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Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls

Received: 23 September 2013     Published: 20 January 2014
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Abstract

The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.

Published in Applied and Computational Mathematics (Volume 3, Issue 1)
DOI 10.11648/j.acm.20140301.11
Page(s) 1-8
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), 2014. Published by Science Publishing Group

Keywords

Unsteady Couette Flow, Magnetic Field, Variable Viscosity, Permeable Walls, Heat Transfer, Entropy Generation, Bejan Number

References
[1] Paoletti, S., Rispoli, F., Sciubba, E. (1980), Calculation of exergetic losses in compact heat exchanger passages, ASME AES, 10, pp. 21-29.
[2] Wood L.C. (1975), Thermodynamics of Fluid Systems, Oxford University Press, Oxford, (1975).
[3] Bejan, A. (1982), Entropy Generation through heat and fluid flow, chapter, 2, New York, USA.
[4] Bejan, A. (1988), Advanced Engineering Thermodynamics, Wiley, USA.
[5] Jery, A.E., Hidouri, N., Magherbi, M., Brahim, A.B. (2010), Effect of an external oriented magnetic field on entropy generation in natural convection, Entropy, 12, pp. 1391-1417.
[6] Salas, H., Cuevas, S., Haro, M.L. (1999), Entropy generation analysis of magnetohydrodynamic induction devices, J. Phys D: Appl Phys. 32, pp.2605–2608.
[7] Mahmud, S., Fraser, R.A. (2004), Magnetohydrodynamic free convection and entropy generation in a square porous cavity, Int. J. Heat Mass Transfer, 47, pp. 3245–3256.
[8] Ibanez, G., Cuevas, S. (2008), Optimum wall conductance ratio in magnetoconvective flow in a long vertical rectangular duct, Int. J. Thermal Sci., 47, pp. 1012–1019.
[9] Eegunjobi A.S., Makinde O.D. (2012), Effects of Navier slip on entropy generation in a porous channel with suction/injection. Journal of Thermal Science and Technology, 7(4), 522 – 535.
[10] Makinde O.D., Eegunjobi A.S. (2013), Effects of convective heating on entropy generation rate in a channel with permeable walls. Entropy 15, 220-233.
[11] Na T.Y. (1979), Computational methods in engineering boundary value problems, Academic press, New York.
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  • APA Style

    David Theuri, Oluwole Daniel Makinde. (2014). Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls. Applied and Computational Mathematics, 3(1), 1-8. https://doi.org/10.11648/j.acm.20140301.11

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    ACS Style

    David Theuri; Oluwole Daniel Makinde. Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls. Appl. Comput. Math. 2014, 3(1), 1-8. doi: 10.11648/j.acm.20140301.11

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    AMA Style

    David Theuri, Oluwole Daniel Makinde. Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls. Appl Comput Math. 2014;3(1):1-8. doi: 10.11648/j.acm.20140301.11

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  • @article{10.11648/j.acm.20140301.11,
      author = {David Theuri and Oluwole Daniel Makinde},
      title = {Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.acm.20140301.11},
      url = {https://doi.org/10.11648/j.acm.20140301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140301.11},
      abstract = {The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.},
     year = {2014}
    }
    

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    T1  - Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls
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    AB  - The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.
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    IS  - 1
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Author Information
  • Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

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