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