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Research Papers: Fundamental Issues and Canonical Flows

# Natural Convection Flow in a Strong Cross Magnetic Field With Radiation

[+] Author and Article Information
S. Siddiqa

Assistant Professor
Department of Mathematics,
COMSATS Institute of Information Technology,
43600 Attock, Pakistan

M. A. Hossain

Rtd. Professor
Department of Mathematics,
University of Dhaka,
e-mail: anwar@univdhaka.edu

Suvash C. Saha

Postdoctoral Research Fellow
School of Chemistry, Physics
and Mechanical Engineering,
Queensland University of Technology,
GPO Box 2434,
Brisbane, QLD 4001, Australia
e-mail: s_c_saha@yahoo.com;
suvash.saha@qut.edu.au

1Corresponding author.

Manuscript received July 21, 2012; final manuscript received January 31, 2013; published online April 8, 2013. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 135(5), 051202 (Apr 08, 2013) (9 pages) Paper No: FE-12-1338; doi: 10.1115/1.4023854 History: Received July 21, 2012; Revised January 31, 2013

## Abstract

The problem of magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed in the presence of strong cross magnetic field with radiative heat transfer. In the analysis radiative heat flux is considered by adopting optically thick radiation limit. Attempt is made to obtain the solutions valid for liquid metals by taking Pr $≪1$. Boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation (SFF) and primitive variable formulation (PVF). Nonsimilar equations obtained from SFF are then simulated by implicit finite difference (Keller-box) method whereas parabolic partial differential equations obtained from PVF are integrated numerically by hiring direct finite difference method over the entire range of local Hartmann parameter, $ξ$. Further, asymptotic solutions are also obtained for large and small values of local Hartmann parameter $ξ$. A favorable agreement is found between the results for small, large and all values of $ξ$. Numerical results are also demonstrated graphically by showing the effect of various physical parameters on shear stress, rate of heat transfer, velocity, and temperature.

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## References

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## Figures

Fig. 1

Coordinate system and physical model

Fig. 2

(a) Variation of shear stress and (b) rate of heat transfer with ξ for Rd=0.0, 1.0, 2.0 while Pr = 0.05 and θw=1.1

Fig. 3

(a) Variation of shear stress and (b) rate of heat transfer with ξ for Pr = 0.005, 0.01, 0.05, Rd=1.0 and θw=1.1

Fig. 4

(a) Variation of shear stress and (b) rate of heat transfer with ξ for Rd=0.0, 1.0, 4.0 while Pr = 0.05 and θw=2.0

Fig. 5

(a) Variation of shear stress and (b) rate of heat transfer with ξ for θw=1.1, 2.0, 3.0 while Pr = 0.05 and Rd=2.0

Fig. 6

(a) Velocity profile and (b) temperature profile for Rd=0.0, 1.0, 2.0 and θw=1.1, 1.7 while Pr = 0.05 and ξ=1.0

Fig. 7

(a) Velocity profile and (b) temperature profile for ξ=0.0, 1.0, 10.0 while Pr = 0.05, Rd=1.0 and θw=1.1

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