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The effect of Rotation on Thermal Convection in a Couple-Stress Fluid Saturating a Porous Medium Using Galerkin method: A Nonlinear Stability Analysis


Affiliations
1 Department of Mathematics, Govt. Degree College, Sarkaghat, Distt. Mandi (H.P.) 175024, India
2 Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
3 Department of Physics, Govt. Degree College, Hamirpur (H.P.) 177005, India
     

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A global nonlinear stability analysis is performed for a rotating couple-stress fluid layer heated from below saturating a porous medium for different conducting boundary systems. Here, the global nonlinear 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 boundaries are solved by using Galerkin method. The effects of couple-stress parameter, Darcy-Brinkman number and Taylor number on the onset of convection are also analyzed.

Keywords

Couple-Stress Fluid, Global Stability, Porous Medium, Rotation, Free-Free, Rigid-Free, Rigid-Rigid Conducting Boundaries, Galerkin Method.
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  • The effect of Rotation on Thermal Convection in a Couple-Stress Fluid Saturating a Porous Medium Using Galerkin method: A Nonlinear Stability Analysis

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Authors

Reeta Devi
Department of Mathematics, Govt. Degree College, Sarkaghat, Distt. Mandi (H.P.) 175024, India
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
Ravinder Paul
Department of Physics, Govt. Degree College, Hamirpur (H.P.) 177005, India

Abstract


A global nonlinear stability analysis is performed for a rotating couple-stress fluid layer heated from below saturating a porous medium for different conducting boundary systems. Here, the global nonlinear 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 boundaries are solved by using Galerkin method. The effects of couple-stress parameter, Darcy-Brinkman number and Taylor number on the onset of convection are also analyzed.

Keywords


Couple-Stress Fluid, Global Stability, Porous Medium, Rotation, Free-Free, Rigid-Free, Rigid-Rigid Conducting Boundaries, Galerkin Method.

References