# Interdisciplinary Applied Mathematics

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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 Скачать в pdf «Interdisciplinary Applied Mathematics» Н. В. Камышова; С.-Петерб. национал. исслед. ун-т информ. технологий, механики и оптики, Ин-т холода и биотехнологийМетки учебные пособия