# Interdisciplinary Applied Mathematics

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For a hard sphere molecular gas under diffuse reflection (av = 1), the slip coefficients are

(15.26)

k0 = -1.2540, Ki = -0.6463, di = 2.4001, a4 = 0.0330,    bi = 0.1068, b2 = 0.4776.

For a BGK gas the slip coefficients are

k0 = -1.01619, ai = 0.76632, a4 = 0.27922, bi = 0.11684, d4 = 0.11169,

Ki = -0.38316, a2 = 0.50000, a5 = 0.26693, b2 = 0.26693, d5 = 1.82181.

di

a2

a6

1.30272,

-0.26632,

0.76644,

(15.27)

ds = 0,

In order to obtain dimensional quantities we need the viscosity and conductivity, which are given by

2

71P0

_^o_.

л/2ДТо ’

k

4

Y2RP0

Ap

л/2ДТо

Remark 1: The second term on the right-hand side of the slip condition of equation (15.24a) shows that a flow is induced over a wall with a temperature gradient along it. This is the thermal creep flow, as we have discussed in Section 5.1. The fifth term on the right-hand side of equation (15.25a) shows the existence of another type of flow, called thermal stress slip flow, which we have also discussed in Section 5.1.

Remark 2: The above equations demonstrate rigorously that in order to simulate steady-state microflows when Re ^ Kn ^ 1, we simply need to

solve the Stokes equations under the slip boundary condition. The effect of gas rarefaction for the macroscopic variables, such as density, flow velocity, and temperature, enters only through the slip boundary condition.

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