Abstract
An analysis is presented for laminar radial flow due to an oscillating source between parallel plates. The source strength varies according to Q=Q 0 cos ωt, and the solution is in the form of an infinite series in terms of a reduced Reynolds number, R *a =Q 0/4πνa/(r/a)2. (Q 0 = amplitude of source strength, ω = frequency, a = half distance between plates, r = radial coordinate, t = time, and ν = kinematic viscosity.) The results are valid for small values of R *a and all values of the frequency Reynolds number, α=ωa 2/ν. The effects of the parameters R *a and α are discussed.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Abbreviations
- a :
-
half distance between plates
- r :
-
radial coordinate
- r :
-
dimensionless radial coordinate, r/a
- z :
-
axial coordinate
- z :
-
dimensionless axial coordinate, z/a
- t :
-
time
- t :
-
dimensionless time, tv/a 2
- R :
-
dimensionless radial coordinate of a cross-section in the flow
- ū :
-
velocity component in radial direction
- u :
-
dimensionless velocity component in radial direction, ūa/ν
- v :
-
velocity component in axial direction
- v :
-
dimensionless velocity component in axial direction, va/v
- p :
-
pressure
- p :
-
dimensionless pressure, pa 2/ρν 2
- Q :
-
instantaneous source strength
- Q 0 :
-
amplitude of source strength
- ω :
-
frequency
- R a :
-
amplitude of source Reynolds number, Q 0/4πνa
- R *a :
-
amplitude of reduced Reynolds number, Q 0/r 2
- α :
-
frequency Reynolds number, ωa 2/ν
- ρ :
-
density
- μ :
-
viscosity
- ν :
-
kinematic viscosity, μ/ρ
- τ 1 :
-
shear stress at the upper boundary
- τ 1 :
-
dimensionless shear stress at the upper boundary, τ 1/(μQ 0/4πa 2r)
References
Uchida, S., ZAMP 7 (1956) 403.
Na, T. Y., E. G. Nielsen and J. D. Grossman, ASME publication 67 - WA/FE - 20, Winter Annual Meeting, Nov. 1967.
Elkouh, A. F., Appl. Sci. Res. 21 (1969) 284.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Elkouh, A.F. Oscillating radial flow between parallel plates. Applied Scientific Research 30, 401–417 (1975). https://doi.org/10.1007/BF00455965
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00455965