Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface

Sujon Nath; Nazma Parveen

doi:doi:10.11648/j.ajam.20140206.11

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Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface

Sujon Nath, Nazma Parveen

Published in American Journal of Applied Mathematics (Volume 2, Issue 6)

Received: 13 November 2014 Accepted: 24 November 2014 Published: 27 November 2014

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Abstract

In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.ajam.20140206.11
Page(s)	197-203
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

Viscous Dissipation, MHD, Heat Generation, Natural Convection, Keller Box Method, Wavy Surface

References

[1]	L. S. Yao, “Natural convection along a vertical wavy surface”, ASME J. Heat Transfer, Vol. 105, pp. 465–468, 1983.
[2]	M.A. Hossain and D.A.S. Rees, “Combined heat and mass transfer in natural convection flow from a vertical wavy surface”, Acta Mechanica, Vol. 136, pp. 133–141, 1999.
[3]	C. C. Wang and C. K. Chen, “Transient force and free convection along a vertical wavy surface in micropolar fluid”, Int. J. Heat Mass Transfer, Vol. 44, pp. 3241–3251, 2001.
[4]	M.A. Hossain, S. Kabir and D.A.S. Rees, “Natural convection of fluid with variable viscosity from a heated vertical wavy surface”, Z. Angew. Math. Phys., Vol. 53, pp. 48–52, 2002.
[5]	J.H. Jang, W.M. Yan and H. C. Liu, “Natural convection heat and mass transfer along a vertical wavy surface”, Int. J. Heat Mass Transfer, Vol. 46, pp. 1075–1083, 2003.
[6]	M. M. Molla, M. A. Hossain and L. S. Yao, “Natural Convection Flow along a Vertical Wavy Surface with Uniform Surface Temperature in Presence of Heat Generation/Absorption”, Int. J. Therm. Sci., vol. 43, pp. 157-163, 2004
[7]	M.M. Molla and M.A. Hossain, “Radiation effect on mixed convection laminar flow along a vertical wavy surface”, Int. J. Thermal Sciences, Vol. 46, pp. 926–935, 2007.
[8]	Md.M.Alam, M.A.Alim and Md.M.K.Chowdhury, “Viscous Dissipation Effects on MHD Natural Convection Flow over a Sphere in the Presence of Heat Generation”, Nonlinear Analysis:Modelling and Con troll,Vol.12,No.4,447-459,2007
[9]	A. A. Mamun, Z. R. Chowdhury, M. A. Azim and M. M. Molla, “MHD–Conjugate Heat Transfer Analysis for a Vertical Flat Plate in Presence of Viscous Dissipation and Heat Generation”, Int. comm. Heat Transfer, vol. 35, pp. 1275-1280, 2008.
[10]	B.K. Jha and A.O. Ajibade, “Effect of viscous dissipation on natural convection flow between vertical parallel plates with time-periodic boundary conditions”, J. Thermophysics and Aeromechanics, Vol.18, Issue 4, pp 561-571, 2011.
[11]	N. Parveen and M.A. Alim, “Joule heating and MHD free convection flow along a vertical wavy surface with viscosity and thermal conductivity dependent on temperature”, J. Naval Architecture and Marine Engineering, Vol. 10 (2), pp. 81–98, 2013.
[12]	H. B. Keller, “Numerical methods in boundary layer theory”, Ann. Rev. Fluid Mech., Vol. 10, pp. 417-433, 1978.

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APA Style

Sujon Nath, Nazma Parveen. (2014). Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. American Journal of Applied Mathematics, 2(6), 197-203. https://doi.org/10.11648/j.ajam.20140206.11

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ACS Style

Sujon Nath; Nazma Parveen. Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. Am. J. Appl. Math. 2014, 2(6), 197-203. doi: 10.11648/j.ajam.20140206.11

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AMA Style

Sujon Nath, Nazma Parveen. Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. Am J Appl Math. 2014;2(6):197-203. doi: 10.11648/j.ajam.20140206.11

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@article{10.11648/j.ajam.20140206.11,
  author = {Sujon Nath and Nazma Parveen},
  title = {Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {197-203},
  doi = {10.11648/j.ajam.20140206.11},
  url = {https://doi.org/10.11648/j.ajam.20140206.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.11},
  abstract = {In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.},
 year = {2014}
}

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TY  - JOUR
T1  - Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface
AU  - Sujon Nath
AU  - Nazma Parveen
Y1  - 2014/11/27
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140206.11
DO  - 10.11648/j.ajam.20140206.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 197
EP  - 203
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.11
AB  - In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.
VL  - 2
IS  - 6
ER  -

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Author Information

Sujon Nath

Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh
Nazma Parveen

Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh

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APA Style

Sujon Nath, Nazma Parveen. (2014). Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. American Journal of Applied Mathematics, 2(6), 197-203. https://doi.org/10.11648/j.ajam.20140206.11

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ACS Style

Sujon Nath; Nazma Parveen. Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. Am. J. Appl. Math. 2014, 2(6), 197-203. doi: 10.11648/j.ajam.20140206.11

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AMA Style

Sujon Nath, Nazma Parveen. Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface. Am J Appl Math. 2014;2(6):197-203. doi: 10.11648/j.ajam.20140206.11

Copy | Download

@article{10.11648/j.ajam.20140206.11,
  author = {Sujon Nath and Nazma Parveen},
  title = {Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {197-203},
  doi = {10.11648/j.ajam.20140206.11},
  url = {https://doi.org/10.11648/j.ajam.20140206.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.11},
  abstract = {In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface
AU  - Sujon Nath
AU  - Nazma Parveen
Y1  - 2014/11/27
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140206.11
DO  - 10.11648/j.ajam.20140206.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 197
EP  - 203
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.11
AB  - In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.
VL  - 2
IS  - 6
ER  -

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