Effects of slip boundary conditions on rayleigh-bénard convection

Abstract

This work studied the Rayleigh-Bénard convection under the first-order slip boundary conditions in both hydrodynamic and thermal fields. The variation principle was applied to find the critical Rayleigh number of instability. The exteneded relations of the critical Rayleigh number (Rc) and the wavenumber (ac) under partially slip boundary conditions were derived. The numerical results showed that both Rc and ac are decreasing with increasing the Knudsen number. The dependence of Rc on the Knudsen number (K) shows that when K ≤ 10-3, the boundary can be considered as nonslip, while K ≥ 10, it can be considered as free boundaries. The maximum change rate occurs when the Knudsen number is around 0.1, indicating that the system would be affected significantly in that range.