Zusammenfassung
Es wird gezeigt, dass der Übergang von der Kontinuumsströmung zur «Gleitströmung» (slip-flow) an einer rotierenden Scheibe durch ihren Abstand von der ruhenden Wand, die Drehgeschwindigkeit und den Gasdruck bestimmt wird. Messungen zeigen, dass die Maxwellsche Grenzbedingung fast bis zur Molekularströmung herab erfüllt bleibt. Trotz der Unterschiede zwischen der theoretischen (unendlich ausgedehnten) und der wirklichen Scheibe werden die Reibungskoeffizienten für beide Fälle sehr ähnlich.
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Abbreviations
- a :
-
outer radius of the disk
- a 1,a 2,a 3,a 4,a 5 :
-
constants of integration defined by Equation (2.10)
- b 1,b 2 :
-
constants of integration defined by Equation (3.8)
- c ϕ :
-
friction coefficient defined by the relation\(c_\phi = \tau _s /({\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}})\varrho _1 r^2 \omega ^2 \)
- c p :
-
specific heat at constant pressure
- G(η) :
-
dimensionless function of the tangential velocity defined by the relationV=RG(η)
- K :
-
dimensionless viscosity or thermal conductivity,μ/μ 1 orλ/λ 1
- L :
-
mean free path
- L :
-
dimensionless mean free path defined byL/L 1
- L s :
-
dimensionless mean free path defined byL s /z 0
- (M)1, (M) r ):
-
Mach numbers defined by
- N ′1 (η):
-
reduced radial velocity function given byU−RN ′1 (η)
- \((N_{Kn} )_{z_0 } ,(N_{Kn} )_d \) :
-
Knudsen numbers defined byL/z 0,L/d
- (N Pr )1 :
-
Prandtl number defined by (c p μ 1)/μ 1
- (N Re )1 :
-
Reynolds number (ϱ1 ωL 21 )/μ 1
- (N Re ) r :
-
Reynolds number (ϱ1 ωr 2/μ 1
- (N Re )0 :
-
Reynolds number (ϱ1 ωz 20 )/μ 1
- p :
-
static pressure
- Q :
-
reduced temperature function for heat exchange
- r, θ, z :
-
cylindrical polar coordinates in the radial, azimuthal, and axial directions
- :
-
gas constant in
- R, Z :
-
dimensionless coordinates,r/L 1,z/L 1
- S :
-
reduced temperature function for dissipation
- S w ,S s :
-
molecular speed ratios
- T :
-
temperature
- u, v, w :
-
components of the velocity in the radial, tangential and axial directions
- U, V, W :
-
dimensionless velocity componentsu/ωL 1,v/ωL 1,w/ωL 1
- z 0 :
-
axial distance between disk and plate
- α:
-
accommodation coefficient
- β1 :
-
dimensionless parameter defined by\(\beta _1 = \sqrt {(N_{Re} )_1 /\sigma } \)
- β0 :
-
dimensionless parameter defined by\(\beta _0 = \sqrt {(N_{Re} )_0 /\sigma } \)
- γ :
-
ratio of specific heats
- Π :
-
dimensionless density given by ϱ/ϱ1
- ζ:
-
dimensionless axial coordinate given byz/z 0
- η :
-
transformed dimensionless axial coordinate defined byβ 1 ψ=−RN(η)
- θ :
-
diemnsionless temperatureT/T 1
- ϰ:
-
constant equal to 75π/128
- λ :
-
thermal conductivity
- μ :
-
viscosity
- ϱ:
-
density
- σ :
-
factor of proportionality defined by (μ/μ 1)=θ(T/T 1)
- ψ :
-
dimensionless stream function
- ω, ω c :
-
angular velocity of rotation of disk and fluid core respectively
- Ω:
-
dimensionless angular velocity
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A study supported by the National Science Foundation under grant No. G-9725. The experimental portion of this paper was performed byZ. N. Sarafa toward a thesis for partial fulfillment of the requirements of the Ph. D. Degree at the University of Illinois.
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Soo, S.L., Sarafa, Z.N. Flow of rarefied gas over an enclosed rotating disk. Journal of Applied Mathematics and Physics (ZAMP) 15, 21–39 (1964). https://doi.org/10.1007/BF01679523
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DOI: https://doi.org/10.1007/BF01679523