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Research Journal of Engineering and Technology
Year : 2015, Volume : 6, Issue : 1
First page : ( 79) Last page : ( 94)
Print ISSN : 0976-2973. Online ISSN : 2321-581X.
Article DOI : 10.5958/2321-581X.2015.00013.6

Stability analysis in a rotating couple-stress fluid heated from below saturating a porous medium with temperature-pressure dependent viscosity

Devi Reeta1,*,  Sunil2

1Department of Mathematics, Govt. Degree College, Sarkaghat, District. Mandi, HP-175024, India

2Department of Mathematics, National Institute of Technology, Hamirpur, HP-177005, India

*Corresponding Author's Email:

Abstract

Stability analysis is performed for a rotating couple-stress fluid heated from below saturating a porous medium with temperature pressure dependent viscosity for free-free, rigid-free and rigid-rigid conducting boundary systems. Here, the non-linear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The eigenvalue problems for different conducting boundary systems are solved by using Galerkin method. The effects of couple-stress parameter F, Darcy-a Brinkman number Da, variable dependent viscosity Γ and Taylor number TA on the onset of convection are also analyzed. Couple-stresses, rotations and medium permeability promote stabilization whereas the variable viscosity destabilizes the system.

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Keywords

Couple-stress fluid, Porous medium, Stability analysis, Temperature-pressure dependent viscosity, Different conducting boundaries (free-free, rigid-free, rigid-rigid).

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