THERMAL SCIENCE

International Scientific Journal

HEAT TRANSFER IN MICROPOLAR FLUID FLOW UNDER THE INFLUENCE OF MAGNETIC FIELD

ABSTRACT
In this paper, the steady flow and heat transfer of an incompressible electrically conducting micropolar fluid through a parallel plate channel is investigated. The upper and lower plates have been kept at the two constant different temperatures and the plates are electrically insulated. Applied magnetic field is perpendicular to the flow, while the Reynolds number is significantly lower than one i. e. considered problem is in induction-less approximation. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and three closed-form solutions are obtained. The velocity, micro-rotation and temperature fields in function of Hartmann number, the coupling parameter and the spin-gradient viscosity parameter are graphically shown and discussed.
KEYWORDS
PAPER SUBMITTED: 2016-04-06
PAPER REVISED: 2016-10-14
PAPER ACCEPTED: 2016-10-17
PUBLISHED ONLINE: 2016-12-25
DOI REFERENCE: https://doi.org/10.2298/TSCI16S5391K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 5, PAGES [S1391 - S1404]
REFERENCES
  1. Eringen, A. C., Theory of Micropolar Fluids, J. Math. Mech., 16 (1966), pp. 1-18
  2. Blum, E. L., et al., Heat and Mass Transfer in the Presence of an Electromagnetic Field, (in Russian), Zinatne, (1967), p. 236
  3. Attia, H. A., Kotb, N. A., MHD Flow between Two Parallel Plates with Heat Transfer, Acta Mechanica, 117 (1996), 1, pp. 215-220
  4. Bodosa, G., Borkakati, A. K., MHD Couette Flow with Heat Transfer between Two Horizontal Plates in the Presence of a Uniform Transverse Magnetic Field, Theoretical and Applied Mechanics, 30 (2003), 1, pp. 1-9
  5. Sivak, B. A., et al., MHD Processes in the Electromagnetic Stirring of Liquid Metal in Continuous Sec-tion and Bloom Casters, Metallurgist, 53 (2009), 7, pp. 469-481
  6. Morley, N. B., et al., Thermo-Fluid Magnetohydrodynamic Issues for Liquid Breeders, Fusion Science and Technology, 47 (2005), 3, pp. 488-501
  7. Abdollahzadeh Jamalabadi, M. Y., Analytical Study of Magnetohydrodynamic Propulsion Stability, Journal of Marine Science and Application, 13 (2014), 3, pp. 281-290
  8. Shatrov, V., Gerbeth, G., On Magnetohydrodynamic Drag Reduction And Its Efficiency, Proceedings, 15th Riga and 6th PAMIR Conference on Fundamental and Applied MHD Instability and Transition to Turbulence in MHD, Riga, Latvia, 2005, pp. 149-152
  9. Saito, S., et al., Boundary Layer Separation Control by MHD Interaction, Proceedings, 46th AIAA Aero-space Sciences Meeting and Exhibit, Reno, Nev., USA, 2008
  10. Nikodijevic, D., Stamenkovic, Z., General Characteristics of Unsteady MHD Temperature Boundary Layer, International Journal of Non-Linear Mechanics, 73 (2015), July, pp. 75-84
  11. Ariman, T., et al., Microcontinuum Field Mechanics - a Review, Int. J. Eng. Sci., 11 (1973), 8, pp. 905-929
  12. Ariman, T., et al., Applications of Microcontinuum Field Mechanics, Int. J. Eng. Sci., 12 (1974), 4, pp. 273-293
  13. Eringen, A. C., Microcontinuum Field Theories: II. Fluent Media, Springer-Verlag, New York, USA, 2001
  14. Lukaszewicz, G., Micropolar Fluids, Theory and Application, Birkhauser, Basel, Switzerland, 1999
  15. Chamkha, A., et al., Unsteady MHD Natural Convection from a Heated Vertical Porous Plate in a Mi-cropolar Fluid with Joule Heating, Chemical Reaction and Radiaton Effects, Meccanica, 46 (2011), 2, pp. 399-411
  16. Bachok, N., et al., Flow and Heat Transfer over an Unsteady Stretching Sheet in a Micropolar Fluid, Meccanica, 46 (2011), 5, pp. 935-942
  17. Ellahi, R., Steady and Unsteady Flow Problems for Newtonian and Non-Newtonian Fluids: Basics, Con-cepts, Methods, VDM Verlag, Germany, 2009
  18. Toshivo, T., et al., Magnetizing Force Modelled and Numerically Solved for Natural Convection of Air in a Cubic Enclosure: Effect of the Direction of the Magnetic Field, International Journal of Heat and Mass Transfer, 45 (2002), 2, pp. 267-277
  19. Sengupta, A., et al., Liquid Crystal Microfluidics for Tunable Flow Shaping, Phys. Rev. Lett., 110 (2013), 4, ID 048303
  20. Mekheimer, Kh. S., El-Kot, M. A., The Micropolar Fluid Model For Blood Flow Through a Tapered Ar-tery with a Stenosis, Acta Mechanica Sinica, 24 (2008), 6, pp. 637-644
  21. Ashraf, M., et al., MHD Non-Newtonian Micropolar Fluid Flow and Heat Transfer in Channel with Stretching Walls, Applied Mathematics and Mechanics, 34 (2013), 10, pp. 1263-1276
  22. Nor-Azizah Y., et al., Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet in a Micropolar Fluid, Thermal Science, 17 (2013), 2, pp. 525- 532
  23. Bakier, A. Y., Natural Convection Heat and Mass Transfer in a Micropolar Fluid Saturated Non-Darcy Porous Regime with Radiation and Thermophoresis Effects, Thermal Science, 15 (2011), Suppl. 2, pp. S317-S326

© 2022 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