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Research Papers: Natural and Mixed Convection

Onset of Thermogravitational Convection in a Ferrofluid Layer With Temperature Dependent Viscosity

[+] Author and Article Information
I. S. Shivakumara

Department of Mathematics,  UGC-CAS in Fluid Mechanics, Central College Campus, Bangalore University, Bangalore-560 001, Indiashivakumarais@gmail.com

Jinho Lee1

 School of Mechanical Engineering, Yonsei University, Seoul 120-749, South Koreajinholee@yonsei.ac.kr

C. E. Nanjundappa

Department of Mathematics,  Dr. Ambedkar Institute of Technology, Bangalore- 560 056, Indiacenanju@hotmail.com

1

Corresponding author.

J. Heat Transfer 134(1), 012501 (Oct 28, 2011) (7 pages) doi:10.1115/1.4004758 History: Received June 16, 2010; Revised July 25, 2011; Accepted July 26, 2011; Published October 28, 2011; Online October 28, 2011

The onset of thermogravitational convection in a horizontal ferrofluid layer is investigated with viscosity depending exponentially on temperature. The bounding surfaces of the ferrofluid layer are considered to be either stress free or rigid-ferromagnetic and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also by a regular perturbation technique for different types of velocity boundary conditions, namely free-free, rigid-rigid, and lower rigid- upper free. It is observed that increasing the viscosity parameter, Λ, and the magnetic number, M1, is to hasten the onset of ferroconvection, while the nonlinearity of fluid magnetization, M3, is found to have no influence on the stability of the system. The critical stability parameters are found to be the same in the limiting cases of either no magnetic forces or no buoyancy forces.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Variation of Rtc as a function of Λ for different values of M1

Grahic Jump Location
Figure 2

Perturbed vertical velocity eigenfunction for two values of Λ when M1=2

Grahic Jump Location
Figure 3

Perturbed vertical velocity eigenfunction for two values of M1 when Λ=2

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