Author(s):
Sumixal Sood, Joginder Singh Dhiman
Email(s):
sumixalsood@gmail.com , jsdhiman66@gmail.com
Address:
Sumixal Sood1*, Joginder Singh Dhiman2
1Department of Mathematics, KDC Govt Degree College Jaisinghpur (Kangra) HP, India.
2Department of Mathematics, Himachal Pradesh University, Shimla, India.
*Corresponding author
Published In:
Conference Proceeding, Proceeding of ICAMAS-2025
Year of Publication:
July, 2025
Online since:
July 11, 2025
DOI:
Not Available
ABSTRACT:
In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation with gravity modulation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite amplitude disturbances. For linear stability, as a first order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second order and third order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M_1) and the measure of nonlinearity of magnetization (M_3) both have destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, the measure of nonlinearity of magnetization. The modulation frequency does not affect heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.
Cite this article:
Sumixal Sood, Joginder Singh Dhiman. Linear and Weakly Non-linear Stability Analysis of Oscillatory Convection in Rotating Ferrofluid Layer with Gravity Modulation. Proceeding of ICAMAS-2025. 5-18.
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