The onset of transient Soret-driven MHD convection confined within a Hele-Shaw cell with nanoparticles suspension

The onset of transient Soret-driven MHD convection of an incompressible electrically-conducting fluid with nanoparticles suspensions confined within a Hele-Shaw cell is studied. A uniform magnetic field is applied vertically. For the case of high concentration Rayleigh number with large negative Soret coefficient, the applied even small temperature on the upper boundary creates the Soret diffusion and therefore, the convective motion sets during the transient diffusion stage. For this transient stability analysis, the governing equations are derived in the global domain and are transformed into the semi-infinite one. The resulting equations are solved by the initial growth rate and the eigen analyses using spectral expansions. It is found that the critical time of instability increases with increasing magnetic number while decreases with increasing both the Hele-Shaw number and the concentration Rayleigh number. Under limiting case, the present stability criteria are also compared with the existing experimental results and good agreement are found.