Skip to main content
SpringerLink
Log in

Hall effect on unsteady couette flow with heat transfer under exponential decaying pressure gradient

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The unsteady Couette flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer taking the Hall effect into consideration. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the ion slip and the uniform suction and injection on both the velocity and temperature distributions is examined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

Viscosity parameter

b :

Thermal conductivity parameter

c p :

Specific heat at constant pressure

Ec :

Eckert number

Ha :

Hartmann number

i :

Unit vector in the axial direction

j :

Unit vector in the vertical direction

k :

Unit vector in thez-direction

J :

Current density

k :

Thermal conductivity

h :

Separation between the two plates

P :

Pressure gradient

Pr:

Prandtl number

Re:

Reynolds number

S :

Suction parameter

t :

Time

T :

Temperature of the fluid

T 1 :

Temperature of the lower plate

T 2 :

Temperature of the upper plate

m :

Hall parameter

u :

Velocity component in thex-direction

w :

Velocity component in thez-direction

U o :

Velocity of the upper plate

v o :

Suction velocity

x :

Axial direction

y :

Distance in the vertical direction

z :

Distance in thez-direction

μ :

Viscosity of the fluid

θ :

Density of the fluid

ρ :

Electrical conductivity of the fluid

β :

Hall factor

References

  • Abo-El-Dahab, E. M. H., 1993, “Effect of Hall Currents on Some Magnetohydrodynamic Flow Problems,” Master Thesis, Dept. of Maths., Faculty of Science, Helwan University, Egypt.

    Google Scholar 

  • Alpher, R. A., 1961, “Heat Transfer in Magnetohydrodynamic Flow Between Parallel Plates,”Int. J. Heat and Mass Transfer, Vol. 3, pp. 108–119.

    Article  Google Scholar 

  • Ames, W. F., 1977,Numerical Solutions of Partial Differential Equations, 2nd ed., Academic Press, New York.

    Google Scholar 

  • Attia, H. A., 1998, “Hall Current Effects on the Velocity and Temperature Fields of an Unsteady Hartmann Flow,”Can. J. Phys., Vol. 76, No. 9, pp. 739–746.

    Article  Google Scholar 

  • Attia, H. A., 2005, “The Effect of Suction and Injection on Unsteady Flow of a Dusty Conducting Fluid in Rectangular Channel,”Journal of Mechanical Science and Technology, Vol. 19, No. 5, pp. 1148–1157.

    Article  Google Scholar 

  • Cramer, K. and Pai, S. -I., 1973,Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill, New York.

    Google Scholar 

  • Hartmann, J. and Lazarus, F., 1937, “Kgl. Danske Videnskab. Selskab,”Mat.-Fys. Medd, Vol. 15, pp. 6–17

    Google Scholar 

  • Nigam, S. D. and Singh, S. N., 1960, “Heat Transfer by Laminar Flow Between Parallel Plates Under the Action of Transverse Magnetic Field,”Quart. J. Mech. Appl. Math., Vol. 13, pp. 85–97.

    Article  MATH  MathSciNet  Google Scholar 

  • Schlichting, H., 1968,Boundary Layer Theory, McGraw-Hill, New York.

    Google Scholar 

  • Soundalgekar, V. M., Vighnesam, N. V. and Takhar, H. S., 1979, “Hall and Ion-slip Effects in MHD Couette Flow with Heat Transfer,”IEEE Trans. Plasma Sci., Vol. PS-7, No. 3, pp. 178–182.

    Google Scholar 

  • Soundalgekar, V. M. and Uplekar, A. G., 1986, “Hall Effects in MHD Couette flow with Heat Transfer,”IEEE Trans. Plasma Sci., Vol. PS-14, No. 5, pp. 579–583.

    Google Scholar 

  • Sutton, G. W. and Sherman, A., 1965,Engineering Magnetohydrodynamics, McGraw-Hill, New York.

    Google Scholar 

  • Tani, I., 1962, “Steady Motion of Conducting Fluids in Channels Under Transverse Magnetic Fields with Consideration of Hall Effect,”J. of Aerospace Sci., Vol. 29, pp. 287–298.

    MathSciNet  Google Scholar 

  • Tao, I. N., 1960, “Magnetohydrodynamic Effects on the Formation of Couette Flow,”J. of Aerospace Sci., Vol. 27, pp. 334–357.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, Al-Qasseem University, P.O. Box 237, 81999, Buraidah, KSA

    Hazem Ali Attia

Authors
  1. Hazem Ali Attia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hazem Ali Attia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ali Attia, H. Hall effect on unsteady couette flow with heat transfer under exponential decaying pressure gradient. J Mech Sci Technol 19, 2053–2060 (2005). https://doi.org/10.1007/BF02916498

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02916498

Key Words

Search

Navigation