Influence of second-order partial slip boundary conditions on thermal convection
D. F. Stranges, John R. De Bruyn and R. E. Khayat
At small length scales, the validity of some common assumptions used in hydrodynamics and heat transfer come into question, including the no-slip boundary condition on both temperature and velocity. The Rayleigh-Benard convection of fluids with second-order hydrodynamic slip and velocity jump boundary conditions are examined. We attempt to extend the limits of the Navier-Stokes Fourier model by incorporating more accurate boundary conditions using a second-order model. The importance of slip at the boundary is described by the Knudsen number, Kn = λ/D. Linear stability analysis of the steady conduction state shows the importance of incorporating slip boundary conditions for large Kn. First- and second-order boundary conditions are compared as their effects are becoming more common with the advent of micro- and nano-structures.