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

David Theuri; Oluwole Daniel Makinde

doi:doi:10.11648/j.acm.20140301.11

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

David Theuri, Oluwole Daniel Makinde

Published in Applied and Computational Mathematics (Volume 3, Issue 1)

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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TY  - JOUR
T1  - Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls
AU  - David Theuri
AU  - Oluwole Daniel Makinde
Y1  - 2014/01/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140301.11
DO  - 10.11648/j.acm.20140301.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140301.11
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.
VL  - 3
IS  - 1
ER  -

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Author Information

David Theuri

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Oluwole Daniel Makinde

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls
AU  - David Theuri
AU  - Oluwole Daniel Makinde
Y1  - 2014/01/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140301.11
DO  - 10.11648/j.acm.20140301.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140301.11
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.
VL  - 3
IS  - 1
ER  -

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