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International Journal of Applied Mechanics and Engineering

The Journal of University of Zielona Góra

Editor-in-Chief: Walicki, Edward

4 Issues per year

CiteScore 2016: 0.12

SCImago Journal Rank (SJR) 2016: 0.127
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Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

K.D. Singh
Published Online: 2016-09-10 | DOI: https://doi.org/10.1515/ijame-2016-0040


An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., T*(y*,z*,t*)=T1+(T2T1)cos(πz*dω*t*) . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

Keywords: magnetohydrodynamics (MHD); span-wise cosinusoidal; convective; porous medium; radiation


  • [1]

    Nield D.A. and Bejan A. (2006): Convection in Porous Media. – New York: Springer.Google Scholar

  • [2]

    Raptis A.A. (1983): Unsteady free convection flow through a porous medium. – Int. J. Engineering. Sci., vol.21, pp.345.CrossrefGoogle Scholar

  • [3]

    Raptis A.A. and Perdikis C.P. (1985): Oscillatory flow through a porous medium by the presence of free convective flow. – Int. J. Engineering. Sci., vol.23, pp.51-55.Google Scholar

  • [4]

    Parsuma T.G., Murthy M.V.R., Ramachryulu N.C.P. and Rao G.V. (2010): Unsteady flow of a viscoelastic fluid through a porous media between two impermeable parallel plates. – J. of Emerging Trends in Engineering and Applied Sciences, vol.1, No.2, pp.220-224.Google Scholar

  • [5]

    Rajgopal K.R. (1983): On Stoke’s problem for non-Netonian fluid. – Acta Mech., vol.48 pp.223-239.Google Scholar

  • [6]

    Pillai K.M.C., Sai K.S., Swamy N.S., Natraja H.R., Tiwari S.B. and Rao B.N. (2004): Heat transfer in a viscoelastic boundary layer flow through porous medium. – Comput. Mech. vol.34, pp.27-37.Google Scholar

  • [7]

    Hossain M.A. and Takhar H.S. (1996): Radiation effect on mixed convection along a vertical plate with uniform surface temperature. – Heat and Mass Transfer, vol.31, pp.243-248.Google Scholar

  • [8]

    Rajgopal K., Veena P.H. and Pravin V.K. (2006): Oscillatory motion of an electrically conducting visco-elastic fluid over a stretching sheet in saturated porous medium with suction/blowing. – Mathematical Problem in Engineering, vol.1, pp.1-14.Google Scholar

  • [9]

    Singh K.D. (2011): Exact solution of an oscillatory MHD flow in a channel filled with porous medium. – Int. J. Applied Mechanics and Engineering, vol.16, pp.277-283.Google Scholar

  • [10]

    Rahman M.M. and Sarkar M.S.A. (2004): Unsteady MHD flow of visco-elastic Oldroyd fluid under time varying body force through a rectangular channel. – Bulletin of Calcutta Mathematical Society, vol.96, pp.463-470.Google Scholar

  • [11]

    Singh A.K. and Singh N.P. (1996): MHD flow of a dusty visco-elastic liquid through a porous medium between two inclined parallel plates. – Proceeding of National Academy of Sciences India, vol.66A, pp.143.Google Scholar

  • [12]

    Attia Hazem Ali and Karem Mahmoud Ewis (2010): Unsteady MHD Couette flow with heat transfer of a viscoelastic fluid under exponential decaying pressure gradient. – Tankang J. Sci. And Engng., vol.13, pp.359-364.Google Scholar

  • [13]

    Choudhary R. and Das U.J. (2012): Heat transfer to MHD oscillatory viscoelastic flow in a channel filled with porous medium. – Physics Research International, .CrossrefGoogle Scholar

  • [14]

    Makinde O.D. and Mhone P.Y. (2005): Heat transfer to MHD oscillatory flow in a channel filled with porous medium. – Rom. Journ. Phys., vol.50, pp.931-938.Google Scholar

  • [15]

    Singh K.D. (2012): Viscoelastic mixed convection MHD oscillatory flow through a porous medium filled in a vertical channel. – Int. J. of Phy. And Math. Sci., vol.3, pp.194-205.Google Scholar

  • [16]

    Singh K.D. (2013): Effect of slip condition on viscoelastic MHD oscillatory forced convection flow in a vertical channel with heat radiation. – Int. J. of Appl. Mech. and Engng., vol.18, No.4, pp.1237-1248.Google Scholar

  • [17]

    Malikov G.K., Lovanov D.L., Malikov K.Y., Lisienko G.V., Viskanta R. and Fedorov A.G. (2001): Direct flame impingement heating for rapid thermal materials processing. – Int. J. Heat and Mass Transfer, vol.44, pp.1751-1758.Google Scholar

  • [18]

    Fedorov A.G., Lee K.H. and Viskanta R. (1998): Inverse optimal design of the radiant heating in materials processing and manufacturing. – J. Materials Engineering and Performance, vol.7, pp.719-726.Google Scholar

  • [19]

    Lentes F.T. and Siedow N. (1999): Three-dimensional radiative heat transfer in glass cooling processes. – Glass Sci. Technology: Glastechnische Berichte, vol.72, No.6, pp.188-196.Google Scholar

  • [20]

    Singh K.D. (1992): Unsteady free convection flow past a hot vertical porous plate with variable temperature. – Proc. Indian Natn. Sci. Acad., vol.58, pp.537-544.Google Scholar

  • [21]

    Singh K.D. and Khem Chand (2000): Unsteady free convective MHD flow past a vertical porous plate with variable temperature. – Proc. Nat. Acad. Sci. India, vol.70, pp.49-58.Google Scholar

  • [22]

    Sumathi K., Anuradha S. and Arunachalam T. (2011): Heat and mass transfer in an unsteady three dimensional mixed convection flow past an infinite vertical porous plate with cosinusoidally fluctuating temperature. – International J. Engineering Science and Technology, vol.3, pp.8569-8578.Google Scholar

  • [23]

    Kumar R. and Singh K.D. (2011): Unsteady MHD flow of radiating and reacting fluid past a vertical porous plate with cosinusoidally fluctuating temperature. – International J. Appl. Math. and Mech., vol.7, pp.19-35.Google Scholar

  • [24]

    Coleman B.D. and Noll W. (1960): An approximation theorem for functional, with applications in continuum mechanics. – Archive for Rational Mechanics and Analysis, vol.6, pp.355-370.Google Scholar

  • [25]

    Markovitz H. and Coleman B.D. (1964): Incompressible second order fluids. – Advances in Applied Mechanics, vol.8, pp.69-101.Google Scholar

  • [26]

    Raptis A.A., Perdikis C. and Leontitsis K. (2003): Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field. – Heat and Mass Transfer, vol.39, pp.771-773. .CrossrefGoogle Scholar

About the article

Received: 2014-08-22

Revised: 2016-06-15

Published Online: 2016-09-10

Published in Print: 2016-08-01

Citation Information: International Journal of Applied Mechanics and Engineering, Volume 21, Issue 3, Pages 667–681, ISSN (Online) 2353-9003, ISSN (Print) 1734-4492, DOI: https://doi.org/10.1515/ijame-2016-0040.

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© 2016 K.D. Singh, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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