Effects of couple-stresses on the dispersion of a soluble matter in a pipe flow of blood |
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Authors: | V M Soundalgekar P Chaturani |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology, P.O. IIT Powai, 400076 Bombay, India |
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Abstract: | Summary An analysis of the effects of couple-stresses on the effective Taylor diffusion coefficient has been carried out with the help of two non-dimensional parameters
based on the concentration of suspensions and
, a constant associated with the couple-stresses. It is observed that the concentration distribution increases with increasing
or
The effective Taylor diffusion coefficient falls rapidly with increasing
when
is negative.
Zusammenfassung Der Einfluß der Momentenspannungen auf den effektiven Taylorschen Diffusionskoeffizienten wird untersucht. Dabei treten zwei dimensionslose Parameter
and
auf: Der erste bezieht sich auf die Suspensionskonzentration, der zweite kennzeichnet die Momentenspannungen. Man findet, daß die Verteilungsgeschwindigkeit mit wachsendem
oder
zunimmt. Dagegen fällt der Taylorsche Diffusionskoeffizient bei wachsendem
stark ab, wenn
negativ ist.
a
Tube radius
-
C
Concentration
-
C
i
Body moment vector
-
C
0
Concentration at the axis of the tube
-
C
m
Mean concentration
-
D
Molecular diffusion coefficient
-
d
ij
Symmetric part of velocity gradient
-
F
Function of
and
characterising effective Taylor diffusion coefficient
-
f
i
Body force vector
-
H
A function of
and
-
K
2
Integration constant
-
K
*
Effective Taylor diffusion coefficient
-
k
Radius of gyration of a unit cuboid with its sides normal to the spatial axes
-
I
n
Modified Bessel's function ofnth order
-
L
Length of the tube over which the concentration is spread
-
M
Function ofH and
-
M
ij
Couple stress tensor
-
P
Function of
-
p
Fluid pressure
-
Q
Volume rate of the transport of the solute across a section of the tube
-
r
Radial distance from the axis of the tube
-
T
ij
Stress tensor
-
t
Time coordinate
-
T
ij
A
Antisymmetric part of the stress tensor
-
u
Relative fluid velocity
-
Average velocity
-
v
i
Velocity vector
-
Fluid velocity at any point of the tube
-
v
0
n
Velocity of Newtonian fluid at the axis of the tube
-
i
Vorticity vector
-
x
Axial coordinate
-
x
1
Relative axial coordinate
-
z
Non-Dimensional radial coordinate
-
Density
-
ij
Symmetric part of the stress tensor
-
µ
Viscosity of the fluid
-
µ
ij
Deviatoric part ofM
ij
-
,
Constants associated with couple-stress
With 3 figures |
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Keywords: | |
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