An electromagnetic free convection flow of a micropolar fluid with relaxation time

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Abstract

In the present investigation, we study the influence of a transverse magnetic field on the one-dimensional motion of an electrically conducting micropolar fluid through a porous medium. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions.

Numerical computations for the temperature, the microrotation and the velocity distributions as well as for the induced magnetic and electric fields are carried out and represented graphically.

AMS Mathematics Subject Classification

76W05 76S05 76A10 

Key words and phrases

Electromagnetic Free convection Micropolar fluid Relaxation time 

List of symbols

density of the fluid

u+

velocity component in thex+ direction

t+

time

g

acceleration due to gravity

β

thermal expansion coefficient

T+

temperature distribution

T+

temperature of the fluid away from the plate

Tω+

mean temperature of the plate

μ

absolute viscosity

μ*

vortex viscosity

y+

coordinate

N+

microrotation

α

Alfven velocity

H0

strength of a constant magnetic field

h+

induced magnetic field

0+

electric permeability

E+

induced electric field

K+

permeability of the porous medium

νm

magnetic diffusivity

σ0+

electric conductivity

μ0+

magnetic permeability

j

micro-inertia density

γ

spin-gradient viscosity

λ+

thermal conductivity

cp

specific heat at constant pressure

τ0+

thermal relaxation time

R

micropolar parameter, μ*

λ

dimensionless material parameter

σ

dimensionless material parameter

Pr

Prandtl number

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References

  1. 1.
    Eringen, A. C.,Theory of micropolar fluids, J. Math. 16(1966),1–18.MathSciNetGoogle Scholar
  2. 2.
    Eringen, A. C.,Theory of thermomicrofluids, J. Math. Anal. Appl. 38.480–469(1972).MATHCrossRefGoogle Scholar
  3. 3.
    Khonsari, M. M.,On the self-excited whirl orbits of a journal in a sleeve bearing lubricated with micropolar fluids. Acta Mech. 81. 235–244(1990).MATHCrossRefGoogle Scholar
  4. 4.
    Khonsari, M. M., Brewe, D,On the performance of finite journal bearings lubricated with micropolar fluids, STLe Tribology Transe. 32. 155–160(1989).CrossRefGoogle Scholar
  5. 5.
    Hudimoto, B., Tokuoka, T,Two-dimensional shear flows of linear micropolar fluids, Int. J. Eng. Sci. 7.515–522(1969).CrossRefGoogle Scholar
  6. 6.
    Lockwood, F., Benchaita, M., Friberg, S,Study of lyotropic liquid crystals in viscometric flow and elastohydrodynamic contact, ASLE Tribology Trans. 30. 539–548(1987).CrossRefGoogle Scholar
  7. 7.
    Lee, J. D., Eringen, A.C,Boundary effects of orientation of noematic liquid crystals, J. Chem. Phys. 55.4509–4512(1971).CrossRefGoogle Scholar
  8. 8.
    Ariman, T., Turk. A., Sylvester, N.D,On steady and pulsatile flow of blood, J. Appl Mech. 41. 1–7(1974).Google Scholar
  9. 9.
    Kolpashchikov, V., Migun, N. P., Prokhorenko, P.P,Experimental determinations of material micropolar coefficients, Int. J. Eng. Sci. 21. 405–411(1983).CrossRefGoogle Scholar
  10. 10.
    Arman, T., Turk. M. A., Sylvester, N. D.,Microcontinuum fluid mechanics -a review, Int. J. Eng. Sci. 11, 905–930(1973).CrossRefGoogle Scholar
  11. 11.
    Arman, T., Turk. M. A., Sylvester, N. D.,Applications of microcontinuum fluids mechanics, Int. J. Eng. Sci. 12. 273–293(1974).CrossRefGoogle Scholar
  12. 12.
    Crane, L. J.,Heat transfer on continuous solid surfaces, J. Apple Math Phys. 21.645–652(1970).CrossRefGoogle Scholar
  13. 13.
    Chiu, C. P., Chou, H. M.,Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface, Acta Mech. 101. 161–174(1993).MATHCrossRefGoogle Scholar
  14. 14.
    Hassanien, I. A., Gorla, R. S. R,Heat transfer to a micropolar fluid from a non-isothermal strething sheet with suction and blowing, Act Mech. 84. 191–199(1990).CrossRefGoogle Scholar
  15. 15.
    Gorla, R. S. R,Mixed convection boundary layer flow of a micropolar fluid on a horizontal plate, Acta Mech. 108. 101–109(1995).MATHCrossRefGoogle Scholar
  16. 16.
    Rama Rao, K. V.,Thermal instability in a micropolar fluid layer subject to a magnetic field, Int. J. Eng. Sci. 18. 741–750(1980).MATHCrossRefGoogle Scholar
  17. 17.
    Ezzat, M. A., Abd-Elaal, M. Z.,State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium, ZAMM. Z. angew. Math. Mech. 3. 197–207(1997).MathSciNetGoogle Scholar
  18. 18.
    Ezzat, M. A., Abd-Eaal, M. Z.,Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium, J. Franklin Inst. 4. 685–706(1997).CrossRefGoogle Scholar
  19. 19.
    Honig, G., Hirdes U,A method for the numerical inversion of the Laplace transform, J. Comp. Appl. Math. 10. 113–132(1984).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2001

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationUniversity of AlexandriaEgypt

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