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MHD Channel Flow with Skewed Applied Magnetic Induction Field

Received: 17 August 2014    Accepted: 30 August 2014    Published: 20 September 2014
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Abstract

The effects of the constant applied magnetic field as a function of its angle with the channel walls is studied using finite elements. This is done for insulating channel walls and for two insulating and two conducting walls forming a short-circuited magnetohydrodynamic generator. The volumetric flow rate is kept constant by regulating the pressure gradient as a function of the applied magnetic induction angle. The necessary pressure gradient diminishes as the angle increases from 0 to 45 degrees because the electrical current flow diminishes. This paper affords a simple and quick method for solving MHD generator problems that defied solution for many years.

DOI 10.11648/j.sr.20140204.12
Published in Science Research (Volume 2, Issue 4, August 2014)
Page(s) 62-77
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Magnetohydrodynamic, Generator, Channel, Insulating and Conducting Walls, Skewed Induction

References
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[3] B.Singh, J. Lal, Finite element method for MHD channel flow with arbitrary wall conductivity, J Math. Phys.Sci. 18 Applied Mathematics 2012, 2(3): 58-65 65 (1984) 501- 516.
[4] L.R.T. Gardner, G.A. Gardner, A two-dimensional bi-cubic B-spline finite element used in a study of MHD duct flow, Comput Methods Appl. Mech. Eng. 124(1995) 365- 375.
[5] M. Tezer-Sezgin, S. Koksal, FEM for solving MHD flow in a rectangular duct, Int. J. Numer. Meth. Fluids 28 (1989) 445-459.
[6] Z. Demendy, T. Nagy, A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers, Acta Mechanica 123 (1997) 135- 149.
[7] K.E. Barrett, Duct flow with a transverse magnetic field at high Hart- mann numbers. Int. J. Numer. Meth. Fluids 50 (2001) 1893-1906.
[8] M. Tezer-Sezgin, BEM solution of MHD flow in a rectangular duct, Internat. J. Numer. Methods Fluids 18 (1994) 937-952.
[9] H.W. Liu, S.P. Zhu, The dual reciprocity boundary element method for magnetohydrodynamic channel flows, ANZIAM J. 44 (2) (2002) 305-322.
[10] A. Carabineanu, A. Dinu, I. Oprea, The application of the boundary element method to magnetohydrodynamic duct flow, ZAMP 46 (1995) 971-981.
[11] C. Bozkaya, M. Tezer-Sezgin, Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme, Int. J. Numer. Meth. Fluids 51 (2006) 567-584.
[12] M. Tezer-Sezgin, Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method, Computers 8 Fluids 33 (2004) 533-547.
[13] H. Korogulu, Chebyshev series solution of linear Fredholm integrodifferential equations, Int. J. Math.Educ.Sci.Techno. 29(4) (1998) 489-500.
[14] M. Dehghan, D. Mirzaei, Meshless local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes, Comput. Phys. Commun. 180/9 (2009) 1458-1466.
[15] I. QELIK, Solution of magnetohydrodynamic flow in a rectangular duct by Chebyshev collocation method, International Journal for Numerical Methods in Fluids, 66 (2011) 1325-1340.
[16] C. C. Chang and T. S. Lundgren, Duct flow in magnetohydrodynamics, Z. angew. Math. Phys. 12 p. 100 (1961)
[17] R. R. Gold, Magnetohydrodynamic pipe flow, Part 1, J. Fluid Mech., 13 p. 505 (1962). This paper has a rather complete list of references.
[18] F. J. Young and J. F. Osterle, on the load capacity of hydromagnetically lubricated slider bearing, Wear, 5, p. 227 (1962).
[19] W. F. Hughes and F. J. Young, The electromagnetodynamics of Fluids, John Wiley 8 Sons, Inc. New York (1966) Library of Congress Catalog Number 66-17621.
[20] F. J. Young, The calculation of magnetically induced electromotive force, Xlibris, ISBN 1-4797-3789-5 (2012).
[21] J. A. Shercliff, Steady motion conducting fluids in pipes under transverse magnetic fields, Proc. Cambridge Philos. Soc. 49 (1953) 136-144.
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Author Information
  • Department of Communications and Arts, University of Pittsburgh at Bradford, PA

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    Frederick J. Young. (2014). MHD Channel Flow with Skewed Applied Magnetic Induction Field. Science Research, 2(4), 62-77. https://doi.org/10.11648/j.sr.20140204.12

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    Frederick J. Young. MHD Channel Flow with Skewed Applied Magnetic Induction Field. Sci. Res. 2014, 2(4), 62-77. doi: 10.11648/j.sr.20140204.12

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    Frederick J. Young. MHD Channel Flow with Skewed Applied Magnetic Induction Field. Sci Res. 2014;2(4):62-77. doi: 10.11648/j.sr.20140204.12

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  • @article{10.11648/j.sr.20140204.12,
      author = {Frederick J. Young},
      title = {MHD Channel Flow with Skewed Applied Magnetic Induction Field},
      journal = {Science Research},
      volume = {2},
      number = {4},
      pages = {62-77},
      doi = {10.11648/j.sr.20140204.12},
      url = {https://doi.org/10.11648/j.sr.20140204.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sr.20140204.12},
      abstract = {The effects of the constant applied magnetic field as a function of its angle with the channel walls is studied using finite elements. This is done for insulating channel walls and for two insulating and two conducting walls forming a short-circuited magnetohydrodynamic generator. The volumetric flow rate is kept constant by regulating the pressure gradient as a function of the applied magnetic induction angle. The necessary pressure gradient diminishes as the angle increases from 0 to 45 degrees because the electrical current flow diminishes. This paper affords a simple and quick method for solving MHD generator problems that defied solution for many years.},
     year = {2014}
    }
    

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    AU  - Frederick J. Young
    Y1  - 2014/09/20
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    N1  - https://doi.org/10.11648/j.sr.20140204.12
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    AB  - The effects of the constant applied magnetic field as a function of its angle with the channel walls is studied using finite elements. This is done for insulating channel walls and for two insulating and two conducting walls forming a short-circuited magnetohydrodynamic generator. The volumetric flow rate is kept constant by regulating the pressure gradient as a function of the applied magnetic induction angle. The necessary pressure gradient diminishes as the angle increases from 0 to 45 degrees because the electrical current flow diminishes. This paper affords a simple and quick method for solving MHD generator problems that defied solution for many years.
    VL  - 2
    IS  - 4
    ER  - 

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