Linear and non-linear analyses of Soret-driven buoyancy convection in a vertically orientated Hele-Shaw cell with nanoparticles suspension

•The transient Soret-driven convection with nanoparticles suspension is studied.•The fluid layer is confined within a Hele-Shaw cell.•The onset time of convection decreases with increasing Hele-Shaw number.•The present results predicted the existing experimental results reasonably.

Linear and non-linear analyses of Soret-driven instability in a vertically orientated Hele-Shaw cell with nanoparticles suspension heated from above is investigated theoretically by employing the spectral method. The horizontal fluid layer is in initially quiescent state but the Soret diffusion creates convective instability and the buoyancy-driven motion sets in during the transient diffusion stage. The onset time of instability and the corresponding wave number of this motion are obtained as a function of the Rayleigh number Ra, the Lewis number Le  , and the separation ratio ψψ for different values of Hele-Shaw number Hs. It is found that the onset time of convective instability decreases with increasing the Hele-Shaw number Hs   and the concentration Rayleigh number Rs(=Raψ/Le)Rs(=Raψ/Le). The results captured in this study are in agreement with the numerical simulations of fully nonlinear problem and the experimental observations reported in the literature.