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Fluids 2017, 2(2), 22; doi:10.3390/fluids2020022

Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer

1
Department of Applied Sciences, National Institute of Technology, Narela, Delhi-110040, India
2
Department of Mathematics, National Institute of Technology, Hamirpur, Himachal Pradesh-177005, India
*
Author to whom correspondence should be addressed.
Academic Editors: D. Andrew S. Rees and Antonio Barletta
Received: 22 March 2017 / Revised: 21 April 2017 / Accepted: 28 April 2017 / Published: 4 May 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results are discussed for all three boundary conditions: when both boundaries are impermeable and conducting; when both boundaries are conducting with lower boundary impermeable and free upper boundary; and when both boundaries are impermeable with lower boundary conducting and upper with constant heat flux. The effect of the Langevin parameter, width of ferrofluid layer, permeability parameter, and nonlinearity of the fluid magnetization has been observed at the onset of penetrative convection for water- and ester-based ferrofluids. It is seen that the Langevin parameter, width of ferrofluid layer, and permeability parameter have stabilizing effects on the onset of convection, while the nonlinearity of the fluid magnetization advances the onset of convection. View Full-Text
Keywords: penetrative convection; internal heating; ferrofluids; magnetic field; porous media penetrative convection; internal heating; ferrofluids; magnetic field; porous media
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Mahajan, A.; Sunil; Sharma, M.K. Linear Stability Analysis of Penetrative Convection via Internal Heating in a Ferrofluid Saturated Porous Layer. Fluids 2017, 2, 22.

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