Asymptotic analysis of channel flows with slip lengths that depend on the pressure

An asymptotic analysis of (two-dimensional) channel flows of incompressible fluids with a slip length that depends on the pressure and/or the axial pressure gradient is performed, and analytical solutions of the leading-order equations for several slip lengths are presented. It is shown that, in general, the pressure drop is not a linear function of the distance along the channel but depends in a nonlinear fashion on both the inlet and outlet pressures. It is also shown that, when the slip length depends on both the pressure and the axial pressure gradient, the pressure distribution can only be determined numerically. A thermal analysis of hydrodynamically fully developed channel flows with slip lengths that depend on the pressure is also reported, and the slip model is generalized to the case that the dynamic viscosity of the fluid is a function of the local pressure in Appendix.