Heat Transfer Effects on Rotating MHD Couette Flow in a Channel Partially Filled by a Porous Medium with Hall Current

Dileep Singh  Chauhan; Priyanka  Rastogi

doi:10.6180/jase.2012.15.3.09

Heat Transfer Effects on Rotating MHD Couette Flow in a Channel Partially Filled by a Porous Medium with Hall Current

Dileep Singh Chauhan This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Priyanka Rastogi¹

¹Department of Mathematics, University of Rajasthan, Jaipur-302004, India

Received: November 11, 2010
Accepted: December 19, 2011
Publication Date: September 1, 2012

Download Citation: ||https://doi.org/10.6180/jase.2012.15.3.09

ABSTRACT

A viscous incompressible electrically conducting fluid flow is considered in a parallel plate horizontal channel in the presence of an inclined magnetic field. The channel is rotating with uniform angular velocity about an axis normal to the plates. A porous material of finite thickness is attached to the lower impermeable plate which is stationary and kept at a constant temperature T0, while the upper impermeable plate is moving with a uniform velocity and kept at a constant temperature T1. For the strong applied magnetic field, the Hall current effects are considered. In the energy equation viscous dissipation and Ohmic dissipation effects are also taken into account. Exact solutions are obtained for the flow, magnetic field and temperature distributions. Effects of the pertinent parameters on the velocity distribution, temperature distribution, induced magnetic field and rate of heat transfer are depicted graphically and discussed.

Keywords: Rotating MHD Couette Flow, Porous Medium, Permeability, Hall Current, Heat Transfer

REFERENCES

[1] McWhirter, J. D., Crawford, M. E. and Klein, D. E., “Magnetohydrodynamic Flows in Porous Media II: Experimental Results,” Fusion Technol., Vol. 34, pp. 187197 (1998).
[2] Geindreau, C. and Auriault, J. L., “Magnetohydrodynamic Flows in Porous Media,” J Fluid Mech., Vol. 466, pp. 343363 (2002).
[3] Seth, G. S., Jana, R. N. and Maiti, M. K., “Unsteady Hydromagnetic Couette Flow in a Rotating System,” Int J Engng Sci., Vol. 20, pp. 989999 (1982).
[4] Singh, A. K., Sacheti, N. C. and Chandran, P., “Transient Effects in Magneto-Hydrodynamic Couette Flow with Rotation: Accelerated Motion,” Int J Engng Sci., Vol. 32, pp. 133139 (1994).
[5] Chauhan, D. S. and Vyas, P., “Heat Transfer in Hydromagnetic Couette Flow of Compressible Newtonian Fluid,” ASCE J of Engng Mech., Vol. 121, pp. 5761 (1995).
[6] Attia, H. A., “Influence of Temperature-Dependent Viscosity in the MHD Couette Flow of Dusty Fluid with Heat Transfer,” Diff Eq and Nonlinear Mechanics, pp. 114 (2006).
[7] Attia, H. A., “Ion Slip Effect on Unsteady Couette Flow with Heat Transfer under Exponential Decaying Pressure Gradient,” Tamkang J Sci Engng., Vol. 12, pp. 209214 (2009).
[8] Attia, H. A. and Ewis, K. M., “Unsteady MHD Couette Flow with Heat Transfer of a Viscoelastic Fluid under Exponential Decaying Pressure Gradient,” Tamkang J Sci Engng., Vol. 13, pp. 359364 (2010).
[9] Seth, G. S., Ansari, M. S. and Nandkeolyar, R., “Unsteady Hydromagnetic Couette Flow within a Porous Channel,” Tamkang J Sci Engng., Vol. 14, pp. 714 (2011).
[10] Attia, H. A., Al-kaisy, A. M. A. and Ewis, K. M., “MHD Couette Flow and Heat Transfer of a Dusty Fluid with Exponential Decaying Pressure Gradient,” Tamkang J Sci Engng., Vol. 14, pp. 9196 (2011).
[11] Cramer, K. R. and Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, NY, USA: McGraw-Hill (1973).
[12] Sato, H., “Hall Effect in the Viscous Flow of Ionized Gas between Parallel Plates under Transverse Magnetic Field,” J Phys Soc Japan, Vol. 16, pp. 1427 1433 (1961).
[13] Sutton, G. W. and Sherman, A., Engineering Magnetohydrodynamics, NY: McGraw-Hill (1965).
[14] Ghosh, S. K. and Bhattacharjee, P. K., “Hall Effects on Steady Hydromagnetic Flow in a Rotating Channel in the Presence of an Inclined Magnetic Field,” Chech J Phys., Vol. 50, pp. 759767 (2000).
[15] Ghosh, S. K., Bég, O. A. and Narahari, M., “Hall Effects on MHD Flow in a Rotating System with Heat Transfer Characteristics,” Meccanica, Vol. 44, pp. 741765 (2009).
[16] Soundalgekar, V. M., Vighnesam, N. V. and Takhar, H. S., “Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer,” IEEE Trans Plasma Sci., Vol. 7, pp. 178182 (1979).
[17] Soundalgekar, V. M. and Uplekar, A. G., “Hall Effects in MHD Couette with Heat Transfer,” IEEE Trans Plasma Sci., Vol. 14, pp. 579583 (1986).
[18] Attia, H. A., “MHD Couette Flow with Temperature Dependent Viscosity and Ion Slip,” Tamkang J Sci Engng., Vol. 8, pp. 1116 (2005).
[19] Mandal, G. and Mandal, K. K., “Effect of Hall Current on MHD Couette Flow between Thick Arbitrarily Conducting Plates in a Rotating System,” J Physical Soc Japan, Vol. 52, pp. 470477 (1983).
[20] Ghosh, S. K., “Effects of Hall Current on MHD Couette Flow in a Rotating System with Arbitrary Magnetic Field,” Czech J Phys., Vol. 52, pp. 5163 (2002).
[21] Krishna, D. V., Prasada Rao, D. R. V. and Ramachandra Murthy, A. S., “Hydromagnetic Convection Flow through a Porous Medium in a Rotating Channel,” J Eng Phys Thermophys, Vol. 75, pp. 281291 (2002).
[22] Bég, O. A., Zueco, J. and Takhar, H. S., “Unsteady Magnetohydrodynamic Hartmann-Couette Flow and Heat Transfer in a Darcian Channel with Hall Current, Ionslip, Viscous and Joule Heating Effects: Network Numerical Solutions,” Commun in Nonlinear Sci and Numer Simulation, Vol. 14, pp. 10821097 (2009).
[23] Ochoa-Tapia, J. A. and Whitaker, S., “Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid-I. Theoretical Development,” Int J Heat Mass Transfer, Vol. 38, pp. 26352646 (1995).
[24] Ochoa-Tapia, J. A. and Whitaker, S., “Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid-I. Comparison with Experiment,” Int J Heat Mass Transfer, Vol. 38, pp. 26472655 (1995b).
[25] Kuznetsov, A. V., “Analytical Investigation of Couette Flow in a Composite Channel Partially Filled with a Porous Medium and Partially with a Clear Fluid,” Int J Heat Mass Transfer, Vol. 41, pp. 25562560 (1998).
[26] Chauhan, D. S. and Rastogi, P., “Hall Current and Heat Transfer Effects on MHD Flow in a Channel Partially Filled with a Porous Medium in a Rotating System,” Turkish J Eng Env Sci., Vol. 33, pp. 167184 (2009).
[27] Chauhan, D. S. and Agrawal, R., “Effects of Hall Current on MHD Flow in a Rotating Channel Partially Filled with a Porous Medium,” Chem Engng Comm., Vol. 197, pp. 830845 (2010).
[28] Chauhan, D. S. and Agrawal, R., “Effects of Hall Current on MHD Couette Flow in a Channel Partially Filled with a Porous Medium in a Rotating System,” Meccanica, DOI 10.1007/s11012-011-9446-9 (2011).
[29] Cowling, T. G., Magnetohydrodynamics, New York: Interscience Pub. Inc (1957).
[30] Nield, D. J. and Bejan, A., Convection in Porous Media, USA: Springer (2006).
[31] Al-Hadhrami, A. K., Elliot, L. and Ingham, D. B., “A New Model for Viscous Dissipation in Porous Media across a Range of Permeability Values,” Transport in Porous Media, Vol. 53, pp. 117122 (2003).