Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T15:58:41.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Combined Free and Forced Convection Couette-Hartmann Flow in a Rotating Channel with Arbitrary Conducting Walls and Hall Effects

Published online by Cambridge University Press:  17 August 2016

G. S. Seth ,
S. Sarkar  and
O. D. Makinde
G. S. Seth
Affiliation:
Department of Applied Mathematics Indian School of Mines Dhanbad, India
S. Sarkar*
Affiliation:
Department of Mathematics School of Applied Sciences KIIT University Bhubaneswar, India
O. D. Makinde
Affiliation:
Faculty of Military Sciences Stellenbosch University Saldanha, South Africa
*
*Corresponding author ([email protected]; [email protected])
Get access

Abstract

Combined free and forced convection Couette-Hartmann flow of a viscous, incompressible and electrically conducting fluid in rotating channel with arbitrary conducting walls in the presence of Hall current is investigated. Boundary conditions for magnetic field and expressions for shear stresses at the walls and mass flow rate are derived. Asymptotic analysis of solution for large values of rotation and magnetic parameters is performed to highlight nature of modified Ekmann and Hartmann boundary layers. Numerical solution of non-linear energy equation and rate of heat transfer at the walls are computed with the help of MATHEMATICA. It is found that velocity depends on wall conductance ratio of moving wall and on the sum of wall conductance ratios of both the walls of channel. There arises reverse flow in the secondary flow direction near central region of the channel due to thermal buoyancy force. Thermal buoyancy force, rotation, Hall current and wall conductance ratios resist primary fluid velocity whereas thermal buoyancy force and Hall current favor secondary fluid velocity in the region near lower wall of the channel. Magnetic field favors both the primary and secondary fluid velocities in the region near lower wall of the channel.

Keywords

Couette-Hartmann rotating flowFree and forced convectionArbitrary wall conductanceViscous and Joule Dissipations
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 613 - 629
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Muzychka, Y. S. and Yovanovich, M. M., “Unsteady Viscous Flows and Stokes's First Problem,” Proceedings of IMECE 2006 ASME International Mechanical Engineering Congress and Exposition, Chicago (2006).Google Scholar
2. Lehnert, B.O., “On the Behavior an Electrically Conducting Liquid in a Magnetic Field,” Arkiv för Fysik, 5, pp. 69–90 (1952).Google Scholar
3. Leadon, B. M., “Plane Couette Flow of a Conducting Gas through a Transverse Magnetic Field,” Canvair Scientific Research Laboratory, RN–13 (1957).Google Scholar
4. Bleviss, Z. O., “Magnetohydrodynamics of Hypersonic Couette Flow,” Journal of Aerospace Science, 25, pp. 601–616 (1958).CrossRefGoogle Scholar
5. Agarwal, J.P., “On Generalized Incompressible Couette Flow in Hydromagnetics,” Applied Scientific Research, B9, pp. 255–266 (1961).Google Scholar
6. Sutton, G. W. and Sherman, A., Engineering Magnetohydrodynamics, McGraw–Hill, New York (1965).Google Scholar
7. Cramer, K. R. and Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw–Hill, New York (1973).Google Scholar
8. Narasimhan, M. N., “Transient Magnetohydrodynamic Flow in an Annular Channel,” Technical Report, University of Wisconsin-Madison Mathematics Research Center, Madison, Wisconsin (1963).Google Scholar
9. Hide, R. and Roberts, P. H. “The Origin of the Earth's Magnetic Field,” Physics and Chemistry of the Earth, 4, pp. 27–98 (1960).CrossRefGoogle Scholar
10. Lund, J., “100 Years of Geothermal Power Production”. Geo-Heat Centre Quarterly Bulletin, Klamath Falls, Oregon Institute of Technology, 25, pp. 11–19 (2004).Google Scholar
11. Takenouchi, K., “Transient Magnetohydrodynamic Channel Flow with Axial Symmetry at a Supersonic Speed,” Jorunal of the Physical Society of Japan, 54, pp. 1329–1338 (1985).CrossRefGoogle Scholar
12. Triwahju Hardianto, T., Sakamoto, N. and Harada, N., “Computational Study of a Diagonal Channel Magnetohydrodynamic Power Generation,” International Journal Energy Technology Policy, 6, pp. 96–111 (2008).CrossRefGoogle Scholar
13. Barmin, A. A. and Uspenskii, V. S., “Development of Pulsation Regimes in One-Dimensional Unsteady MHD Flows with Switching Off of the Electrical Conductivity,” Fluid Dynamics, 21, pp. 604–610 (1986).CrossRefGoogle Scholar
14. Chang, C. C. and Lundgren, T. S., “The Flow of an Electrically Conducting Fluid through a Duct With Transverse Magnetic Field,” Proceedings of Heat Transfer Fluid Mechanics Institute, University of California, Los Angeles., pp. 41–54 (1959).Google Scholar
15. Viskanta, R., “Effect of Transverse Magnetic Field on Heat Transfer to an Electrically Conducting and Thermal Radiating Fluid Flowing in a Parallel-Plate Channel,” Zeitschrift für angewandte Mathematik und Physik, 14, pp. 353–368 (1963).CrossRefGoogle Scholar
16. Snyder, W. T., “The Influence of Wall Conductance on Magnetohydrodynamic Channel-Flow Heat Transfer,” Journal of Heat Transfer, 86, pp. 552–556 (1964).CrossRefGoogle Scholar
17. Soundalgekar, V. M., “On Heat Transfer in Crossed Fluids MHD Channel Flow Between Conducting Walls,” Proceedings of National Institute of Science, 35, pp. 329–342 (1969).Google Scholar
18. Gill, W. N. and Casal, E. D., “A Theoretical Investigation of Natural Convection Effects in Forced Horizontal Flows,” AlChE Journal, 8, pp. 513–518 (1962).CrossRefGoogle Scholar
19. Mori, Y., “On Combined Free and Forced Convection Laminar MHD Flow and Heat Transfer in Channel with Transverse Magnetic Field,” International Developments in Heat Transfer, 3, pp. 1031–1037 (1961).Google Scholar
20. Singer, R. M., “Combined Thermal Convective Magneto-Hydrodynamic Flow,” Applied Scientific Research, B12, 375–404 (1965).CrossRefGoogle Scholar
21. Yu, C. P., “Combined Forced and Free Convective Channel in MHD,” AIAA Journal, 3, pp. 1184–1185 (1965).CrossRefGoogle Scholar
22. Gupta, A. S., “Combined Free and Forced Convection Effects on the Magnetohydrodynamic Flow through a Channel,” Zeitschrift für angewandte Mathematik und Physik, 20, pp. 506–513 (1969).CrossRefGoogle Scholar
23. Marr, H. S., “Electromagnetic Stirring in Continuous Casting of Steel,” Proceedings Metallurgical Applications of MHD, Proctor, M. R. E. & Moffat, H. K. eds., The Metals Society, Cambridge, pp. 143–153 (1984).Google Scholar
24. Acheson, D. J. and Hide, R. “Hydromagnetics of Rotating Fluids,” Report on Progress in Physics, 36, pp. 159–221 (1973).CrossRefGoogle Scholar
25. Mohan, M., “Combined Effects of Free and Forced Convection on Magnetohydrodynamic Flow in a Rotating Channel,” Proceedings Indian Academy Sciences, A85, pp. 383–401 (1977).CrossRefGoogle Scholar
26. Prasad Rao, D. R. V. and Krishna, D. V., “Hall Effects on Free and Forced Convective Flow in a Rotating Channel,” Acta Mechanica, 43, pp. 49–59 (1982).CrossRefGoogle Scholar
27. Ghosh, S. K. and Bhattacharjee, P. K., “Magnetohydrodynamic Convective Flow in a Rotating Channel,” Archives of Mechanics, 52, pp. 303–318 (2000).Google Scholar
28. Seth, G. S. and Singh, M. K. “Combined Free and Forced Convection MHD Flow in a Rotating Channel with Perfectly Conducting Walls,” Indian Journal of Theoretical Physcis, 56, pp. 203–222 (2008).Google Scholar
29. Seth, G. S. and Ansari, Md. S., “Magnetohydrodynamic Convective Flow in a Rotating Channel with Hall Effects,” International Journal of Theoretical and Applied Mechanics, 4, pp. 205–222 (2009).Google Scholar
30. Fife, J., “Hybrid-PIC Modeling and Electrostatic Probe Survey of Hall thrusters,” Ph.D. Dissertation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S. (1998).Google Scholar
31. Shang, J.S., Surzhikov, S. T., Kimmel, R., Gaitonde, D., Menart, J. and Hayes, J., “Mechanisms of Plasma Actuators for Hypersonic Flow Control,” Progress in Aerospace Science, 41 pp. 642–668 (2005).CrossRefGoogle Scholar
32. Kholshchevnikova, E. K., “Influence of the Hall Effect on the Characteristics of a MHD Generator with Two Pairs of Electrodes,” Journal of Applied Mechanics and Technical Physics, 7, pp. 48–54 (1966).CrossRefGoogle Scholar
33. Michaeli, K., Tikhonov, K. S. and Finkel'stein, A. M., “Hall Effect in Superconducting Films,” Physical Review, B86, 014515 (2012).Google Scholar
34. Sivaprasad, R., Prasad Rao, D.R.V. and Krishna, D.V., “Hall Effects on Unsteady MHD Free and Forced Convection Flow in a Porous Rotating Channel,” Indian Journal of Pure Applied Mathematics, 19, pp. 688–696 (1988).Google Scholar
35. Seth, G. S., Mahato, G. K. and Singh, J. K., “Combined Free and Forced Convection Couette-Hartmann Flow in a Rotating System with Hall Effects,” Journal of Nature Science and Sustainable Technology, 6, pp. 125–150 (2012).Google Scholar
36. Chang, C. C. and Yen, J. T., “Magneto-hydrodynamic Channel Flow as Influenced by Wall Conductance,” Zeitschrift für angewandte Mathematik und Physik, 13, pp. 266–272 (1962).CrossRefGoogle Scholar
37. Yen, J.T. and Chang, C.C., “Magnetohydrodynamic Couette Flow as Affected by Wall Conductance,” Zeitschrift für angewandte Mathematik und Physik, 15, pp. 400–407 (1964).CrossRefGoogle Scholar
38. Yen, J.T., “Effect of Wall Electrical Conductance on Magnetohydrodynamic Heat Transfer in a Channel,” Journal of Heat Transfer, 85, pp. 371–377 (1963).CrossRefGoogle Scholar
39. Jagdeesan, K., “Heat Transfer due to Hydromagnetic Channel Flow with Conducting Walls,” AIAA Journal, 2, pp. 756–758 (1964).CrossRefGoogle Scholar
40. Nagy, T. and Demendy, Z., “Influence of Wall Properties on Hartmann Flow and Heat Transfer in a Rotating System,” Acta Physica Hungarica, 73, pp. 291–310 (1993).CrossRefGoogle Scholar
41. Yu, C. P. and Yang, H. K., “Effect of Wall Conductances on Convective Magnetohydro-Dynamic Channel Flow,” Applied Scientific Research, 20, pp. 16–24 (1969).CrossRefGoogle Scholar
42. Yu, C. P., “Convective Magnetohydrodynamic Flow in a Vertical channel,” Applied Scientific Research, 22, pp. 127–140 (1970).CrossRefGoogle Scholar
43. Jana, R.N., “Wall Conductance Effects on Convective Horizontal Channel Flow,” Zeitschrift für angewandte Mathematik und Physik, 26, pp. 315–324 (1975).CrossRefGoogle Scholar
44. Prasad Rao, D.R.V., Krishna, D.V. and Debnath, L., “Combined Effect of Free and Forced Convection on MHD Flow in a Rotating Porous Channel,” International Journal of Mathematics and Mathematical Sciences, 5, pp. 165–182 (1982).Google Scholar
45. Seth, G.S., Mahto, N., Ansari, Md. S. and Nandkeolyar, R., “Combined Free and Forced Convection Flow in a Rotating Channel with Arbitrary Conducting Walls,” International Journal of Engineering Science and Technology, 2, pp. 184–197 (2010).CrossRefGoogle Scholar
46. Seth, G. S. and Singh, J. K., “Mixed Convection Hydromagnetic Flow in a Rotating Channel with Hall and Wall Conductance Effects,” Applied Mathematical Modelling, 40, pp. 2783–2803 (2016).CrossRefGoogle Scholar
47. Greenspan, H. P., The Theory of Rotating Fluids, Cambridge University Press, Cambridge (1969).Google Scholar