Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a Cubic–Quintic Ginzburg–Landau Equation Using the Center Manifold Theorem

被引:0
作者
P. G. Siddheshwar
T. S. Sushma
机构
[1] CHRIST (Deemed to be University),Department of Mathematics
[2] B.N.M. Institute of Technology,Department of Mathematics
[3] CMR Institute of Technology,Department of Mathematics (VTU RC)
来源
Differential Equations and Dynamical Systems | 2024年 / 32卷
关键词
Center manifold; Ferrofluid convection; Electroconvection; Ginzburg–Landau; Lorenz model; Glukhovsky–Dolzhansky system; Quintic;
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摘要
The differential geometric method of the center manifold theorem is applied to the magnetic-Lorenz model of ferrofluid convection in an electrically non-conducting ferrofluid. The analytically intractable tri-modal nonlinear autonomous system (magnetic-Lorenz model) is reduced to an analytically tractable uni-modal cubic–quintic Ginzburg–Landau equation. The inadequacy of the cubic Ginzburg–Landau equation and the need for the cubic–quintic one is shown in the paper. The heat transport is quantified using the solution of the cubic–quintic equation and the effect of ferrofluid parameters on it is demonstrated. The stable and unstable regions in the conductive regime and the conductive-convective regime is depicted using a bifurcation diagram. The noticeable discrepancy between the results of the two models is highlighted and the quintic non-linearity effects are delineated.
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页码:151 / 169
页数:18
相关论文
共 54 条
[1]  
Danumjaya P(2005)Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation J. Comput. Appl. Math. 174 101-117
[2]  
Pani AK(2006)Numerical methods for the extended Fisher–Kolmogorov (EFK) equation Int. J. Numer. Anal. Model. 3 186-210
[3]  
Danumjaya P(1970)Convective instability of ferromagnetic fluids J. Fluid Mech. 40 753-767
[4]  
Pani AK(2007)Application of a non-linear local analysis method for the problem of mixed convection instability Int. J. NonLinear Mech. 42 981-988
[5]  
Finlayson BA(1969)Dynamical systems and stability J. Math. Anal. Appl. 26 39-59
[6]  
Guillet C(2010)Stability and uniqueness of ferrofluids Int. J. Eng. Sci. 48 1350-1356
[7]  
Mare T(1967)Stability of the center-stable manifold J. Math. Anal. Appl. 18 336-344
[8]  
Nguyen CT(1967)The stable, center-stable, center, center-unstable, unstable manifolds J. Differ. Equ. 3 546-570
[9]  
Hale JK(1982)The role of center manifolds in ordinary differential equations Equadiff 5 179-189
[10]  
Kaloni PN(2013)Chaotic convection in a ferrofluid Commun. Nonlinear Sci. Numer. Simul. 18 2436-2447