Effect of Coriolis Force on Bénard–Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity

C. E. Nanjundappa; I. S. Shivakumara; Jinho Lee

doi:10.1007/s12217-014-9410-0

Effect of Coriolis Force on Bénard–Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity

C. E. Nanjundappa, I. S. Shivakumara, Jinho Lee

Department of Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

The simultaneous effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of Bénard-Marangoni convection in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid while the upper free boundary is open to the atmosphere and at which the temperature-dependent surface tension effect is allowed for. The Galerkin technique is employed to extract the critical stability parameters numerically. The results show that the onset of Bénard-Marangoni ferroconvection is delayed with an increase in the MFD viscosity parameter Λ, Taylor number Ta, magnetic susceptibility χ and Biot number Bi but opposite is the case with an increase in the value of magnetic number M₁ and nonlinearity of fluid magnetization M₃. Further, increase in M₁,M₃ and decrease in Λ,Ta, χ and Bi is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found.

Original language	English
Pages (from-to)	27-37
Number of pages	11
Journal	Microgravity Science and Technology
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s12217-014-9410-0
Publication status	Published - 2014 Feb

Bibliographical note

Funding Information:
One of the authors (CEN) gratefully acknowledges the financial support received in the form of a VTU research grant scheme from Visvesvaraya Technological University, Belgaum, Karnataka State, India. The authors wish to thank the reviewers for their helpful suggestions.

Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Engineering(all)
Physics and Astronomy(all)
Applied Mathematics

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title = "Effect of Coriolis Force on B{\'e}nard–Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity",

abstract = "The simultaneous effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of B{\'e}nard-Marangoni convection in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid while the upper free boundary is open to the atmosphere and at which the temperature-dependent surface tension effect is allowed for. The Galerkin technique is employed to extract the critical stability parameters numerically. The results show that the onset of B{\'e}nard-Marangoni ferroconvection is delayed with an increase in the MFD viscosity parameter Λ, Taylor number Ta, magnetic susceptibility χ and Biot number Bi but opposite is the case with an increase in the value of magnetic number M1 and nonlinearity of fluid magnetization M3. Further, increase in M1,M3 and decrease in Λ,Ta, χ and Bi is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found.",

author = "Nanjundappa, {C. E.} and Shivakumara, {I. S.} and Jinho Lee",

note = "Funding Information: One of the authors (CEN) gratefully acknowledges the financial support received in the form of a VTU research grant scheme from Visvesvaraya Technological University, Belgaum, Karnataka State, India. The authors wish to thank the reviewers for their helpful suggestions. Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",

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doi = "10.1007/s12217-014-9410-0",

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AU - Shivakumara, I. S.

AU - Lee, Jinho

N1 - Funding Information: One of the authors (CEN) gratefully acknowledges the financial support received in the form of a VTU research grant scheme from Visvesvaraya Technological University, Belgaum, Karnataka State, India. The authors wish to thank the reviewers for their helpful suggestions. Publisher Copyright: © 2014, Springer Science+Business Media Dordrecht.

PY - 2014/2

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N2 - The simultaneous effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of Bénard-Marangoni convection in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid while the upper free boundary is open to the atmosphere and at which the temperature-dependent surface tension effect is allowed for. The Galerkin technique is employed to extract the critical stability parameters numerically. The results show that the onset of Bénard-Marangoni ferroconvection is delayed with an increase in the MFD viscosity parameter Λ, Taylor number Ta, magnetic susceptibility χ and Biot number Bi but opposite is the case with an increase in the value of magnetic number M1 and nonlinearity of fluid magnetization M3. Further, increase in M1,M3 and decrease in Λ,Ta, χ and Bi is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found.

AB - The simultaneous effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of Bénard-Marangoni convection in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid while the upper free boundary is open to the atmosphere and at which the temperature-dependent surface tension effect is allowed for. The Galerkin technique is employed to extract the critical stability parameters numerically. The results show that the onset of Bénard-Marangoni ferroconvection is delayed with an increase in the MFD viscosity parameter Λ, Taylor number Ta, magnetic susceptibility χ and Biot number Bi but opposite is the case with an increase in the value of magnetic number M1 and nonlinearity of fluid magnetization M3. Further, increase in M1,M3 and decrease in Λ,Ta, χ and Bi is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found.

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Effect of Coriolis Force on Bénard–Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity

Abstract

Bibliographical note

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