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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Weakly Nonlinear and Nonlinear Magneto-convection under Thermal Modulation

Journal of Applied Nonlinear Dynamics 6(4) (2017) 487--508 | DOI:10.5890/JAND.2017.12.005

Palle Kiran$^{1}$; B.S. Bhadauria$^{2}$; Y. Narasimhulu$^{1}$

$^{1}$ Department of Mathematics, Rayalaseema University, Kurnool-518002, Andhra Pradesh, India

$^{2}$ Department of Applied Mathematics, BBA University, Lucknow-226025, 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 Ginzburg-Landau 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 in-phase 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 NBHM-Post-doctoral Fellowship (Lett. No: 2/40(27)/2015/R&D-II/9470). The authors are grateful to the unknown referees for their comments and suggestions.

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