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Research Papers

Effect of Boundary Conditions on the Onset of Thermomagnetic Convection in a Ferrofluid Saturated Porous Medium

[+] Author and Article Information
I. S. Shivakumara1

Department of Mathematics, UGC-Centre for Advanced Studies in Fluid Mechanics, Bangalore University, Bangalore 560 001, Indiashivakumarais@gmail.com

C. E. Nanjundappa

Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore 560 056, Indiacenanju@hotmail.com

M. Ravisha

Department of Mathematics, East Point College of Engineering and Technology, Bangalore 560 049, Indiapmravisha@yahoo.co.in

1

Corresponding author.

J. Heat Transfer 131(10), 101003 (Jul 28, 2009) (9 pages) doi:10.1115/1.3160540 History: Received September 20, 2008; Revised March 14, 2009; Published July 28, 2009

The onset of thermomagnetic convection in a ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated for a variety of velocity and temperature boundary conditions. The Brinkman–Lapwood extended Darcy equation, with fluid viscosity different from effective viscosity, is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective-radiative exchange at the upper boundary, which encompasses fixed temperature and heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by using regular perturbation technique when both boundaries are insulated to temperature perturbations. It is found that the increase in the Biot number and the viscosity ratio, and the decrease in the magnetic as well as in the Darcy number is to delay the onset of ferroconvection. Besides, the nonlinearity of fluid magnetization has no effect on the onset of convection in the case of fixed heat flux boundary conditions.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 2

Variation in critical Rayleigh number Rc as a function of Da−1 for different values of Bi when M3=1, M1=5, and Λ=1

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Figure 11

Vertical velocity eigenfunctions for different values of Da−1 when M1=2 and Λ=2

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Figure 12

Vertical velocity eigenfunctions for different values of Λ when M1=2 and Da−1=25

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Figure 13

Vertical velocity eigenfunctions for different values of M1 when Λ=2 and Da−1=25

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Figure 3

Variation in critical Rayleigh number Rc as a function of Da−1 for different values of Λ when M3=1, M1=5, and Bi=2

Grahic Jump Location
Figure 4

Variation in critical Rayleigh number Rc as a function of Da−1 for different values of M1 when M3=1, Λ=5, and Bi=2

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Figure 5

Variation in critical Rayleigh number Rc as a function of Da−1 for different values of M3 when M1=5, Λ=6, and Bi=2

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Figure 6

Variation in critical Rayleigh number Rc as a function of Nc for different values of M3 when Da−1=100, Λ=6, and Bi=2

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Figure 7

Variation in critical wave number ac as a function of Da−1 for different values of Bi when M3=1, M1=5, and Λ=1

Grahic Jump Location
Figure 8

Variation in critical wave number ac as a function of Da−1 for different values of Λ when M3=1, M1=5, and Bi=2

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Figure 1

Geometrical configuration

Grahic Jump Location
Figure 9

Variation in critical wave number ac as a function of Da−1 for different values of M1 when M3=1, Λ=5, and Bi=2

Grahic Jump Location
Figure 10

Variation of critical wave number ac as a function of Da−1 for different values of M3 when M1=5, Λ=6, and Bi=2

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