Journal of Applied Nonlinear Dynamics
Weakly Nonlinear and Nonlinear Magnetoconvection under Thermal Modulation
Journal of Applied Nonlinear Dynamics 6(4) (2017) 487508  DOI:10.5890/JAND.2017.12.005
Palle Kiran$^{1}$; B.S. Bhadauria$^{2}$; Y. Narasimhulu$^{1}$
$^{1}$ Department of Mathematics, Rayalaseema University, Kurnool518002, Andhra Pradesh, India
$^{2}$ Department of Applied Mathematics, BBA University, Lucknow226025, Utter Pradesh, India
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Abstract
Both oscillatory and chaotic convection are studied using weakly non linear and nonlinear theories. A weakly nonlinear analysis was em ployed to derive Complex GinzburgLandau amplitude equation. The time dependent temperatures of the plates are considered in three ways, out of phase, lower plate and in phase modulation. The first two temperature profiles show impact on heat and mass transfer and the dynamics of the problem. It is also found that inphase tempera ture modulation has negligible effect; while out of phase modulation and only lower plate modulation have significant effects on heat and mass transport. Heat mass transfer is measured in the system in terms of the Nusselt and Sherwood numbers. Heat mass transfer be comes rapid on either increasing Rs,Pr, &lamda, &delta or decreasing Q, &Gamma, &epsilon, &Omega. Further, the Lorentz model has been simplified under modulation ef fect, and it is observed that, the chaotic nature of the system may altered with modulation. Unstable solution for OPM, stable solu tions for IPM, LBMO is found depending on the suitable values of modulation parameters.
Acknowledgments
The author Dr. Palle Kiran is grateful to the Department of Atomic Energy, Government of India, for providing him financial assistance in the form of NBHMPostdoctoral Fellowship (Lett. No: 2/40(27)/2015/R&DII/9470). The authors are grateful to the unknown referees for their comments and suggestions.
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