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Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current

Abstract

The aim of the present paper is to study the unsteady magneto-hydrodynamic viscous Couette flow with heat transfer in a Darcy porous medium between two infinite parallel porous plates considering Hall effect, and temperature dependent physical properties under constant pressure gradient. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is flowing through a porous medium that is assumed to obey Darcy’s law. A numerical solution for the governing nonlinear partial differential equations coupled with set of momentum equations and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions are investigated. It is found that the porosity number M has a marked effect on decreasing the velocity distribution (owing to a simultaneous increase in Darcy porous drag). Also the temperature T is decreased considerably with increasing porosity number. With increasing Hall current parameter m, the velocity component u (x-direction) is considerably increased, whereas velocity component w (z-direction) is reduced. Temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing m.

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References

  1. Alpher R A 1961 Heat transfer in Magneto-Hydrodynamic flow between parallel plates. Int. J. Heat and Mass Transfer 3: 108–112

  2. Ames W F 1977 Numerical solutions of partial differential equations. 2nd Ed. New York: Academic Press

  3. Attia H A 1998 Hall current effects on the velocity and temperature fields of an unsteady Hartmann flow. Can. J. Phys. 76: 739–746

  4. Attia H A 2005 Hall effect on Couette flow with heat transfer of a dusty conducting fluid in the presence of uniform suction and injection. Afr. J. Math. Phys. 2: 97–110

  5. Attia H A 2007 Velocity and temperature distributions between parallel porous plates with Hall effect and variable properties. Chem. Eng. Comm. 194: 1355–1373

  6. Attia H A and Kotb N A 1996 MHD flow between two parallel plates with heat transfer. Acta Mechanica 117: 215–220

  7. Attia H A and Mostafa A M Abdeen 2013 On the effectiveness of variation of physical variables on steady flow between parallel plates with heat transfer in a porous medium. J. Theoretical Appl. Mech. 51: 53–61

  8. Attia H A, Mostafa A M Abdeen and Abd El-Meged W 2013 Transient generalized Couette flow of viscoelastic fluid through a porous medium with variable viscosity and pressure gradient. Arabian J. Sci. Eng. 38: 3451–3458

  9. Attia H A, Abbas W, Mostafa A M Abdeen and Emam M S 2014 Effect of porosity on the flow of a dusty fluid between parallel plates with heat transfer and uniform suction and injection. European J. Environ. Civil Eng. 18: 241–251

  10. Cramer K and Pai S 1973 Magnetofluid dynamics for engineers and applied physicists. New York: McGraw-Hill

  11. Das S S, Maity M and Das J K 2012 Unsteady hydro-magnetic Convective flow past an infinite vertical porous flat plate in a porous medium. Int. J. Energy and Environ. 1: 109–118

  12. Devika B, Narayana P V and Venkataramana S 2013 MHD oscillatory flow of a visco-elastic fluid in a porous channel with chemical reaction. Int. J. Eng. Sci. Invention 2: 26–35

  13. Eguia P, Zueco J, Granada E and Patiõ D 2013 NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity. Appl. Mathematical Modelling 35: 303–316

  14. Hartmann J and Lazarus F 1937 Experimental investigations on the flow of mercury in an homogeneous magnetic field. Det. Kgl. Danske Videnskab. Selskab. Math. Fys. Medd 15: 1–45

  15. Ingham D B and Pop I 2002 Transport phenomena in porous media. Oxford: Pergamon

  16. Joaquín Z, Pablo E, Enrique G, José L M and Osman A B 2010 An electrical network for the numerical solution of transient MHD couette flow of a dusty fluid: Effects of variable properties and hall current. Int. Comm. Heat Mass Transf. 37: 1432–1439

  17. Joseph D D, Nield D A and Papanicolaou G 1982 Nonlinear equation governing flow in a saturated porous media. Water Resources Research 18: 1049–1052

  18. Khaled A R A and Vafai K 2003 The role of porous media in modeling flow and heat transfer in biological tissues. Int. J. Heat and Mass Transfer 46: 4989–5003

  19. Klemp K, Herwig H and Selmann M 1990 Entrance flow in channel with temperature dependent viscosity including viscous dissipation effects. Proceedings of the Third International Congress of Fluid Mechanics Cairo Egypt 3: 1257–1266

  20. Mostafa A M Abdeen, Attia H A, Abbas W and Abd El-Meged W 2013 Effectiveness of porosity on transient generalized Couette flow with Hall effect and variable properties under exponential decaying pressure gradient. Indian J. Phys. 87: 767–775

  21. Nield D A and Kuznetsov A V 2010 Forced convection in cellular porous material: Effect of temperature-dependent conductivity arising from radiative transfer. Int. J. Heat and Mass Transfer 53: 2680–2684

  22. Pal D and Talukdar B 2011 Unsteady Hydro-Magnetic oscillating flowpast a porous medium with suction/injection and slip effects. Int. J. Appl. Math. and Mech. 7: 58–71

  23. Ravikumar V, Raju M C and Raju G S S 2012 MHD three dimensional Couette flow past a porous plate with heat transfer. IOSR J. Math. 1: 3–9

  24. Soundalgekar V M and Uplekar A G 1986 Hall effects in MHD Couette flow with heat transfer. IEEE Transactions on Plasma Sci. 14: 579–583

  25. Soundalgekar V M, Vighnesam N V and Takhar H S 1979 Hall and ion-slip effects in MHD Couette flow with heat transfer. IEEE Transactions on Plasma Sci. 7: 178–182

  26. Sutton G W and Sherman A 1965 Engineering magnetohydrodynamics. New York: McGraw-Hill

  27. Tao L N 1960 Magnetohydrodynamic effects on the formation of Couette flow. J. Aerospace Sci. 27: 334–347

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Correspondence to MOSTAFA A M ABDEEN.

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ATTIA, H.A., ABBAS, W., M ABDEEN, M.A. et al. Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current. Sadhana 40, 183–197 (2015). https://doi.org/10.1007/s12046-014-0307-9

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Keywords

  • Flow between two parallel plates
  • Couette flow
  • porous medium
  • heat transfer
  • finite differences.