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Double Diffusive Magneto-Convection Fluid Flow in a Strong Cross Magnetic Field With Uniform Surface Heat and Mass Flux

[+] Author and Article Information
Sadia Siddiqa

 Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad, 44000 Pakistansaadiasiddiqa@gmail.com

Md. Anwar Hossain1

 Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad, 44000 Pakistananwar@univdhaka.edu

Suvash C. Saha2

 School of Chemistry, Physics & Mechanical Engineering, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australias_c_saha@yahoo.com;

1

Former Professor of Mathematics, University of Dhaka, Bangladesh.

2

Corresponding author.

J. Heat Transfer 134(11), 114506 (Sep 28, 2012) (9 pages) doi:10.1115/1.4007130 History: Received September 02, 2011; Revised June 03, 2012; Published September 28, 2012; Online September 28, 2012

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. Asymptotic solutions are obtained for small (≪1) and large (≫1) values of local Hartmann parameter, ξ, through regular perturbation method and matched asymptotic expansion technique, respectively. However, for all values of ξ the boundary layer equations are transformed to a suitable form by using the free variable formulation (FVF) as well as the stream function formulation (SFF). The equations obtained through FVF are integrated via direct finite difference method together with Gaussian elimination technique while the others obtained through SFF are integrated numerically via Thomas algorithm. Discussion is carried out for fluids having small Pr ≪1. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw , rate of heat transfer, qw , and rate of mass transfer, mw , for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10.0.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate system and physical model

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Figure 2

(a) Variation of shear stress, (b) rate of heat transfer, and (c) rate of mass transfer with ξ for N = 0.0, 2.0, 5.0 while Pr = 0.054 and Sc = 10.0

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Figure 3

(a) Velocity, (b) temperature, and (c) concentration profiles for ξ = 0.0, 1.0, 3.0, 6.0, 10.0, 20.0 while Pr = 0.054, Sc = 10.0 and N = 5.0

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Figure 4

(a) Velocity, (b) temperature, and (c) concentration profiles for Sc = 1.0, 5.0, 20.0 while Pr = 0.054, ξ = 1.0 and N = 5.0

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Figure 5

(a) Velocity, (b) temperature, and (c) concentration profiles for N = 0.0, 1.0, 2.0, 5.0, 7.0, 10.0 while Pr = 0.054, ξ = 1.0 and Sc = 10.0

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Figure 6

(a) Velocity, (b) temperature, and (c) concentration profiles for Pr = 0.001, 0.054, 0.1 while N = 5.0, ξ = 1.0 and Sc = 10.0

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