American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(3), 86-92
DOI: 10.12691/ajams-7-3-1
Open AccessArticle

Stability Analysis of a Magneto Micropolar Fluid Layer by Variational Method

Joginder Singh Dhiman1 and Gurdeep Singh2,

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

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

Pub. Date: April 04, 2019

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

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