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Time-dependent MHD Couette flow of rotating fluid with Hall and ion-slip currents

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Abstract

The unsteady magnehydrodynamics (MHD) Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions are obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction are discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip parameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.

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Abbreviations

Ha :

Hartmann number

r :

Laplace parameter

t′:

dimensional time

t :

dimensionless time

U :

constant

u′,v′,w′ :

components of velocity field V

u,v,w :

dimensionless velocity components

x′,y′,z′ :

Cartesian coordinates

z′ :

coordinate normal to plates

z :

dimensionless coordinate normal to plates

µ:

coefficient of viscosity

ν :

kinematic viscosity

β :

Hall factor

β e :

Hall parameter

β i :

ion-slip parameter

ρ :

density

σ :

electrical conductivity

τ :

skin friction

Ω′:

constant angular velocity along z′-axis

Ω:

rotation parameter

References

  1. Abo-Eldahab, E. M. and El-Aziz, M. A. Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents. Applied Mathematical Modelling, 29, 579–595 (2005)

    Article  MATH  Google Scholar 

  2. Singh, A. K. and Kumar, N. Unsteady hydromagnetic Couette flow. Wear, 89, 125–129 (1983)

    Article  Google Scholar 

  3. Singh, A. K., Sacheti, N. C., and Chandran, P. Transient effects on magnetohydrodynamics Couette flow with rotation: accelerated motion. International Journal of Engineering Science, 32, 133–139 (1994)

    Article  MATH  Google Scholar 

  4. Seth, G. S., Jana, R. N., and Maiti, M. K. Unsteady hydromagnetic Couette flow in a rotating system. International Journal of Engineering Science, 20, 989–999 (1982)

    Article  Google Scholar 

  5. Guria, M., Jana, R. N., and Ghosh, S. K. Unsteady Couette flow in a rotating system. International Journal of Non-Linear Mechanics, 41, 838–843 (2006)

    Article  Google Scholar 

  6. Guria, M., Jana, R. N., and Ghosh, S. K. Oscillatory Couette flow in the presence of an inclined magnetic field. Meccanica, 44, 555–564 (2009)

    Article  MathSciNet  Google Scholar 

  7. Seth, G. S., Nandkeolyar, R., Mahto, N., and Singh, S. K. MHD Couette flow in a rotating system in the presence of an inclined magnetic field. Applied Mathematical Sciences, 3, 2919–2932 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Das, S., Maji, S. L., Guria, M., and Jana, R. N. Unsteady MHD Couette flow in a rotating system. Mathematical and Computer Modelling, 50, 1211–1217 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sutton, G. and Sherman, A. Engineering Magnetohydrodynamics, McGraw-Hill, New York (1965)

    Google Scholar 

  10. Tillack, M. S. and Morley, N. B. Standard Handbook for Electrical Engineers: Magnetodynamics, McGraw-Hill, New York (1998)

    Google Scholar 

  11. Deka, R. K. Hall effects on MHD flow past an accelerated plate. Journal of Theoretical and Applied Mechanics, 35, 333–346 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mazumdar, B. S. Combined effect of Hall current and rotation on hydromagnetic flow over an oscillating porous plate. International Journal of Engineering Science, 15, 601–606 (1977)

    Article  Google Scholar 

  13. Ghosh, S. K. Effect of Hall current on MHD Couette flow in a rotating system with arbitrary magnetic field. Czechoslov Journal of Physics, 52, 51–63 (2002)

    Article  Google Scholar 

  14. Ghosh, S. K. and Pop, I. Hall effects on MHD Couette flow in a rotating environment. International Journal of Applied Mechanics and Engineering, 9, 293–304 (2004)

    MATH  Google Scholar 

  15. Debnath, L., Ray, S. C., and Chatterjee, A. K. Effect of Hall current and rotation on unsteady hydromagnetic flow past a porous plate in a rotating system. ZAMM, 59, 469–471 (1979)

    Article  MATH  Google Scholar 

  16. Mandal, G. and Mandal, K. K. Effect of Hall current on MHD Couette flow between thick arbitrarily conducting plate in a rotating system. Journal of the Physical Society of Japan, 52, 470–477 (1983)

    Article  Google Scholar 

  17. Tiwari, R. and Singh, K. Effect of Hall current on unsteady hydromagnetic boundary layers in rotating dusty fluid. Indian Journal of Pure and Applied Mathematics, 14, 159–165 (1983)

    MathSciNet  MATH  Google Scholar 

  18. Ghosh, S. K. and Pop, I. Hall effects on unsteady hydromagnetic flow in a rotating system with oscillatory pressure gradient. International Journal of Applied Mechanics and Engineering, 8, 43–56 (2003)

    MATH  Google Scholar 

  19. Attia, H. A. MHD Couette flow with temperature dependent viscosity and the ion-slip. Tamkang Journal of Science and Engineering, 8, 11–16 (2005)

    Google Scholar 

  20. Attia, H. A. Unsteady Couette flow with heat transfer considering ion-slip. Turkish Journal of Physics, 29, 379–388 (2005)

    Google Scholar 

  21. Ram, P. C. Effects of Hall and ion-slip currents on free convective heat generating flow in a rotating fluid. International Journal of Energy Research, 19, 371–376 (1995)

    Article  Google Scholar 

  22. Jha, B. K. and Apere, C. A. Combined effect of Hall and ion-slip currents on unsteady MHD Couette flow in a rotating system. Journal of the Physical Society of Japan, 79, 1–9 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

    B. K. Jha & C. A. Apere

Authors
  1. B. K. Jha
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  2. C. A. Apere
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Correspondence to C. A. Apere.

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Jha, B.K., Apere, C.A. Time-dependent MHD Couette flow of rotating fluid with Hall and ion-slip currents. Appl. Math. Mech.-Engl. Ed. 33, 399–410 (2012). https://doi.org/10.1007/s10483-012-1559-9

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  • DOI: https://doi.org/10.1007/s10483-012-1559-9

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