Flow of second-order fluids over an enclosed rotating disc |
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Authors: | S K Sharma and H G Sharma |
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Institution: | (1) Department of Mathematics, University of Roorkee, Roorkee, India |
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Abstract: | Summary This paper is devoted to a study of the flow of a second-order fluid (flowing with a small mass rate of symmetrical radial outflow m, taken negative for a net radial inflow) over a finite rotating disc enclosed within a coaxial cylinderical casing. The effects of the second-order terms are observed to depend upon two dimensionless parameters 1 and 2. Maximum values 1 and 2 of the dimensionless radial distances at which there is no recirculation, for the cases of net radial outflow (m>0) and net radial inflow (m<0) respectively, decrease with an increase in the second-order effects represented by T(=1+2)]. The velocities at 1 and 2 as well as at some other fixed radii have been calculated for different T and the associated phenomena of no-recirculation/recirculation discussed. The change in flow phenomena due to a reversal of the direction of net radial flow has also been studied. The moment on the rotating disc increases with T.Nomenclature
, , z
coordinates in a cylindrical polar system
-
z
0
distance between rotor and stator (gap length)
-
=/z
0, dimensionless radial distance
-
=z/z
0, dimensionless axial distance
-
s
=
s/z0, dimensionless disc radius
-
V
=(u, v, w), velocity vector
-
dimensionless velocity components
-
uniform angular velocity of the rotor
-
, p
fluid density and pressure
-
P
=p/(2
z
02
2
, dimensionless pressure
-
1, 2, 3
kinematic coefficients of Newtonian viscosity, elastico-viscosity and cross-viscosity respectively
-
1, 2
2/z
0
2
, resp.
3/z
0
2
, dimensionless parameters representing the ratio of second-order and inertial effects
-
m
=
, mass rate of symmetrical radial outflow
-
l
a number associated with induced circulatory flow
-
Rm
=m/(z
01), Reynolds number of radial outflow
-
R
l
=l/(z
01), Reynolds number of induced circulatory flow
-
Rz
=z
0
2
/1, Reynolds number based on the gap
-
1,
2
maximum radii at which there is no recirculation for the cases Rm>0 and Rm<0 respectively
-
1(T),
2(T)
1 and
2 for different T
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U
1(T)
(+)
=
dimensionless radial velocity, Rm>0
-
V
1(T)
(+)
=
, dimensionless transverse velocity, Rm>0
-
U
2(T)
(–)
=
, dimensionless radial velocity, Rm=–Rn<0, m=–n
-
V
2(T)
(–)
=
, dimensionless transverse velocity, Rm<0
-
C
m
moment coefficient |
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Keywords: | |
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