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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 1, 2005

Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient

Hazem Attia
From the journal Open Physics

Abstract

In the present study, the unsteady Hartmann flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.

[1] J. Lohrabi:Investigation of magnetohydrodynamic heat transfer in two-phase flow, Thesis (PhD), Tennessee Technological University, 1980. Search in Google Scholar

[2] A.J. Chamkha: “Unsteady laminar hydromagnetic fluid-particle flow and heat transfer in channels and circular pipes”, International J. of Heat and Fluid Flow, Vol. 21, (2000), pp. 740–746. http://dx.doi.org/10.1016/S0142-727X(00)00031-X10.1016/S0142-727X(00)00031-XSearch in Google Scholar

[3] P.G. Saffman: “On the stability of a laminar flow of a dusty gas”, Journal of Fluid Mechanics, Vol. 13, (1962), pp. 120–131. http://dx.doi.org/10.1017/S002211206200055510.1017/S0022112062000555Search in Google Scholar

[4] R.K. Gupta and S.C. Gupta: “Flow of a dusty gas through a channel with arbitrary time varying pressure gradient”, J. Appl. Mat. Phys., Vol. 27, (1976), pp. 119–133. http://dx.doi.org/10.1007/BF0159524810.1007/BF01595248Search in Google Scholar

[5] V.R. Prasad and N.C.P. Ramacharyulu: “Unsteady flow of a dusty incompressible fluid between two parallel plates under an impulsive pressure gradient”, Def. Sci. Journal, Vol. 30, (1979), pp. 125–137. Search in Google Scholar

[6] L.A. Dixit: “Unsteady flow of a dusty viscous fluid through rectangular ducts”, Indian J. of Theoretical Phys., Vol. 28(2), (1980), pp. 129–142. Search in Google Scholar

[7] A.K. Ghosh and D.K. Mitra: “Flow of a dusty fluid through horizontal pipes”, Rev. Roum. Phys., Vol. 29, (1984), pp. 631–646. Search in Google Scholar

[8] K.K. Singh: “Unsteady flow of a conducting dusty fluid through a rectangular channel with time dependent pressure gradient”, Indian J. Pure App. Mat., Vol. 8(9), (1976), pp. 1124–1136. Search in Google Scholar

[9] P. Mitra and P. Bhattacharyya: “Unsteady hydromagnetic laminar flow of a conducting dusty fluid between two parallel plates started impulsively from rest”, Acta Mech., Vol. 39, (1981), pp. 171–188. http://dx.doi.org/10.1007/BF0117034010.1007/BF01170340Search in Google Scholar

[10] K. Borkakotia and A. Bharali: “Hydromagnetic flow and heat transfer between two horizontal plates, the lower plate being a stretching sheet”, Q. Appl. Mat., (1983), pp. 461–474. Search in Google Scholar

[11] A.A. Megahed, A.L. Aboul-Hassan and H. Sharaf El-Din: “Effect of Joule and viscous dissipation on temperature distributions through electrically conducting dusty fluid”, In:Fifth Miami International Symposium on Multi-Phase Transport and Particulate Phenomena; Miami Beach, Florida, Vol. 3, 1988, pp. 111–123. Search in Google Scholar

[12] A.L. Aboul-Hassan, H. Sharaf El-Din and A.A. Megahed: “Temperature due to the motion of one of them”, In:First International Conference of Engineering Mathematics and Physics, Cairo, (Egypt), 1991, pp. 723–734. Search in Google Scholar

[13] K.R. Crammer and S.-I. Pai:Magnetofluid dynamics for Engineer and scientists, McGraw-Hill, New York, 1973. Search in Google Scholar

[14] G.W. Sutton and A. Sherman:Engineering Magnetohydrodynamics, McGraw-Hill, New York, 1965. Search in Google Scholar

[15] V.M. Soundalgekar, N.V. Vighnesam and H.S. Takhar: “Hall and Ion-Slip effects in MHD Couette flow with heat transfer”, IEEE T. Plasma Sci., Vol. PS-7(3), (1979), pp. 178–182. Search in Google Scholar

[16] V.M. Soundalgekar and A.G. Uplekar: “Hall effects in MHD Couette flow with heat transfer”, IEEE T. Plasma Sci., Vol. PS-14(5), (1986), pp. 579–583. http://dx.doi.org/10.1109/TPS.1986.431660010.1109/TPS.1986.4316600Search in Google Scholar

[17] H.A. Attia: “Hall current effects on the velocity and temperature fields of an unsteady Hartmann flow”, Can. J. Phys., Vol. 76(9), (1998), pp. 739–746. http://dx.doi.org/10.1139/cjp-76-9-73910.1139/cjp-76-9-739Search in Google Scholar

[18] H.A. Attia: “Transient Hartmann flow with heat transfer consideration the ion slip”, Phys. Scripta, Vol. 66, (2002), pp. 470–475. http://dx.doi.org/10.1238/Physica.Regular.066a0047010.1238/Physica.Regular.066a00470Search in Google Scholar

[19] A.L. Aboul-Hassan and H.A. Attia: “Hydromagnetic flow of a dusty fluid in a rectangular channel with Hall current and heat transfer”, Can. J. Phys., Vol. 80, (2002), pp. 579–589. http://dx.doi.org/10.1139/p01-12510.1139/p01-125Search in Google Scholar

[20] M.R. Spiegel:Theory and problems of Laplace Transforms, McGraw-Hill, New York, 1986. Search in Google Scholar

[21] H. Schlichting:Boundary layer theory, McGraw-Hill, New York, 1968. Search in Google Scholar

[22] W.F. Ames:Numerical solutions of partial differential equations, Academic Press, New York, 1977. 10.1016/B978-0-12-056760-7.50009-8Search in Google Scholar

Published Online: 2005-12-1
Published in Print: 2005-12-1

© 2005 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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