Stability Analysis of a Magneto Micropolar Fluid Layer by Variational Method

Joginder Singh Dhiman¹ and Gurdeep Singh^2,

¹Department of Mathematics, Himachal Pradesh University, Shimla 171005, India

²Department of Mathematics, GSSS Ghanari Distt Una, Himachal Pradesh 177212, India

Cite this paper

Joginder Singh Dhiman and Gurdeep Singh. Stability Analysis of a Magneto Micropolar Fluid Layer by Variational Method. American Journal of Applied Mathematics and Statistics. 2019; 7(3):86-92. doi: 10.12691/AJAMS-7-3-1

Abstract

This Paper deals with the Stability of a micropolar fluid layer heated from below in the presence of uniform magnetic field. The basic hydrodynamic equations of magneto-microploar fluid layer heated from below are modified by using Boussinesq approximation and then the linearized perturbation equations are converted into a characteristic value problem with the help of Normal mode analysis. The expressions for Rayleigh number are obtained by using the variational principle. The effect of magnetic field and micropolar parameter on the Rayleigh numbers are discussed andupper bounds of critical Rayleigh number for all type of boundaries are obtained by using variational method.

Keywords

Rayleigh number, principle of exchange of stabilities, Variational principle, micro rotation, Boussinesq approximation, magnetic induction

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

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