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Lee J.,Yonsei University | Shivakumara I.S.,Yonsei University | Shivakumara I.S.,Bangalore University | Ravisha M.,Smt Rukmini Shedthi Memorial National Government First Grade College
Transport in Porous Media | Year: 2011

The effect of local thermal non-equilibrium (LTNE) on the onset of thermomagnetic convection in a ferromagnetic fluid-saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. A modified Forchheimer-extended Darcy equation is employed to describe the flow in the porous medium, and a two-field model is used for temperature representing the solid and fluid phases separately. It is found that both the critical Darcy-Rayleigh number and the corresponding wave number are modified by the LTNE effects. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient Ht are presented and compared with those computed numerically. An excellent agreement is obtained between the asymptotic and the numerical results. Besides, the influence of magnetic parameters on the instability of the system is also discussed. The available results in the literature are recovered as particular cases from the present study. © 2010 Springer Science+Business Media B.V. Source


Shivakumara I.S.,Bangalore University | Lee J.,Yonsei University | Nanjundappa C.E.,National Institute of Technology Jalandhar | Ravisha M.,Smt Rukmini Shedthi Memorial National Government First Grade College
Transport in Porous Media | Year: 2011

The effect of Coriolis force on the onset of ferromagnetic convection in a rotating horizontal ferrofluid saturated porous layer in the presence of a uniform vertical magnetic field is studied. The boundaries are considered to be either stress free or rigid. The modified Brinkman-Forchheimer-extended Darcy equation with fluid viscosity different from effective viscosity is used to characterize the fluid motion. The condition for the occurrence of direct and Hopf bifurcations is obtained analytically in the case of free boundaries, while for rigid boundaries the eigenvalue problem has been solved numerically using the Galerkin method. Contrary to their stabilizing effect in the absence of rotation, increasing the ratio of viscosities, Λ, and decreasing the Darcy number Da show a partial destabilizing effect on the onset of stationary ferromagnetic convection in the presence of rotation, and some important observations are made on the stability characteristics of the system. Moreover, the similarities and differences between free-free and rigid-rigid boundaries in the presence of buoyancy and magnetic forces together or in isolation are emphasized in triggering the onset of ferromagnetic convection in a rotating ferrofluid saturated porous layer. For smaller Taylor number domain, the stress-free boundaries are found to be always more unstable than in the case of rigid boundaries. However, this trend is reversed at higher Taylor number domain because the stability of the stress-free case is increased more quickly than the rigid case. © 2010 Springer Science+Business Media B.V. Source


Shivakumara I.S.,Yonsei University | Shivakumara I.S.,Bangalore University | Lee J.,Yonsei University | Ravisha M.,Smt Rukmini Shedthi Memorial National Government First Grade College | Gangadhara Reddy R.,AMC Engineering College
International Journal of Heat and Mass Transfer | Year: 2011

The combined effect of magnetic field dependent (MFD) viscosity and a local thermal non-equilibrium (LTNE) on the criterion for the onset of ferromagnetic convection in a ferrofluid saturated horizontal porous layer heated from below in the presence of a uniform vertical magnetic field is studied analytically using linear stability theory. A modified Darcy equation is used to describe the flow in the porous medium and a two-field model for temperature each representing the solid as well as fluid phases separately is used for energy equation. It is demonstrated that the principle of exchange of stability is valid. The results indicate that the onset of ferromagnetic convection is delayed with an increase in the MFD viscosity parameter but shows no influence on the critical wave number. Moreover, the system is found to be more stable when the magnetic forces alone are present. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient Ht are presented and compared with those computed numerically. An excellent agreement is obtained between the asymptotic and the numerical results. Besides, the influence of magnetic and LTNE parameters on the stability characteristics of the system is also discussed. © 2011 Elsevier Ltd. All rights reserved. Source


Shivakumara I.S.,Yonsei University | Shivakumara I.S.,Bangalore University | Lee J.,Yonsei University | Ravisha M.,Smt Rukmini Shedthi Memorial National Government First Grade College | Reddy R.G.,AMC Engineering College
International Journal of Heat and Mass Transfer | Year: 2011

The onset of ferroconvection in a horizontal layer of ferrofluid saturated Brinkman porous medium heated uniformly from below in the presence of a uniform vertical magnetic field is investigated when the solid and fluid phases of the porous medium are in local thermal non-equilibrium (LTNE) using linear stability theory. The modified Brinkman-Forchheimer-extended Darcy equation is employed to describe the flow in the porous medium and a two-field model for energy equation each representing the solid and fluid phases separately is used. It is established that the principle of exchange of stability is valid. The authenticity of LTNE model over LTE model and also the ferromagnetic effects on the stability of the system are discussed in detail. The system is found to be more stable when the magnetic forces alone are present. Asymptotic analysis for both small and large values of scaled inter-phase heat transfer coefficient H t is presented and the results are found to be in good agreement with those obtained from the exact formula. The established results in the literature have been reproduced as particular cases from the present study. © 2011 Elsevier Ltd. All rights reserved. Source


Nanjundappa C.E.,National Institute of Technology Jalandhar | Ravisha M.,Smt Rukmini Shedthi Memorial National Government First Grade College | Lee J.,Yonsei University | Shivakumara I.S.,Yonsei University | Shivakumara I.S.,Bangalore University
Acta Mechanica | Year: 2011

Penetrative convection in a horizontal ferrofluid-saturated porous layer in the presence of a uniform applied vertical magnetic field has been investigated via the internal heating model using the Brinkman-extended Darcy equation. The rigid-isothermal boundaries of the porous layer are considered to be either paramagnetic or ferromagnetic. The eigenvalue problem is solved numerically using the Galerkin method with either thermal or magnetic Rayleigh number as the eigenvalue. The stability of the system is significantly affected by the internal heating in the porous layer. It is noted that the paramagnetic boundaries with large magnetic susceptibility delay the onset of penetrative ferroconvection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. An increase in the value of magnetic Rayleigh number (R m ), heat source strength (N S ) and non-linearity of magnetization (M 3) is to hasten the onset of ferroconvection. In addition, the stability of the system when heated from above and also in the absence of thermal buoyancy has been discussed in detail. © 2010 Springer-Verlag. Source

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