Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell

Ankuj Bala; Ramesh Chand

doi:doi:10.11648/j.fm.20160201.12

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Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell

Ankuj Bala, Ramesh Chand

Published in Fluid Mechanics (Volume 2, Issue 1)

Received: 26 September 2016 Accepted: 19 October 2016 Published: 2 November 2016

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Abstract

Linear thermal instability analysis of a ferrofluid layer confined between in Hele-Shaw cell is investigated. The stability theory is based upon perturbation method and normal mode technique and the resulting equations are solved by using Galerkin weighted residuals method to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed in the problem. It is found that Hele-Shaw number delays the onset of convection while magnetization parameter and buoyancy magnetization parameter hasten the onset of convection.

Published in	Fluid Mechanics (Volume 2, Issue 1)
DOI	10.11648/j.fm.20160201.12
Page(s)	8-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Ferrofluid, Perturbation Method, Galerkin Method, Hele-Shaw Number, Magnetization Parameter

References

[1]	R. E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge 1985.
[2]	S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1961.
[3]	B. A. Finlayson, Convective instability of ferromagnetic fluids, Journal of Fluid Mech., 1970, 40, 753-767.
[4]	D. P. Lalas and S. Carmi, Thermoconvective stability of Ferrofluid, Phys. of Fluids, 1971, 14, 436-437.
[5]	P. J. Blennerhassett, F. Lin and P. J. Stiles, Heat transfer through strongly magnetized ferrofluids, Proc. R. Soc. A, 1991, 433,165-177.
[6]	Sunil, P. K. Bharti and R. C. Sharma, Thermosolutal convection in ferromagnetic field, Arch. Mech., 2004, 56(2), 117-135.
[7]	A. Mahajan, Stability of ferrofluids: Linear and Nonlinear, Lambert Academic Publishing, Germany 2010.
[8]	R. Chand and A. Bala, On the onset of Rayleigh-Bénard convection in a layer of Ferrofluid, International Journal of Engineering Research and Applications, 2013, 3(4), 1019-1025.
[9]	R. Chand and A. Bala, Effect of rotation on the onset of Rayleigh-Bénard convection in a layer of Ferrofluid, International Journal of Modern Engineering Research, 2013, 3(4), 2042-2047.
[10]	A. Bala and R. Chand, Thermal instability in a horizontal layer of Ferrofluid in Brinkman porous medium, Journal of Scientific and Engineering Research, 2014, 1(2), 25-34.
[11]	A. Bala and R. Chand, Variable gravity effect on the thermal instability of Ferrofluid in a Brinkman porous medium, International Journal of Astronomy, Astrophysics and Space Science,2015, 2(5), 39-44.
[12]	A. Bala and R. Chand, Thermal instability in a horizontal layer of ferrofluid in anisotropic porous medium, Open Science Journal of Mathematics and Application, 2015, 3(6), 176-180.
[13]	H. S. J. Hele-Shaw, Trans. Inst. Naval Archit, 40, 21.
[14]	R. A. Wooding, Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell, Journal of Fluid Mech., 1961, 7,501-515.

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APA Style

Ankuj Bala, Ramesh Chand. (2016). Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mechanics, 2(1), 8-12. https://doi.org/10.11648/j.fm.20160201.12

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ACS Style

Ankuj Bala; Ramesh Chand. Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mech. 2016, 2(1), 8-12. doi: 10.11648/j.fm.20160201.12

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AMA Style

Ankuj Bala, Ramesh Chand. Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mech. 2016;2(1):8-12. doi: 10.11648/j.fm.20160201.12

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@article{10.11648/j.fm.20160201.12,
  author = {Ankuj Bala and Ramesh Chand},
  title = {Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell},
  journal = {Fluid Mechanics},
  volume = {2},
  number = {1},
  pages = {8-12},
  doi = {10.11648/j.fm.20160201.12},
  url = {https://doi.org/10.11648/j.fm.20160201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20160201.12},
  abstract = {Linear thermal instability analysis of a ferrofluid layer confined between in Hele-Shaw cell is investigated. The stability theory is based upon perturbation method and normal mode technique and the resulting equations are solved by using Galerkin weighted residuals method to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed in the problem. It is found that Hele-Shaw number delays the onset of convection while magnetization parameter and buoyancy magnetization parameter hasten the onset of convection.},
 year = {2016}
}

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TY  - JOUR
T1  - Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell
AU  - Ankuj Bala
AU  - Ramesh Chand
Y1  - 2016/11/02
PY  - 2016
N1  - https://doi.org/10.11648/j.fm.20160201.12
DO  - 10.11648/j.fm.20160201.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 8
EP  - 12
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20160201.12
AB  - Linear thermal instability analysis of a ferrofluid layer confined between in Hele-Shaw cell is investigated. The stability theory is based upon perturbation method and normal mode technique and the resulting equations are solved by using Galerkin weighted residuals method to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed in the problem. It is found that Hele-Shaw number delays the onset of convection while magnetization parameter and buoyancy magnetization parameter hasten the onset of convection.
VL  - 2
IS  - 1
ER  -

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Author Information

Ankuj Bala

Department of Mathematics, Dravidian University Srinivasavanam Kuppam, Chittoor, Andhra Pradesh, India
Ramesh Chand

Department of Mathematics, Government Arya Degree College Nurpur, Himachal Pradesh, India

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APA Style

Ankuj Bala, Ramesh Chand. (2016). Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mechanics, 2(1), 8-12. https://doi.org/10.11648/j.fm.20160201.12

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ACS Style

Ankuj Bala; Ramesh Chand. Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mech. 2016, 2(1), 8-12. doi: 10.11648/j.fm.20160201.12

Copy | Download

AMA Style

Ankuj Bala, Ramesh Chand. Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell. Fluid Mech. 2016;2(1):8-12. doi: 10.11648/j.fm.20160201.12

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@article{10.11648/j.fm.20160201.12,
  author = {Ankuj Bala and Ramesh Chand},
  title = {Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell},
  journal = {Fluid Mechanics},
  volume = {2},
  number = {1},
  pages = {8-12},
  doi = {10.11648/j.fm.20160201.12},
  url = {https://doi.org/10.11648/j.fm.20160201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20160201.12},
  abstract = {Linear thermal instability analysis of a ferrofluid layer confined between in Hele-Shaw cell is investigated. The stability theory is based upon perturbation method and normal mode technique and the resulting equations are solved by using Galerkin weighted residuals method to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed in the problem. It is found that Hele-Shaw number delays the onset of convection while magnetization parameter and buoyancy magnetization parameter hasten the onset of convection.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Thermal Instability in a Horizontal Layer of Ferrofluid Confined Within Hele-Shaw Cell
AU  - Ankuj Bala
AU  - Ramesh Chand
Y1  - 2016/11/02
PY  - 2016
N1  - https://doi.org/10.11648/j.fm.20160201.12
DO  - 10.11648/j.fm.20160201.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 8
EP  - 12
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20160201.12
AB  - Linear thermal instability analysis of a ferrofluid layer confined between in Hele-Shaw cell is investigated. The stability theory is based upon perturbation method and normal mode technique and the resulting equations are solved by using Galerkin weighted residuals method to find expressions for Rayleigh number and critical Rayleigh number. ‘Principle of Exchange of Stabilities’ hold and the oscillatory modes are not allowed in the problem. It is found that Hele-Shaw number delays the onset of convection while magnetization parameter and buoyancy magnetization parameter hasten the onset of convection.
VL  - 2
IS  - 1
ER  -

Copy | Download