Temperature dependent viscosity effect on stability convection of double diffusive binary fluid

In this thesis, the thermal instability in a double diffusive binary fluid with temperature dependent viscosity effect is formulated mathematically based on Boussinesq approximation. The linear stability analysis is applied to the governing equations. The resulting eigenvalue obtained are solved numerically using single-term Galerkin method with respect to different velocities and temperature conditions. The systems considered in this analysis are designed in one fluid layer system or saturated in an anisotropic porous medium. The mathematical model is then extended in a viscoelastic fluid where the oscillatory mode was presented. The Darcy model is used to describe the flow regime in the porous medium while the Oldroyd model is implemented for the viscoelastic fluid. The impact of temperature dependent viscosity, double diffusive coefficients, vertical magnetic field, feedback control, Coriolis force, and internal heat generation, anisotropic and viscoelastic parameters on the onset of Rayleigh-B´enard in the system are analyzed and presented graphically. It is found that an increase of the temperature dependent viscosity, Soret number, Lewis number always delayed the onset of convection in the system, meanwhile elevating the effects of vertical magnetic field, Dufour number, Coriolis force, feedback control, and solutal Rayleigh number hastened the instability of the system. For the effect of mechanical anisotropic on the porous medium, results show that the mechanical anisotropy destabilizes the system while the thermal anisotropy stabilizes the porous system. The effect of stress relaxation and strain retardation in the oscillatory mode of convection in the viscoelastic fluid were also discussed. Findings revealed that the critical Rayleigh-B´enard increased as the stress relaxation decreased and strain retardation increased.

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