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Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer

[+] Author and Article Information
C. E. Nanjundappa

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

I. S. Shivakumara1

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

1

Corresponding author.

J. Heat Transfer 130(10), 104502 (Aug 06, 2008) (5 pages) doi:10.1115/1.2952742 History: Received January 02, 2007; Revised March 22, 2008; Published August 06, 2008

A variety of velocity and temperature boundary conditions on the onset of ferroconvection in an initially quiescent ferrofluid layer in the presence of a uniform magnetic field is investigated. The lower boundary of the ferrofluid 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 a fixed heat flux at the lower boundary and a general convective, radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by the regular perturbation technique when both boundaries are insulated to temperature perturbations. It is observed that an increase in the magnetic number and the nonlinearity of fluid magnetization as well as a decrease in Biot number are to destabilize the system. Further, the nonlinearity of fluid magnetization is found to have no effect on the onset of ferroconvection in the absence of the Biot number.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Variation of Rc as a function of Bi when M3=1

Grahic Jump Location
Figure 2

Variation of Rc as a function of Bi when M1=5

Grahic Jump Location
Figure 3

Variation of Rc as a function of Rmc when Bi=2

Grahic Jump Location
Figure 4

Variation of ac as a function of Bi when M3=1

Grahic Jump Location
Figure 5

Variation of ac as a function of Bi when M1=5

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