The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium |
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Authors: | C E Nanjundappa I S Shivakumara M Ravisha |
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Institution: | 1.Department of Mathematics,Dr. Ambedkar Institute of Technology,Bangalore,India;2.UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics,Bangalore University,Bangalore,India;3.Department of Mathematics,East Point College of Engineering and Technology,Bangalore,India |
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Abstract: | The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence
of a uniform vertical magnetic field is investigated. 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-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid 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 fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically
using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M
1 and non-linearity of magnetization M
3 is to delay the onset of ferroconvection in a porous medium. Further, increase in M
1, M
3, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells. |
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