, Mahesha N, Tawade J (2009) Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field. Appl Math Modell doi: 10.1016/j.apm.2008.11.021
  6. 6.
    Kandasamy MR, Khamis AB (2008) Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction. Appl Math Mech Engl Ed 29(10):1309–1317zbMATHCrossRefGoogle Scholar
  7. 7.
    Ishak A, Nazar R, Pop I (2006) Flow of a micropolar fluid on a continuous moving surface. Arch Mech 58(6):529–541MathSciNetzbMATHGoogle Scholar
  8. 8.
    Ishak A, Nazar R, Pop I (2008) MHD boundary-layer flow of a micropolar fluid past a wedge with variable wall temperature. Acta Mech 196:75–86zbMATHCrossRefGoogle Scholar
  9. 9.
    Lohrasbi J, Sahai V (1998) Magnetohydrodynamic heat transfer in two phase flow between parallel plates. Appl Sci Res 45:53–66CrossRefGoogle Scholar
  10. 10.
    Kumar JP, Umavathi JC, Chamkha AJ, Pop I (2010) Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel. Appl Math Model 34:1175–1186MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Muthuraj R, Srinivas S (2010) Fully developed MHD flow of a micropolar and viscous fluids in a vertical porous space using HAM. Int J Appl Math Mech 6(11):55–78MathSciNetGoogle Scholar
  12. 12.
    Alireza S, Sahai V (1990) Heat transfer in developing magnetohydrodynamic Poiseuille flow and variable transport properties. Int J Heat Mass Transf 33(8):1711–1720zbMATHCrossRefGoogle Scholar
  13. 13.
    Malashetty MS, Umavathi JC, Kumar JP (2001) Convective magnetohydrodynamic two fluid flow and heat transfer in an inclined channel. Heat Mass Transf 37:259–264CrossRefGoogle Scholar
  14. 14.
    Malashetty MS, Umavathi JC, Kumar JP (2004) Two fluid flow and heat transfer in an inclined channel containing porous and fluid layer. Heat Mass Transf 40:871–876CrossRefGoogle Scholar
  15. 15.
    Umavathi JC, Mateen A, Chamkha AJ, Mudhaf AA (2006) Oscillatory Hartmann two-fluid flow and heat transfer in a horizontal channel. Int J Appl Mech Eng 11(1):155–178zbMATHGoogle Scholar
  16. 16.
    Umavathi JC, Chamkha AJ, Mateen A, Al-Mudhaf A (2005) Unsteady two-fluid flow and heat transfer in a horizontal channel. Heat Mass Transf 42:81–90CrossRefGoogle Scholar
  17. 17.
    Malashetty MS, Umavathi JC, Kumar JP (2006) Magnetoconvection of two immiscible fluids in vertical enclosure. Heat Mass Transf 42:977–993CrossRefGoogle Scholar
  18. 18.
    Misuri T, Andrenucci M (2007) Tikhonov’s MHD channel theory: a review. 30th international electric propulsion conference, Florence, ItalyGoogle Scholar
  19. 19.
    Sele T (1977) Instabilities of the metal surface in electrolytic cells. Light Metals, 7–24Google Scholar
  20. 20.
    Gerbeau JF, Le Bris C, Lelièver T (2006) Mathematical methods for the Magnetohydrodynamics of Liquid Metals. Oxford University PressGoogle Scholar
  21. 21.
    Chinyoka T, Renardy YY, Renardy M, Khismatullin DB (2005) Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids. J Nonnewtonian Fluid Mech 130:45–56zbMATHCrossRefGoogle Scholar
  22. 22.
    Huppert HE, Hallworth MA (2007) Bi-directional flows in constrained systems. J Fluid Mech 578:95–112MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Ghosh SK (2002) Effects of Hall current on MHD Couette flow in a rotating system with arbitrary magnetic field. Czechoslovak J Phys 52:51–63CrossRefGoogle Scholar
  24. 24.
    Seth GS, Nandkeolyar R (2009) MHD couette flow in a rotating system in the presence of an inclined magnetic field. Appl Math Sci 3(59):2919–2932MathSciNetzbMATHGoogle Scholar
  25. 25.
    Smolentsev S, Cuevas S, Beltrán A (2010) Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows. J Comput Phys 229:1558–1572MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Moreau R (1990) Magnetohydrodynamics. Kluwer Academic Publishers, Dordrecht/Boston/LondonzbMATHGoogle Scholar
  27. 27.
    Ishii M, Hibiki T (2006) Thermo-fluid dynamics of two-phase flow. Springer, New YorkGoogle Scholar
  28. 28.
    Li F, Ozen O, Aubry N, Papageorgiou DT, Petropoulos PG (2007) Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel. J Fluid Mech 583:347–377MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Malashetty MS, Umavathi JC (1997) Two-phase magnetohydrodynamic flow and heat transfer in an inclined channel. Int J Multiphase Flow 23(3):545–560zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Fluid Mechanics, Faculty of Mechanical EngineeringUniversity of NisNisSerbia

Personalised recommendations