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Global Stability of a Couple-Stress Fluid in a Porous Medium Using a Thermal Non-Equilibrium Model


Affiliations
1 Department of Mathematics, National Institute of Technology, Hamirpur, H.P., India
2 Department of Mathematics, Govt. College Sujanpur, Distt. Hamirpur, H.P., India
     

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We show that the global nonlinear stability threshold for convection in a couple stress fluid with a thermal nonequilibrium model 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. It is also found that the couple stress fluid is more stable than the ordinary viscous fluid and then the effects of couple stress parameter, interface heat transfer coefficient, Darcy-Brinkman number and porosity modified conductivity ratio on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Keywords

Couple-Stress Fluid, Porous Medium, Global Stability, Thermal Non-Equilibrium Model.
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  • Global Stability of a Couple-Stress Fluid in a Porous Medium Using a Thermal Non-Equilibrium Model

Abstract Views: 186  |  PDF Views: 0

Authors

Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, H.P., India
Reeta Devi
Department of Mathematics, National Institute of Technology, Hamirpur, H.P., India
Divya Sharma
Department of Mathematics, Govt. College Sujanpur, Distt. Hamirpur, H.P., India

Abstract


We show that the global nonlinear stability threshold for convection in a couple stress fluid with a thermal nonequilibrium model 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. It is also found that the couple stress fluid is more stable than the ordinary viscous fluid and then the effects of couple stress parameter, interface heat transfer coefficient, Darcy-Brinkman number and porosity modified conductivity ratio on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Keywords


Couple-Stress Fluid, Porous Medium, Global Stability, Thermal Non-Equilibrium Model.