Onset of thermal convection in non-colloidal suspensions

This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin (J. Fluid Mech., vol. 724, 2013, pp. 527-552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number (Pe) and the particle volume fraction (φ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions ranging from 0 to 0.3. The critical Rayleigh number grows gradually by increasing from the critical value for a pure Newtonian fluid, while the critical wavenumber remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid. The heat transfer in moderately dense suspensions is significantly enhanced by convection rolls for small Rayleigh number (Ra) close to. We also found a power-law increase of the Nusselt number (Nu) with Ra, namely, for relatively large values of Ra where the scaling exponent b decreases with. Finally, it turns out that the shear-induced migration of particles can modify the heat transfer.