American Journal of Applied Mathematics

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

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.

DOI 10.11648/j.ajam.20140206.11
Published in American Journal of Applied Mathematics (Volume 2, Issue 6, December 2014)
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), 2024. 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.
Author Information
  • Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh

  • 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

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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://download.sciencepg.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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    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.
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