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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Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer
C. E. Nanjundappa,
C. E. Nanjundappa
Department of Mathematics,
e-mail: cenanju@hotmail.com
Dr. Ambedkar Institute of Technology
, Bangalore 560 056, India
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I. S. Shivakumara
I. S. Shivakumara
UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics,
e-mail: isshivakumara@hotmail.com
Bangalore University
, Bangalore 560 001, India
Search for other works by this author on:
C. E. Nanjundappa
Department of Mathematics,
Dr. Ambedkar Institute of Technology
, Bangalore 560 056, Indiae-mail: cenanju@hotmail.com
I. S. Shivakumara
UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics,
Bangalore University
, Bangalore 560 001, Indiae-mail: isshivakumara@hotmail.com
J. Heat Transfer. Oct 2008, 130(10): 104502 (5 pages)
Published Online: August 6, 2008
Article history
Received:
January 2, 2007
Revised:
March 22, 2008
Published:
August 6, 2008
Citation
Nanjundappa, C. E., and Shivakumara, I. S. (August 6, 2008). "Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer." ASME. J. Heat Transfer. October 2008; 130(10): 104502. https://doi.org/10.1115/1.2952742
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