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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Druckformat: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.2018016842
pages 389-398

THERMAL INSTABILITY OF HOT FERROFLUID LAYER WITH TEMPERATURE-DEPENDENT VISCOSITY

Joginder Singh Dhiman
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla, Himachal Pradesh 171005, India
Nivedita Sharma
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla, Himachal Pradesh 171005, India

ABSTRAKT

In this paper stability analysis of the ferrofluid layer heated from below when viscosity is temperature dependent is carried out analytically for the general nature of bounding surfaces. Using the analytical method of Pellew and Southwell [Proc. Roy. Soc. A, vol. 176, pp. 312–343, 1940] of conjugate eigenfunctions, the principle of exchange of stabilities (PES) is proved to be valid for the problem for very small values of magnetic parameter. This result yields that the ferroconvection is through the stationary mode only and the result is uniformly valid whether viscosity is temperature dependent or constant. However, for certain classes of hot fluids (in some astrophysical situations) the magnetic parameter can have large values, and this quantitative effect has a qualitative effect on the instability of ferrofluids. It is shown here that for large values of magnetic parameter oscillatory instability can exist and hence the bounds for the growth rate of unstable oscillatory modes of the problem are also derived herein.


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