eng
Science and Education Publishing
American Journal of Applied Mathematics and Statistics
2328-7292
2019-04-04
7
3
86
92
10.12691/ajams-7-3-1
AJAMS2019731
article
Stability Analysis of a Magneto Micropolar Fluid Layer by Variational Method
Joginder Singh Dhiman
1
Gurdeep Singh
math.gurdeep@gmail.com
2
Department of Mathematics, Himachal Pradesh University, Shimla 171005, India
Department of Mathematics, GSSS Ghanari Distt Una, Himachal Pradesh 177212, India
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.
http://pubs.sciepub.com/ajams/7/3/1/ajams-7-3-1.pdf
Rayleigh number
principle of exchange of stabilities
Variational principle
micro rotation
Boussinesq approximation
magnetic induction