Research Journal of Engineering and Technology

Reeta Devi ¹, Sunil ²

Affiliations
1 Department of Mathematics, Govt. Degree College, Sarkaghat, District. Mandi, HP - 175024, IN
2 Department of Mathematics, National Institute of Technology, Hamirpur, HP - 177005, IN

Abstract

Stability analysis is performed for a rotating couple-stress fluid heated from below saturating a porous medium with temperaturepressure 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- Brinkman number ˜D a , variable dependent viscosity T and Taylor number T_A on the onset of convection are also analyzed. Couple- stresses, rotations and medium permeability promote stabilization whereas the variable viscosity destabilizes the system.

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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Sunil ¹, Reeta Devi ¹, Divya Sharma ²

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

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.

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