Abstract
An analysis is presented for laminar radial flow due to a linear source between two parallel stationary infinite disks. The source strength varies according toQ=Q 0(νt/h 2) (t>0) and the solution is in the form of an infinite series in terms of a reduced Reynolds number\(R_a^* = \left( {\frac{{Q_0 }}{{4\pi h}}} \right)/\left( {\frac{r}{h}} \right)^2 \). The results are valid for small values ofR * a andt(=νt/h 2). The effect of the parameterR * a on the radial velocity distribution, pressure distribution, shear stress at the upper disk at different times is discussed.
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Abbreviations
- h :
-
half distance between disks
- r:
-
radial coordinate
- r :
-
r/h=dimensionless radial coordinate
- z:
-
axial coordinate
- z :
-
z/h=dimensionless axial coordinate
- t:
-
time
- t :
-
νt/h 2=dimensionless time
- R :
-
dimensionless radial coordinate of a cross-section in the flow domain
- u:
-
radial velocity
- u :
-
hu/ν=dimensionless radial velocity
- v:
-
axial velocity
- v :
-
hv/ν=dimensionless axial velocity
- p :
-
pressure
- p :
-
\(\frac{{ph^2 }}{{\rho v^2 }} = dimensionless\) pressure
- Q :
-
instantaneous source strength
- Q 0 :
-
gradient of source strength
- R a :
-
Q 0/4πνh=gradient of source Reynolds number
- R * a :
-
R a r 2=gradient of reduced Reynolds number
- ϱ:
-
density
- μ:
-
viscosity
- ν:
-
μ/ϱ=kinematic viscosity
- τ1 :
-
shear stress at the upper disk
- τ1 :
-
\(\tau _1 /\left( {\frac{{\mu Q_0 }}{{4\pi h^2 r}}} \right) = dimensionless\) shear stress at the upper disk
References
S. Uchida, Z.A.M.P.,7, 403, 1956.
A. F. Elkouh, Appl. Sci. Res.,30, 401, 1975.
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Dube, S.N. Linear radial flow of a viscous liquid between two parallel coaxial stationary infinite disks. Acta Physica 40, 95–103 (1976). https://doi.org/10.1007/BF03157092
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DOI: https://doi.org/10.1007/BF03157092