Effect of Hall Currents and Variable Fluid Properties on MHD Flow past Stretching Vertical Plate by the Presence of Radiation
Author(s)
Khaled K. Jaber*
Affiliation(s)
Department of Mathematics, Faculty of Science and Information Technology, Zarqa University, Zarqa, Jordan.
Department of Mathematics, Faculty of Science and Information Technology, Zarqa University, Zarqa, Jordan.
ABSTRACT
This paper investigates the effects of Hall currents
and radiation on free-convective steady laminar boundary-layer flow past a semi-infinite vertical plate for large
temperature differences. A uniform magnetic field is applied perpendicular to
the plate. The fluid density is assumed to vary exponentially and the thermal
conducting linearly with temperature. The fluid viscosity is assumed to vary as
a reciprocal of a linear function of temperature. The usual Boussinesq
approximation is neglected. The nonlinear boundary layer equations governing
the problem under consideration are solved numerically by applying an efficient
numerical technique based on the shooting method. The effects of the magnetic
parameter , the Hall parameter m, the density/temperature
parameter n, the radiation parameter N , the thermal conductivity parameter S, the viscosity temperature 
, and the temperature ratio parameter 
are examined on
the velocity and temperature distribution as well as the coefficient of heat
flux and shearing stress at the plate.
Cite this paper
Jaber, K. (2014) Effect of Hall Currents and Variable Fluid Properties on MHD Flow past Stretching Vertical Plate by the Presence of Radiation. Journal of Applied Mathematics and Physics, 2, 888-902. doi: 10.4236/jamp.2014.29101.
Jaber, K. (2014) Effect of Hall Currents and Variable Fluid Properties on MHD Flow past Stretching Vertical Plate by the Presence of Radiation. Journal of Applied Mathematics and Physics, 2, 888-902. doi: 10.4236/jamp.2014.29101.
References
[1] Sakiadis, B.C. (1961) Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow. AIChE Journal, 7, 26-28.
http://dx.doi.org/10.1002/aic.690070108 [2] Erickson, L.E., Fan, L.T. and Fox, V.G. (1966) Heat and Mass Transfer on Moving Continuous Flat Plate with Suction or Injection. Industrial and Engineering Chemistry Fundamentals, 5, 19.
http://dx.doi.org/10.1021/i160017a004 [3] Cogley, A.C., Vinecti, W.G. and Gilles, S.E. (1968) Differential Approximation for Radiative Transfer in a Nongrey Gas near Equilibrium. AIAA Journal, 6, 551. [4] Varjavelu, K. and Hadyinicolaou, A. (1997) Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching Surface with Uniform Free Stream. International Journal of Engineering Science, 35, 1237. [5] Griffith, R.M. (1964) Velocity, Temperature, and Concentration Distributions during Fiber Spinning. Industrial and Engineering Chemistry Fundamentals, 3, 245-250. http://dx.doi.org/10.1021/i160011a013 [6] Chin, D.T. (1975) Mass Transfer to a Continuous Moving Sheet Electrode. Journal of the Electrochemical Society, 122, 643-646. http://dx.doi.org/10.1149/1.2134281 [7] Gupta, P.S. and Gupta, A.S. (1977) Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing. The Canadian Journal of Chemical Engineering, 55, 744-746.
http://dx.doi.org/10.1002/cjce.5450550619 [8] Gorla, R.S.R. (1978) Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrode. Journal of the Electrochemical Society, 125, 865-869. http://dx.doi.org/10.1149/1.2131569 [9] Chakabarti, A. and Gupta, A.S. (1979) Hydromagnetic Flow and Heat Transfer over a Stretching Sheet. The Quarterly of Applied Mathematics, 37, 73. [10] Rajagobal, K.R., Na, T.Y. and Gupta, A.S. (1987) A Non-Similar Boundary Layer on a Stretching Sheet in a Non-Newtonian Fluid with Uniform Free Stream. Journal of Mathematical and Physical Sciences, 21, 189. [11] Chamkha, A.J. (1999) Hydromagnetic Three-Dimensional Free Convection on a Vertical Stretching Surface with Heat Generation or Absorption. International Journal of Heat and Fluid Flow, 20, 84-92.
http://dx.doi.org/10.1016/S0142-727X(98)10032-2 [12] Elbashbashy, E.M.A. (1998) Heat Transfer over a Stretching Surface with Variable Surface Heat Flux. Journal of Physics D: Applied Physics, 31, 1951. [13] Lai, F.C. and Kulaki, F.A. (1990) The Effect of Variable Viscosity on Convective Heat Transfer along a Vertical Surface in a Saturated Porous Medium. International Journal of Heat and Mass Transfer, 33, 1028-1031.
http://dx.doi.org/10.1016/0017-9310(90)90084-8 [14] Jaber, K.K. and Al-Athari, F. (2014) Hall Current Effect on Unsteady MHD Flow between Two Horizontal Plates with Constant Suction. IJARET, 5, 1. [15] Pop, I. and Watanabe, T. (1993) Magnetohydrodynamic Free Convection Flow over a Wedge in the Presence of a Transverse Magnetic Field. International Communications in Heat and Mass Transfer, 20, 871-881.
http://dx.doi.org/10.1016/0735-1933(93)90040-3 [16] Abo-Eldahab, E.M. (2001) Hall Effects on Magnetohydrodynamic Free-Convection Flow at a Stretching Surface with a Uniform Free-Stream. Physica Scripta, 63, 29-35.
http://dx.doi.org/10.1238/Physica.Regular.063a00029 [17] Khaled, K. (2013) Non Newtonian Fluid Flow under the Effect of Chemical Reaction and Ion and Hall Currents over a Moving Cylinder. Jaber Journal of Purity, Utility Reaction and Environment, 2, 1-13. [18] El-Hakiem, M.A., Mohammadein, A.A. and El-Kabeir, S.M.M. (1999) Joule Heating Effects on Magnetohydrodynamic Free Convection Flow of a Micropolar Fluid. International Communications in Heat and Mass Transfer, 26, 219-227. [19] Sparrow, E.M. and Cess, R.D. (1978) Radiation Heat Transfer. Hemisphere Publishing Corporation, Washington DC. [20] Kakac, S. and Yener, Y. (1995) Convective Heat Transfer. CRC Press, Boca Raton, 312. [21] Aboeldahab, E.M. (2004) The Effects of Temperature-Dependent Fluid Properties on Free Convective Flow along a Semi-Infinite Vertical Plate by the Presence of Radiation. Heat Mass Transfer, 41, 163. [22] Jaber, K.K. (2012) Transient MHD Mixed Double Diffusive Convection along a Vertical Plate Embedded in a Non-Darcy Porous Medium with Suction or Injection. Journal of Mathematics and Statistics, 8, 1. [23] Aboeldahab, E.M. and El-Gendy, M.S. (2000) Radiation Effect on Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching Surface with Variable Viscosity and Uniform Free Stream. Physica Scripta, 62, 321.
http://dx.doi.org/10.1238/Physica.Regular.062a00321 [24] Aboeldahab, E.M. and Salem, A.M. (2001) Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-Infinite Vertical Plate with Variable Viscosity. International Journal of Computational Fluid Dynamics, 14, 243-252.
http://dx.doi.org/10.1080/10618560108940727
[1] Sakiadis, B.C. (1961) Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow. AIChE Journal, 7, 26-28.
http://dx.doi.org/10.1002/aic.690070108 [2] Erickson, L.E., Fan, L.T. and Fox, V.G. (1966) Heat and Mass Transfer on Moving Continuous Flat Plate with Suction or Injection. Industrial and Engineering Chemistry Fundamentals, 5, 19.
http://dx.doi.org/10.1021/i160017a004 [3] Cogley, A.C., Vinecti, W.G. and Gilles, S.E. (1968) Differential Approximation for Radiative Transfer in a Nongrey Gas near Equilibrium. AIAA Journal, 6, 551. [4] Varjavelu, K. and Hadyinicolaou, A. (1997) Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching Surface with Uniform Free Stream. International Journal of Engineering Science, 35, 1237. [5] Griffith, R.M. (1964) Velocity, Temperature, and Concentration Distributions during Fiber Spinning. Industrial and Engineering Chemistry Fundamentals, 3, 245-250. http://dx.doi.org/10.1021/i160011a013 [6] Chin, D.T. (1975) Mass Transfer to a Continuous Moving Sheet Electrode. Journal of the Electrochemical Society, 122, 643-646. http://dx.doi.org/10.1149/1.2134281 [7] Gupta, P.S. and Gupta, A.S. (1977) Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing. The Canadian Journal of Chemical Engineering, 55, 744-746.
http://dx.doi.org/10.1002/cjce.5450550619 [8] Gorla, R.S.R. (1978) Unsteady Mass Transfer in the Boundary Layer on a Continuous Moving Sheet Electrode. Journal of the Electrochemical Society, 125, 865-869. http://dx.doi.org/10.1149/1.2131569 [9] Chakabarti, A. and Gupta, A.S. (1979) Hydromagnetic Flow and Heat Transfer over a Stretching Sheet. The Quarterly of Applied Mathematics, 37, 73. [10] Rajagobal, K.R., Na, T.Y. and Gupta, A.S. (1987) A Non-Similar Boundary Layer on a Stretching Sheet in a Non-Newtonian Fluid with Uniform Free Stream. Journal of Mathematical and Physical Sciences, 21, 189. [11] Chamkha, A.J. (1999) Hydromagnetic Three-Dimensional Free Convection on a Vertical Stretching Surface with Heat Generation or Absorption. International Journal of Heat and Fluid Flow, 20, 84-92.
http://dx.doi.org/10.1016/S0142-727X(98)10032-2 [12] Elbashbashy, E.M.A. (1998) Heat Transfer over a Stretching Surface with Variable Surface Heat Flux. Journal of Physics D: Applied Physics, 31, 1951. [13] Lai, F.C. and Kulaki, F.A. (1990) The Effect of Variable Viscosity on Convective Heat Transfer along a Vertical Surface in a Saturated Porous Medium. International Journal of Heat and Mass Transfer, 33, 1028-1031.
http://dx.doi.org/10.1016/0017-9310(90)90084-8 [14] Jaber, K.K. and Al-Athari, F. (2014) Hall Current Effect on Unsteady MHD Flow between Two Horizontal Plates with Constant Suction. IJARET, 5, 1. [15] Pop, I. and Watanabe, T. (1993) Magnetohydrodynamic Free Convection Flow over a Wedge in the Presence of a Transverse Magnetic Field. International Communications in Heat and Mass Transfer, 20, 871-881.
http://dx.doi.org/10.1016/0735-1933(93)90040-3 [16] Abo-Eldahab, E.M. (2001) Hall Effects on Magnetohydrodynamic Free-Convection Flow at a Stretching Surface with a Uniform Free-Stream. Physica Scripta, 63, 29-35.
http://dx.doi.org/10.1238/Physica.Regular.063a00029 [17] Khaled, K. (2013) Non Newtonian Fluid Flow under the Effect of Chemical Reaction and Ion and Hall Currents over a Moving Cylinder. Jaber Journal of Purity, Utility Reaction and Environment, 2, 1-13. [18] El-Hakiem, M.A., Mohammadein, A.A. and El-Kabeir, S.M.M. (1999) Joule Heating Effects on Magnetohydrodynamic Free Convection Flow of a Micropolar Fluid. International Communications in Heat and Mass Transfer, 26, 219-227. [19] Sparrow, E.M. and Cess, R.D. (1978) Radiation Heat Transfer. Hemisphere Publishing Corporation, Washington DC. [20] Kakac, S. and Yener, Y. (1995) Convective Heat Transfer. CRC Press, Boca Raton, 312. [21] Aboeldahab, E.M. (2004) The Effects of Temperature-Dependent Fluid Properties on Free Convective Flow along a Semi-Infinite Vertical Plate by the Presence of Radiation. Heat Mass Transfer, 41, 163. [22] Jaber, K.K. (2012) Transient MHD Mixed Double Diffusive Convection along a Vertical Plate Embedded in a Non-Darcy Porous Medium with Suction or Injection. Journal of Mathematics and Statistics, 8, 1. [23] Aboeldahab, E.M. and El-Gendy, M.S. (2000) Radiation Effect on Convective Heat Transfer in an Electrically Conducting Fluid at a Stretching Surface with Variable Viscosity and Uniform Free Stream. Physica Scripta, 62, 321.
http://dx.doi.org/10.1238/Physica.Regular.062a00321 [24] Aboeldahab, E.M. and Salem, A.M. (2001) Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-Infinite Vertical Plate with Variable Viscosity. International Journal of Computational Fluid Dynamics, 14, 243-252.
http://dx.doi.org/10.1080/10618560108940727