Interdisciplinary Applied Mathematics

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M


If l‘: where R is the pipe radius. In Table 15.5 (adopted and modified from (Sharipov and Sleznev, 1998) we present values of the normalized flowrate as a function of the rarefaction parameter S and the accommodation coefficient av. The data for the diffuse scattering (av = 1) are from (Cercignani and Sernagiotto, 1966), and they are solutions to the BGK model equations. The data for the hybrid diffuse-specular scattering is due to Porodnov et al. (Porodnov et al., 1978; Porodnov and Tuchvetov, 1979), and they are also solutions of the BGK equation.


In Figure 15.16 we plot the normalized flowrate versus the rarefaction parameter S for both the channel and pipe; the data are from Tables 15.3, 15.4, and 15.5. We observe the familiar Knudsen’s minimum discussed earlier in Section 4.2, with the asymptote for a pipe only as S ^ 0, which is equivalent to Kn ^ to.


TABLE 15.5. Pressure-driven flow in a pipe: Normalized flowrate Mp vs. rarefaction parameter (S) and accommodation coefficient (av). Solutions of BGK equations by Porodnov and Tuchvetov (1979).


Mp


6


a = 1


a = 0.94


a = 0.90


(7 = 0.84


(7 = 0.80


a = 0.6


0.01


1.4768


1.657


1.791


2.026


2.187


3.374


0.02


1.4608


1.635


1.764


1.983


2.144


3.255


0.04


1.4391


1.605


1.728


1.933


2.085


3.137


0.08


1.4131


1.569

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