Interdisciplinary Applied Mathematics

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Mc


M


HPifSi ’ where M is the mass flow rate, H is the channel height, Pi is the pressure at the inlet, and the parameter pi is defined as


Pi


m

2кв% ’ where Ti is the temperature at the inlet. In Tables 15.3 and 15.4 (adopted and modified from (Sharipov and Sleznev, 1998)) we list values of the normalized flowrate as a function of the rarefaction parameter 6 defined as


1

“iTKn’ where the Knudsen number is based on the channel’s height H (6 is the same as the parameter D defined in Section 6.1). These results are obtained for different accommodation coefficients employing Maxwell’s scattering kernel. More specifically, the fully diffuse scattering case (av = 1)


TABLE 15.3. Pressure-driven flow in a channel: Normalized flowrate Mc vs. S (rarefaction parameter) and av (accommodation coefficient) (0 < S < 1).


Mc


Loyalka (1975)a


Loyalka and Hickey (1991 )b


6


a = 1


(7 = 0.92


(7 = 0.88


cr = 0.84


cr = 0.80


cr = 0.75


cr = 0.50


0.01


3.0489


3.2417


3.6697


3.9085


4.1695


0.02


2.7107


3.0548


3.2463


3.4530


3.6771


0.03


2.5234


3.0381


3.0131


3.2021


3.4070


0.04


2.3964


2.6915


2.8556


3.0328


3.2249


0.05


2.3016


2.5823


2.7383


2.9069

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