International Scientific Journal


The magnetohydordynamic flow and heat transfer of two viscous incompressible fluids through porous medium has been investigated in the paper. Fluids flow through porous medium between two parallel fixed isothermal plates in the presence of an inclined magnetic and perpendicular electric field. Fluids are electrically conducting, while the channel plates are insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained. Solutions with appropriate boundary conditions for velocity and temperature fields have been obtained. The analytical results for various values of the Hartmann number, load factor, viscosity and porosity parameter have been presented graphically to show their effect on the flow and heat transfer characteristics.
PAPER REVISED: 2016-10-09
PAPER ACCEPTED: 2016-10-11
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 5, PAGES [S1405 - S1417]
  1. Blum, E . Ya., Heat and Mass Transfer in MHD Flow Past Bodies, Magnetohydrodynamics, 6 (1970), 2, pp. 212-218
  2. Darcy, H., The Flow of Fluids through Porous Media, McGraw-Hill, New York, USA, 1937
  3. Cunningham, R. E., Williams, R. J., Diffusion in Gases and Porous Media, Plenum Press, New York, USA, 1980
  4. McWhirter, J., et al., Magnetohydrodynamic Flows in Porous Media II: Experimental results, Fusion Technology, 34 (1998), 3, pp. 187-197
  5. Prescott, P. J., Incropera, F. P., Magnetically Damped Convection During Solidification of a Binary Metal Alloy, Journal of Heat Transfer, 115 (1993), 2, pp. 302-310
  6. Lehmann, P., et al., Modification of Inter-Dendritic Convection in Directional Solidification by a Uniform Magnetic Field, Acta Materialia, 46 (1998), 11, pp. 1067-4079
  7. Bodosa, G., Borkakati, A. K., MHD Couette Flow with heat Transfer between Two Horizontal Plates in the Presence of a Uniform Transverse Magnetic Field, Journal of Theoretical and Applied Mechanics, 30 (2003), 1, pp. 1-9
  8. Attia, H. A., On the Effectiveness of Variation in the Physical Variables on the MHD Steady Flow between Parallel Plates with Heat Transfer, International Journal for Numerical Methods in Engineering, 65 (2006), 2, pp. 224-235
  9. Singha, K. G., Analytical Solution to the Problem of MHD Free Convective Flow of an Electrically Conducting Fluid between Two Heated Parallel Plates in the Presence of an Induced Magnetic Field, International Journal of Applied Mathematics and Computation, 1 (2009), 4, pp. 183-193
  10. Nikodijević, D., et al., Flow and Heat Transfer of Two Immiscible Fluids in the Presence of Uniform Inclined Magnetic Field, Mathematical Problems in Engineering, 2011 (2011), ID 132302
  11. Alpher, R. A,. Heat Transfer in Magnetohydrodynamic Flow between Parallel Plates, International Journal of Heat & Mass transfer, 3 (1961), 2, pp. 108-112
  12. Cox, S. M., Two Dimensional Flow of a Viscous Fluid in a Channel with Porous Wall, Journal of Fluid Mechanics, 227 (1991), June, pp. 1-33
  13. Tawil, M. A. E., Kamel, M. H., MHD Flow under Stochastic Porous Media, Energy Conservation Management, 35 (1994), 11, pp. 991-997
  14. Yih, K. A., Radiation Effect on Natural Convection over a Vertical Cylinder Embedded in Porous Media, International Communications in Heat and Mass Transfer, 26 (1999), 2, pp. 259-267
  15. Vidhya, M., Sundarammal, K., Laminar Convection through Porous Medium between Two Vertical Parallel Plates with Heat Source, Frontiers in Automobile and Mechanical Engineering (FAME), (2010), pp. 197-200, doi: 10.1109/FAME.2010.5714846
  16. Geindreau, C., Auriault, J., Magnetohydrodynamic Flows in Porous Media, Journal of Fluid Mechanics, 466 (2002), Sept., pp. 343-363
  17. Singh, R. D., Rakesh, K., Heat and Mass Transfer in MHD Flow of a Viscous Fluid through Porous Medium with Variable Suction and Heat Source, Proceedings of Indian National Science Academy, 75 (2002), 1, pp. 7-13
  18. Tzirtzilakis, E. E., A Mathematical Model for Blood Flow in Magnetic Field, Physics of Fluids, 17 (2005), 7, pp. 077103/1-077103/15
  19. Bird, R.B., et al., Transport Phenomena, John Wiley and Sons, New York, USA, 1960
  20. Bhattacharya, R. N., The Flow of Immiscible Fluids between Rigid Plates with a Time Dependent Pressure Gradient, Bulletin of the Calcutta Mathematical Society, 60 (1968), 3, pp. 129-136
  21. Mitra, P., Unsteady Flow of Two Electrically Conducting Fluids between Two Rigid Parallel Plates, Bulletin of the Calcutta Mathematical Society, 74 (1982), pp. 87-95
  22. Chamkha, A. J., Flow of Two-Immiscible Fluids in Porous and Non-Porous Channels, ASME Journal of Fluids Engineering, 122 (2000), 1, pp. 117-124
  23. Lohrasbi, J., Sahai, V., Magnetohydrodynamic Heat Transfer in Two Phase Flow between Parallel Plates, Applied Scientific Research, 45 (1988), 1, pp. 53-66
  24. Alireza, S., Sahai, V., Heat Transfer in Developing Magnetohydrodynamic Poiseuille Flow and Variable Transport Properties, International Journal of Heat and Mass Transfer, 33 (1990), 8, pp.1711-1720
  25. Malashetty, M. S. et al., Convective MHD Two Fluid Flow and Heat Transfer in an Inclined Channel, Heat and Mass Transfer, 37 (2001), 2-3, pp. 259-264
  26. Malashetty, M. S., et al., Two Fluid Flow and Heat Transfer in an Inclined Channel Containing Porous and Fluid Layer, Heat and Mass Transfer, 40 (2001), 11, pp. 871-876

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence