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 (R c ) and the wavenumber (a c ) under partially slip boundary conditions were derived. The numerical results showed that both R c and a c are decreasing with increasing the Knudsen number. The dependence of R c on the Knudsen number (K) shows that when K < 1(T 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.

Weakly nonlinear analysis of Rayleigh–Bénard convection in shear-thinning fluids: nature of the bifurcation and pattern selection

“…Navier-type boundary conditions with a slip parameter. Note that, for Newtonian fluids with a Navier slip boundary conditions, only the linear stability of the Rayleigh-Bénard problem has been studied by Webber (2006), Kuo & Chen (2009). Here, a general weakly nonlinear analysis is performed.…”

The effect of wall slip on the stability of the Rayleigh–Bénard Poiseuille flow of viscoplastic fluids

“…Only a few studies, e.g. [11][12][13][14][15] very few situations (e.g. small scale flow configurations or hydrophobic solid surfaces).…”

“…In this configuration, the transition to turbulence is delayed due to slip. However, [14,15] deal with the effect of slip boundaries on 2D thermal convection. They show that the flow is destabilized when the slip increases at the walls.…”

Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method

“…1 plots DR h (0.4, r h ) and DR v (r v , 0.4) as functions of r. It implies that one equation is enough to describe DR v and D R h , no need to distinguish either vertical-wise or horizontal-wise normalization. The one-term approximation in [11] gives the hint to find out the fitting curve as follows:…”

“…The hydrodynamic boundary conditions imposed for most of researches are either no-slip, or slip boundary conditions [9,10]. The theoretical study of the transitions from complete slip boundary conditions to complete no-slip boundary conditions within an infinite layer, which are related to partial slip boundary conditions, has recently been reported by [11]. With more slippery boundaries, the critical Rayleigh number for instability will be lower.…”