Influence of variable viscosity and gravity fluctuation on double diffusive convection in a fluid layer with boundary slab of finite conductivity

The linear stability analysis is carried out for the onset of double-diffusive convection in a fluid layer with a boundary slab along with temperature-dependent viscosity and gravity fluctuation. The authors proposed three types of gravity fluctuation. We considered three cases of gravity field fluctuation: (a) linear and (b)parabolic and (c) cubic. An analytical solution for the subsequent problem is acquired through the perturbation technique. The findings demonstrate that the viscosity variation parameter, the thermal conductivity ratio, the gravity parameter, the depth ratio, and the soret parameter accelerate the start of convection, while the increasing Lewis number slow down the convective motion. Additionally, the system was found to be more stable for the linear type of gravity field fluctuation and more unstable for the cubic type of gravity field fluctuation.