Free convection effects on a perfectly conducting couple stress fluid

• Autorzy: Ezzat M. , Zakaria M. , Samaan A. , Abd-el Bary A.
• Języki publikacji: EN

Abstrakty

EN

We have introduced a magnetohydrodynamic model of boundary-layer equations for a perfectly conducting couple-stress fluid. This model is applied to study the effects of free convection currents with thermal relaxation on the flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface. The state space formulation developed in EZZAT [1] and [2j is introduced. The formulation is valid for problems with or without heat sources. The resulting formulation, together with the Laplace transform technique, are applied to a variety of problems. The solution to a thermal shock problem and to the problem of the flow in the whole space with a plane distribution of heat sources are obtained. It is also applied to a semispace problem with a plane distribution of heat sources located inside the fluid. A numerical method is employed for the inversion of the Laplace transforms. The effects of Grashof number, material parameters, Alfven velocity, relaxation time, Prandtl number and the permeability parameter on the velocity, the temperature and the angular velocity distributions are discussed. The effects of cooling and heating of a couple-stress fluid have also been discussed. Numerical results are given and illustrated graphically for the problems considered.

Słowa kluczowe

EN

magnetohydrodynamic; couple stress fluid; state space approach

PL

magnetohydrodynamika; płyn doskonale przewodzący; prąd przewodzenia

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2006
• Tom: Vol. 47, no 1
• Strony: 5--30
• Opis fizyczny: Bibliogr. 24 poz., wykr.

Twórcy

autor

Ezzat M.

autor

Zakaria M.

autor

Samaan A.

autor

Abd-el Bary A.

• Department of Mathematics, Faculty of Education El-Shatby, Alexandria University, Alexandria, Egypt,

Bibliografia

• 1. M. EZZAT, State space approach to unsteady free convection flow through a porous medium, J. Appl. Math. Comput., 64, 191, 1995.
• 2. M. EZZAT, State space approach to unsteady two-dimensional free convection flow through a porous medium, Can. J. Phys., 72, 311, 1994.
• 3. H. C. BRINKMAN, A calculation of the viscous forces extended by a flowing fluid on a dense swarm of particles, Sci. Res., Al, 27, 1947.
• 4. K. YAMAMOTO, N. IWAMURA, Flow with convective acceleration through a porous medium, J. Engng. Maths., 10, 41, 1976.
• 5. A. RAPTIS, G. TZIVANIDIS, N. KAFOUSIAS, Free convection and mass transfer flow through a porous medium bounded by an infinite vertical limiting surface with constant suction, Lett. Heat Mass Transfer, 8, 417, 1981.
• 6. A. RAPTIS, N. KAPOUSIAS, C. MASSALAS, Free convection and mass transfer flow through a porous medium bounded by an infinite vertical porous plate with constant heat flux, ZAMM, 62, 489, 1982.
• 7. A. RAPTIS, Unsteady free convection flow through a porous medium, Int. J. Engng. Sci., 21, 345, 1983.
• 8. E.L. AERO, A.N. BULYGIN, E.V. KUVSCHINSKI, Asymmetric hydromechanics, J. Appl. Math. Mech.. 29, 333, 1965.
• 9. N.V. D'EP, Equations of a fluid boundary layer with couple stresses, J. Appl. Math. Mech., 32, 777, 1968.
• 10. M.T. KAMEL, P.N. KALONI, E.M TORY, Two-dimensional internal flows of polar fluids, J. Rheol. 23, 141, 1979.
• 11. A. RAPTIS, Effects of couple stresses on the flow through a porous medium, Rheol. Acta, 21, 736, 1982
• 12. P.S. HIEMATH, P.M. PATIAL, Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium, Acta Mechanica, 98, 143, 1993.
• 13. M.J. LIGHTHILL, The response of laminar skin friction and heat transfer to fluctuations in the stream velocity, Pioc. R. Soc. London, Ser. A, 224, 1-23, 1954.
• 14. J. T. STUART, A solution of the Navier-Stokes and energy equations illustrating the response of skin friction and temperature of an infinite plate thermometer to fluctuations in the stream velocity, Proc. R. Soc. London Ser. A, 231, 116, 1955.
• 15. M.A. EZZAT, M.Z. ABD-ELAAL, State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium, Z. Angew. Math. Mech., 77, 197, 1997.
• 16. M. EZZAT, M. ABD-ELAAL, Free convection effects on a viscoelastic boundary- layer flow with one relaxation time through a porous medium, J. Franklin Inst., 334B, 685, 1997.
• 17. M. EZZAT, State space approach to generalized magneto-thermoelasticity with two relaxation times in a medium of perfect conductivity.. Int. J. Engng. Sci., 35, 741, 1997.
• 18. G. HONIG, U.J. HIRDES, Comp. Appl. Math., 10, 113, 1984.
• 19. M. EZZAT, Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources, JAM, 4, 271, 2004.
• 20. J.P. HOLMAN, Heat transfer. Me Graw-Hill/Kogahusha, Tokyo 1976.
• 21. H. LORD, Y. SHULMAN, A generalized dynamical theory of thermoelasticity, 3. Mech. Phys. Solids., 15, 299-309, 1967.
• 22. W. NOWACKI, Some dynamic problems of theroelasticity. Arch. Mech. Stos., 11, 259-283, 1959.
• 23. K. OGATA, State space analysis control system, Prentice-Hall. Englewood Cliffs. N.J. Chap. 6, 1967.
• 24. M. EZZAT, State space approach to generalized magneto-thermoelasticity with two relaxation times in a medium of perfect conductivity. Int. J. Engng. Sci., 39, 741-752, 2001.