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Variable Gravity Effect on the Thermal Instability of Ferrofluid in a Brinkman Porous Medium
Current Issue
Volume 2, 2015
Issue 5 (October)
Pages: 39-44   |   Vol. 2, No. 5, October 2015   |   Follow on         
Paper in PDF Downloads: 83   Since Sep. 16, 2015 Views: 1827   Since Sep. 16, 2015
Authors
[1]
Ankuj Bala, Department of Mathematics, Dravidian University Srinivasavanam Kuppam, Chittoor, Andhra Pradesh, India.
[2]
Ramesh Chand, Department of Mathematics, Government Arya Degree College Nurpur, Himachal Pradesh, India.
Abstract
Effect of variable gravity on the thermal instability in a horizontal layer of ferrofluid in a Brinkman porous medium is investigated by using Galerkin weighted residuals method. Linear stability theory based upon perturbation method and normal mode technique is used to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed. It is found that decreasing gravity parameter has stabilizing effect while increasing gravity parameter has destabilizing effect on the stationary convection. It is also found that magnetization parameters M3 and buoyancy magnetization M1 have destabilizing effect while Brinkman Darcy number D̃a has stabilizing effect on the fluid layer.
Keywords
Ferrofluid, Brinkman Darcy Number, Variable Gravity, Perturbation Method, Galerkin Method
Reference
[1]
RE Rosensweig “Ferrohydrodynamics” Cambridge University Press, Cambridge 1985.
[2]
BA Finlayson “Convective in stability of ferromagnetic fluids” J. Fluid Mech. Vol. 40; P753-767; 1970.
[3]
DP Lalas and S Carmi “Thermoconvective stability of Ferrofluid” Phys. Fluids vol 14, P 436-437; 1971.
[4]
PJ Blennerhassett, F Lin and PJ Stiles “Heat transfer through strongly magnetized ferrofluids” Proc. R. Soc. A vol 433, P 165-177; 1991.
[5]
Sunil, D Sharma and RC Sharma “Effect of dust particles on thermal convection in ferromagnetic fluid saturating a porous medium” J. Magn. Magn. Mater vol 288, P183-195; 2005.
[6]
MD Gupta and AS Gupta “Convective instability of a layer of ferromagnetic fluid rotating about a vertical axis” Int.J.Eng.Sci.vol17; P271-277; 1979.
[7]
A Mahajan “Stability of ferrofluids: Linear and Nonlinear” Lambert Academic Publishing, Germany 2010.
[8]
Ramesh Chand and Ankuj Bala “On the onset of Rayleigh-Bénard convection in a layer of Ferrofluid” International Journal of Engineering Research and Applications vol 3(4), P 1019-1025; 2013.
[9]
Ramesh Chand and Ankuj Bala “Effect of rotation on the onset of Rayleigh-Bénard convection in a layer of Ferrofluid” International Journal of Modern Engineering Research vol 3(4), P 2042-2047; 2013.
[10]
Ankuj Bala and Ramesh Chand “Thermal instability in a horizontal layer of Ferrofluid in Brinkman porous medium” Journal of Scientific and Engineering Research vol 1(2), P25-34; 2014.
[11]
ER Lapwood “Convection of a fluid in porous medium”, Proc. Camb. Phil. Soc. vol 44, P508-519; 1948.
[12]
RA Wooding “Rayleigh instability of a thermal boundary layer in flow through a porous medium” J. Fluid Mech. vol 9, P183-192; 1960.
[13]
DD Ingham and L Pop “Transport Phenomena in Porous Media” Elsvier, New York 1981.
[14]
KA Vafai and HA Hadim “Hand Book of Porous Media” M. Decker, New York, 2000.
[15]
DA Nield and A Bejan “Convection in Porous Medium” Springer, New York 2006.
[16]
Ramesh Chand and GC Rana “On the onset of thermal convection in rotating nanofluid layer saturating a Darcy–Brinkman porous medium” International Journal of Heat and Mass Transfer vol 55, P 5417-5424; 2012.
[17]
Ramesh Chand and GC Rana “Effect of rotation on thermal instability of Oldroydian visco-elastic fluid saturated by Brinkman-Darcy porous medium” Research J. Engineering and Tech. vol 3(2), P92-99; 2012.
[18]
Ramesh Chand and GC Rana “Thermal instability in a Brinkman porous medium saturated by nanofluid with no nanoparticle flux on boundaries” Special Topics & Reviews in Porous Media: An International Journal vol5 (4), P 277-286; 2014.
[19]
GK Pradhan, PC Samal and UK Tripathy “Thermal stability of a fluid layer in a variable gravitational field”Indian J. Pure Appl. Math. vol 20(7), P 736-745; 1989.
[20]
SM Alex, RP Prabhamani and KS Vankatakrishan “Variable gravity effects on thermal instability in a porous medium with internal heat source and inclined temperature gradient” Fluid Dynamics Research vol 29, P 1-6; 2001.
[21]
Kirti Prakesh and Ramesh Chand “Thermal instability of Oldroydian visco-elastic fluid in the presence of Finite Larmor Radius rotation and variable gravity in porous medium” Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. vol 72 (4), P373-386; 2002.
[22]
Ramesh Chand “Gravitational effect on Thermal instability of Maxwell visco-elastic fluid in porous medium” Ganita Sandesh vol 24(2), P166-170; 2010.
[23]
Ramesh Chand “Effect of suspended particles on thermal instability of Maxwell visco-elastic fluid with variable gravity in porous medium” Antarctica J. Math vol8(6), P487-497; 2011.
[24]
Ramesh Chand “Thermal instability of rotating Maxwell visco-elastic fluid with variable gravity in porous medium” Journal of the Indian Math. Soc. vol 80(1-2), P23-31; 2013.
[25]
Ramesh Chand, GC Rana and S Kumar “Variable gravity effects on thermal instability of Nanofluid in anisotropic porous medium” Int. J. of Applied Mechanics and Engineering vol 18(3), P631-642; 2013.
[26]
Ramesh Chand, GC Rana and SK Kango “Effect of variable gravity on thermal instability of rotating nanofluid in porous medium” FME Transactions vol 43, P 62-69; 2015.
[27]
SK Kango, GC Rana and Ramesh Chand “Triple-diffusive convection in Walters’ (Model B') fluid with varying gravity field saturating a porous medium” Studia Geotechnica et Mechanicavol XXXV(3), P45-56; 2013.
[28]
S. Chandrasekhar “Hydrodynamic and hydromagnetic Stability” Dover, New York 1981.
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