Mass Transfer Effects On Nonlinear MHD Boundary Layer Flow Of Liquid Metal Over A Porous Nonlinearly Stretching Surface Through Porous Medium With Nonlinear Radiation

s mohammed ibrahim*
Department of Mathematics, Priyadarshini College of Engineering & Technology, Nellore, Andhra Pradesh, India
Periodicity:January - March'2014
DOI : https://doi.org/10.26634/jmat.3.1.2941

Abstract

The paper investigates the nonlinear radiation effects on two-dimensional, steady MHD laminar boundary layer flow with heat and mass transfer characteristic of an incompressible, viscous, electrically conducting fluid over a nonlinearly stretching surface through a porous medium. The liquid metal is assumed to be gray, emitting, and absorbing, but nonscattering medium. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with fourth order Runge-Kutta integration scheme. Pertinent results with respect to embedded parameters are displayed graphically for the velocity, temperature, concentration, skin-friction coefficient, rate of heat transfer and rate of mass transfer profiles and were discussed quantitatively.

Keywords

Nonlinear Radiation, Porous Medium, Mass Transfer, Boundary Layer, Non-Linear Stretching Surface, Variable MHD (Magnetohydrodynamics).

How to Cite this Article?

Ibrahim, S.M. (2014). Mass Transfer Effects On Nonlinear MHD Boundary Layer Flow Of Liquid Metal Over A Porous Nonlinearly Stretching Surface Through Porous Medium With Nonlinear Radiation. i-manager’s Journal on Mathematics, 3(1), 35-45. https://doi.org/10.26634/jmat.3.1.2941

References

[1]. M Arunachalam and N.R Rajappa (1978). Thermal boundary layer in liquid metals with variable thermal conductivity, Appl. Sci. Res, Vol. 34, pp. 179- 185.
[2]. B. Lubarsky and S.J Kaufman (1955). Review of Experimental investigation of Liquid metal heat transfer, Report NACA TN 3336.
[3]. R.N Lyon (1951). Liquid Metal heat transfer coefficient, Chem. Eng. Progr., Vol. 47, No. 2, pp. 75-79.
[4]. B. C. Sakiadios (1961). Boundary layer behaviour on continuous solid surfaces, American Institute of Chemical Engineers, Vol. 7, pp. 26–28.
[5]. L. E. Erickson, L.T. Fan, and V. G. Fox (1966). Heat and mass transfer on a moving continuous moving surface, Industrial & Engineering Chemistry Fundamentals, Vol. 5, pp. 19–25.
[6]. J. E. Danberg and K. S. Fansler (1979). A nonsimilar moving wall boundary-layer problem, Quarterly of Applied Mathematics, Vol. 34, pp. 305–309.
[7]. P. S. Gupta and A. S. Gupta (1977). Heat and mass transfer on a stretching sheet with suction or blowing, The Canadian Journal of Chemical Engineering, Vol. 55, pp. 744–746.
[8]. V. G. Fox, L. E. Erickson, and L.T. Fan (1969). Heat and mass transfer on a moving continuous flat plate with suction or injection, American Institute of Chemical Engineers, Vol. 15, pp. 327–333.
[9]. K. R. Rajagopal, T. Y. Na, and A. S. Gupta (1984). Flow of a viscoelastic fluid over a stretching sheet, Rheologica Acta, Vol. 23, No. 2, pp. 213–215.
[10]. W. C. Troy, E. A. Overman, II, G. B. Ermentrout, and J. P. Keener (1987). Uniqueness of flow of a second order fluid past a stretching sheet, Quarterly of Applied Mathematics, Vol. 44, No. 4, pp. 753–755.
[11]. K. Vajravelu and T. Roper (1999). Flow and heat transfer in a second grade fluid over a stretching sheet, International Journal of Non-Linear Mechanics, Vol. 34, No. 6, pp. 1031–1036.
[12]. K. Vajravelu (2001). Viscous flow over a nonlinearly stretching sheet, Applied Mathematics and Computation, Vol. 124, No. 3, pp. 281–288.
[13]. R. Cortell (2007). MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species, Chemical Engineering and Processing, Vol. 46, No. 8, pp. 721–728.
[14]. R. Cortell (2007). Viscous flow and heat transfer over a nonlinearly stretching sheet, Applied Mathematics and Computation, Vol. 184, No. 2, pp. 864–873.
[15]. R. Cortell (2008). Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Physics Letters, Section A, Vol. 372, No. 5, pp. 631–636.
[16]. D.A Nield and A Bejan (1999). Convection in Porous Media, 2nd Edition. Springer, New York.
[17]. K. Vafai (2000). Handbook of Porous Media. Marcel Dekker, New York.
[18]. I. Pop and D. B. Ingham, (2001). Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon, Elsevier Science, Oxford, UK, 2001.
[19]. R.N Barik., G.C Dash and P.K Rath (2012). Heat and Mass transfer on MHD flow through a porous medium over a stretching surface with heat source, Mathematical Theory and Modeling, Vol.2, No. 7, pp. 49-59.
[20]. S.M Alharbi., M.A.A Bazid and S.El Gendy (2010). Heat and Mass transfer in MHD visco-elastic fluid flow through a porous medium over a stretching sheet with chemical reaction, Applied Mathematics, Vol. 1, pp. 446-455.
[21]. Anuar Ishak (2011). MHD Boundary layer flow due to an exponentially stretching sheet with radiation effect, Sains Malaysiana, Vol. 40, No. 4,pp. 391-395.
[22]. O.D Makinde, and A. Ogulu (2008). The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, Vol.195, No. 12, pp. 1575-1584.
[23]. S. Shateyi and M Petersen (2008). Thermal radiation and buoyancy effects on heat and mass tra over a semi-infinite stretching surface with suction and blowing, Journal of Applied Mathematics, Vol.2, pp. 1–12 .
[24]. A.J Chamkha., H.S Thkhar and V.M Soundalgekar (2001). Radiation effects on free convection flow past a semi- infinite vertical plate with mass transfer, Chemical Engineering Journal, Vol. 84,pp. 335-342.
[25]. E.M.A. Elbashbeshy (2000). Free convection flow with variable viscosity and thermal diffusivity along a vertical plate in the presence of magnetic field, International Journal of Engineering Science, Vol.38. No.2, pp. 207-213.
[26]. A. Raptis and C. Perdikis (2006). Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field, International Journal of Non-Linear Mechanics, Vol.41, No.4, pp. 527–529.
[27]. S. Awang Kechil and I. Hashim (2008). Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field, Physics Letters, Section A, Vol. 372, No. 13, pp. 2258–2263.
[28]. Z. Abbas and T. Hayat (2008). Radiation effects on MHD flow in a porous space, International Journal of Heat and Mass Transfer, Vol. 51, No. 5-6, pp. 1024–1033.
[29]. E.M. Ouaf Mahmoud (2005). Exact solution of thermal radiation on MHD flow over a stretching porous sheet, Applied Mathematics and Computation., Vol. 170, pp. 1117-1125.
[30]. S. Mukhopadhyay, G.C. Layek and R.S.R. Gorla (2007). MHD combined convective flow and heat transfer past a porous stretching surface, International Journal of Fluid Mechanics Research, Vol. 34(3),pp. 244-257.
[31]. A.D.M Gururaj and C. Pavithra (2013). Nonlinear MHD boundary layer of a liquid metal with heat transfer over a porous stretching surface with nonlinear radiation effects, Advances in Applied Science Research, Vol. 4, No. 2, pp. 77-92.
[32]. S.P Anjali Devi and A.D.M Gururaj (2012). Effects of variable viscosity and nonlinear radiation on MHD flow with heat transfer over a surface with a power-law velocity, Advances in Applied Science Research, Vol. 3, No. 1, pp. 319-334.
[33]. S Mohammed Ibrahim., T Sankar Reddy and N Bhaskar Reddy ( 2012). Radiation and chemical reaction effects on MHD convective flow past a moving vertical porous plate, Int. J. of Applied Mathematical Analysis and Applications, Vol. 7, No.1, pp. 1-16.
[34]. T. C. Chaim. Hydromagnetic flow over a surface stretching with a power law velocity, International Journal of Engineering Science, Vol. 33, No. 3, 1995, pp. 429-435.
[35]. M. E. Ali. Heat transfer characteristics of a continuous stretching surface, Heat and Mass Transfer, Vol. 29, No. 4, pp. 227–234, 1994.
[36]. Michael Modest, (2003). Radiative Heat Transfer, 2nd ed. McGraw-Hill, New York.
[37]. M.A Hossain and I Pop, (1999). Effect of heat transfer on compressible boundary layer flow past a sphere, Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), Vol. 79, pp. 715-720.
[38]. M.K Jain., S.R.K Iyengar and R.K Jain (1985). Numerical methods for scientific and engineering computations, Wiley Eastern Ltd., New Delhi, India.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Online 15 15

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.