Interdisciplinary Applied Mathematics

Скачать в pdf «Interdisciplinary Applied Mathematics»


tion coefficient (Cr (Kn) = 1 + a Kn) was introduced in order to model the reductions    in    the    intermolecular    collisions    of the    molecules    as    Kn    is


increased. In    duct flows, both    the    height    and    the    width    of the    duct    are


important length scales, and comparison of these length scales to the local mean free path is an important factor in the variation of a. It is seen in Figure 4.28 that the transition in a occurs later for high aspect ratio ducts, as expected.


Similar to the pipe flow case, an approximate analytical formula can be derived to describe the mass flowrate in ducts of various aspect ratios as


M



C(AR) (1 +



6Kn


. +i-ъШ


where Kn is evaluated at average pressure as before. In Figure 4.29 we present the variation of flowrate nondimensionalized with the corresponding no-slip value as a function of Kn in the slip and early transitional flow

FIGURE 4.29. Normalized flowrate variation in the slip and early transitional flow regimes for various aspect ratio (AR) duct flows. Symbols are the linearized Boltzmann solution of (Sone and Hasegawa, 1987). Comparisons with the proposed model are also presented by lines.


TABLE 4.3. Parameters of the model for various aspect ratio duct flows. The only free parameters    are    a    and в,    as ao    is    determined from    the    asymptotic    constant


limit of flowrate as Kn ^ to.


(AR) = w/h


C(AR)


<y. 0


a i


/3


1


0.42173


1.7042


8.0


0.5


2


0.68605


1.4400


3.5


0.5


4


0.84244

Скачать в pdf «Interdisciplinary Applied Mathematics»

Метки