Thermal convection in a rectangular box saturated by nanofluid with convective boundary condition

The combined effect of Brownian diffusion and thermophoretic (collision between molecules of base fluid and nanoparticles) on the onset of convection in a rectangular box has been investigated in the present paper. Convective boundary condition and modified mass flux condition are considered. Darcy model is used for porous media. The linear stability of nanofluid is analysed by calculating the critical Rayleigh number using normal mode technique and resulting equations are solved by the Galerkin residual method. The critical Rayleigh number is determined as a function of the nanofluid parameters, Biot number, and aspect ratios of the rectangular box. It is observed that modified diffusivity ratio, nanoparticle Rayleigh number, and Lewis number, destabilise the system, while Biot number and porosity stabilise the system. It is also found that effect of nanoparticles on convection is independent to the aspect ratio of a rectangular box. The stabilising/destabilising effects of various governing parameters on the convection have also been presented graphically.