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Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection

Ram Kaka, Prakash Jyoti, Kumari Kultaran, Kumar Pankaj

Studia Geotechnica et Mechanica

2022

Vol. 44, nr 2

114--122

It is proved analytically that the complex growth rate σ= σr+iσi (σr and σi are the real and imaginary parts of σ, respectively) of an arbitrary oscillatory motion of neutral or growing amplitude in ferrothermohaline convection in a ferrofluid layer for the case of free boundaries is located inside a semicircle in the right half of the σrσi-plane, whose center is at the origin and (formula) where Rs is the concentration Rayleigh number, Pr′ is the solutal Prandtl number, M1′ is the ratio of magnetic flux due to concentration fluctuation to the gravitational force, and M5 is the ratio of concentration effect on magnetic field to pyromagnetic coefficient. Further, bounds for the case of rigid boundaries are also derived separately.

Effect of magnetic field dependent viscosity and rotation on ferrothermohaIine convection in the presence of dust particIes

Sunil, Sharma A., Shandil R. G.

International Journal of Applied Mechanics and Engineering

2007

Vol. 12, no 1

197-213

This paper deals with the theoretical investigation of the combined effect of magnetic field dependent (MFD) viscosity and rotation on ferrothermohaline convection in the presence of dust particles subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis method. The cases of stationary convection and oscillatory modes have been discussed. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.