Inclined layer convection in a colloidal suspension with negative Soret coefficient at large solutal Rayleigh numbers

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle θ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection (θ≈0∘), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for θ≈0∘ disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration (θ=90∘). We confirm the existence of critical angles during the transition θ:0∘→90∘, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-θ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

Onset and nonlinear regimes of ternary mixture convection in a square cavity

We present the results of numerical simulations of onset and nonlinear regimes of a ternary mixture convection in a square cavity subjected to the gravity field and vertical gradients of temperature and concentration. The stability problem for the non-convective state of the mixture is solved using a software package for the investigation of the stability of flows. Nonlinear regimes of convection are studied numerically by the finite difference method. The dependences of critical parameters on the net separation ratio are obtained for the cases of heating from above and below. Numerical data on the temporal evolution of the integral characteristics of flow and heat and mass transfer and of the fields of stream function, temperature and concentration are obtained for different values of the Rayleigh number and net separation ratio.