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Research Papers: Natural and Mixed Convection

Uniform Solution on the Combined Effect of Magnetic Field and Internal Heat Generation on Rayleigh–Bénard Convection in Micropolar Fluid

[+] Author and Article Information
I. K. Khalid, N. M. Arifin

Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Malaysia

N. F. M. Mokhtar

Centre of Foundation Studies,
Universiti Putra Malaysia,
43400 UPM, Serdang, Malaysia
e-mail: norfadzillah.mokhtar@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received September 18, 2012; final manuscript received May 4, 2013; published online September 11, 2013. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 135(10), 102502 (Sep 11, 2013) (6 pages) Paper No: HT-12-1510; doi: 10.1115/1.4024576 History: Received September 18, 2012; Revised May 04, 2013

Combined effect of magnetic field and internal heat generation on the onset of Rayleigh–Bénard convection in a horizontal micropolar fluid layer is studied. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid, and free-free with combination isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. The influence of various parameters on the onset of convection has been analyzed. It is shown that the presence of magnetic field always has a stability effect on the Rayleigh–Bénard convection in micropolar fluid.

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References

Figures

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Fig. 1

Schematic diagram of Rayleigh–Bénard situation for micropolar fluid

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Fig. 2

Variation of Ra with a for different values of H and Q = 0

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Fig. 3

Variation of Ra with a for different values of Q and H = 0

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Fig. 4

Variation of Rac with different values of H when Q = 0, Q = 5, and Q = 20

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Fig. 5

Critical Rayleigh number, Rac, as a function of coupling parameter, N1 for different values of H

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Fig. 6

Critical Rayleigh number, Rac, as a function of coupling parameter, N3, for different values of H

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Fig. 7

Critical Rayleigh number, Rac, as a function of coupling parameter, N5, for different values of H

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