Abstract
Abstract We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity 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 has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.
Highlights
Convection hydrodynamic stability theory is mainly concerned with the determination of critical values of Rayleigh number, demarcating a region of stability from that of instability
By using the Galerkin-type method developed by Chandrasekhar [52], we find approximations to the critical thermal Rayleigh number for different values of the variable dependent viscosity Γ, couple-stress parameter F
The critical wave number ac and critical thermal Rayleigh number Rc depend on the couple-stress parameter F and variable dependent viscosity Γ
Summary
Convection hydrodynamic stability theory is mainly concerned with the determination of critical values of Rayleigh number, demarcating a region of stability from that of instability. The potentials of the linear theory of stability and of the energy method are complementary to each other in the sense that the linear theory gives conditions under which hydrodynamic systems are definitely unstable. Energy theory gives conditions under which hydrodynamic systems are definitely stable. The nonlinear approach becomes inevitable to investigate the effects of finite disturbances
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