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Magnetohydrodynamic Poiseuille-Couette Flow and Heat Transfer in an Inclined Channel

Published online by Cambridge University Press:  03 October 2011

J. C. Umavathi ,
I-C. Liu  and
J. Prathap Kumar
J. C. Umavathi*
Affiliation:
Department of Mathematics, Gulbarga University, Gulbarga 585106, Karnataka, India
I-C. Liu*
Affiliation:
Department of Civil Engineering, National Chi Nan University, Nantou, Taiwan 54561, R.O.C.
J. Prathap Kumar*
Affiliation:
Department of Mathematics, Gulbarga University, Gulbarga 585106, Karnataka, India.
*
* Professor
** Professor, corresponding author
*** Reader
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Abstract

An analysis of the Poiseuille-Couette flow of two immiscible fluids between inclined parallel plates is investigated. One of the fluids is assumed to be electrically conducting while the other fluid and channel walls are assumed to be electrically insulating. The viscous and Ohmic dissipation terms are taken into account in the energy equation. The coupled nonlinear equations are solved both analytically valid for small values of the product of Prandtl number and Eckert number (= ε) and numerically valid for all ε. Solutions for large ε reveal a marked change on the flow and rate of heat transfer. The effects of various parameters such as Hartmann number, Grashof number, angle of inclination, ratios of viscosities, widths and thermal conductivities are presented and discussed in detail.

Keywords

Poiseuille-couette flowMagnetohydrodynamic convectionImmiscible fluidsInclined channelHartman number
Type
Research Article
Information
Journal of Mechanics , Volume 26 , Issue 4 , December 2010 , pp. 525 - 532
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

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References

REFERENCES

1. Andereck, C. D., Colovas, P. W., Degen, M. M. and Renardy, Y. Y., “Instabilities in Two Layer Rayleigh-Benard Convection: Overview and Outlook,” International Journal of Engineering Science, 36, pp. 1451–1470 (1998).CrossRefGoogle Scholar
2. Degen, M. M., Colovas, P. W. and Andereck, C. D., “Time Dependent Patterns in the Two-Layer Rayleigh-Benard System,” Physics Review E, 57, pp. 6647–6659 (1988).CrossRefGoogle Scholar
3. Oreper, G. M. and Szekely, J., “The Effect of an Externally Imposed Magnetic Field on Buoyancy Driven Flow in Rectangular Cavity,” Journal of Crystal Growth, 64, pp. 505–515 (1983).CrossRefGoogle Scholar
4. Shail, R., “On Laminar Two-Phase Flow in Magnetohy-drodynamics,” International Journal of Engineering Science, 11, pp. 1103–1108 (1973).CrossRefGoogle Scholar
5. Lohrasbi, J. and Sahai, V., “Magnetohydrodynamic Heat Transfer in Two Phase Flow Between Parallel Plates,” Applied Science Research, 45, pp. 53–66 (1988).CrossRefGoogle Scholar
6. Umavathi, J. C., Malashetty, M. S. and Mateen, A., “Fully Developed Flow and Heat Transfer in a Horizontal Channel Containing an Electrically Conducting Fluid Sandwiched Between Two Fluid Layers,” International Journal of Applied Mechanics and Engineering, 9, pp. 781–794 (2004).Google Scholar
7. Umavathi, J. C., Mateen, A., Chamkha, A. J. and Al-Mudhaf, A., “Oscillatory Hartmann Two-Fluid Flow and Heat Transfer in a Horizontal Channel,” International International Journal of Applied Mechanics and Engineering, 11, pp. 155–178 (2006).Google Scholar
8. Malashetty, M. S. and Umavathi, J. C., “Two Phase Magnetohydrodynamic Flow and Heat Transfer in an Inclined Channel,” International Journal of Multiphase Flow, 23, pp. 545–560 (1997).CrossRefGoogle Scholar
9. Malashetty, M. S., Umavathi, J. C. and Prathap Kumar, J., “Convective Magneto-Hydrodynamic Two Fluid Flow and Heat Transfer in an Inclined Channel,” Heat and Mass Transfer, 37, pp. 259–264 (2001).CrossRefGoogle Scholar
10. Malashetty, M. S., Umavathi, J. C. and Prathap Kumar, J., “Magnetoconvection of Two- Immiscible Fluids in Vertical Enclosure,” Heat and Mass Transfer, 42, pp. 977–993 (2006).CrossRefGoogle Scholar
11. Makar, M., “Magnetohydrodynamic Plane Couette Flow of an Elasto-Viscous Fluid,” Il Nuovo Cimento D, 19, pp. 565–569 (1996).CrossRefGoogle Scholar
12. Jha, B. K., “Natural Convection in Unsteady MHD Couette Flow,” Heat and Mass Transfer, 37, pp. 329–331 (2001).CrossRefGoogle Scholar
13. Ogulu, A. and Motsa, S., “Radiative Heat Transfer to Magnetohydrodynamic Couette Flow with Variable Wall Temperature,” Physica Scripta, 71, pp. 336–339 (2005).CrossRefGoogle Scholar
14. Attia, H. A., “Unsteady Couette-Poiseuille Flow with Temperature Dependent Physical Properties in the Presence of a Uniform Magnetic Field,” Malaysian Journal of Science, 24, pp. 51–57 (2005).Google Scholar
15. Kumar, Sanjeev, “A Mathematical Model for the MHD Couette Flow Through Porous Medium with Heat Transfer,” In International Conference: Dynamical Systems and Applications, Turkey (2007).Google Scholar
16. Attia, H. A., “The Effect of Variable Properties on the Unsteady Couette Flow with Heat Transfer Considering the Hall Effect,” Communications in Nonlinear Science and Numerical Simulation, 13, pp. 1596–1604 (2008).CrossRefGoogle Scholar
17. Romig, M. F., “The Influence of Electric and Magnetic Fields on Heat Transfer to Electrically Conducting Fluids,” Advances in Heat Transfer, 1, pp. 267–354 (1964).CrossRefGoogle Scholar