  In this paper, we study the 1D steady Boltzmann flow in a channel. The walls
of the channel are assumed to have vanishing velocity and given temperatures
$\theta_0$ and $\theta_1$. This problem was studied by Esposito et al [13,14]
where they showed that the solution tends to a local Maxwellian with parameters
satisfying the compressible Navier-Stokes equation with no-slip boundary
condition. However, a lot of numerical experiments reveal that the fluid layer
does not entirely stick to the boundary. In the regime where the Knudsen number
is reasonably small, the slip phenomenon is significant near the boundary.
Thus, we revisit this problem by taking into account the slip boundary
conditions. Following the lines of [9], we will first give a formal asymptotic
analysis to see that the flow governed by the Boltzmann equation is accurately
approximated by a superposition of a steady CNS equation with a temperature
jump condition and two Knudsen layers located at end points. Then we will
establish a uniform $L^\infty$ estimate on the remainder and derive the slip
boundary condition for compressible Navier-Stokes equations rigorously.
