Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow |
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Authors: | J P Hartnett E Y Kwack |
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Affiliation: | (1) Energy Resources Center, University of Illinois at Chicago, P.O. Box 4348, 60680 Chicago, Illinois, USA |
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Abstract: | Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature
cp
Specific heat of fluid, J · kg–1 · K–1
-
d
Diameter of tube, m
-
f
Fanning friction factor,
w/(V2/2)
-
h
Convective heat-transfer coefficient, q
w(T
w{T
b), W · m–2 · K–1
-
k
Thermal conductivity of fluid, W · m–1 · K–1
-
j
H
Heat-transfer j-factor, StPr
a
2/3
-
L
e
Entrance length, m
-
Nu
Nusselt number, hd/k
-
Pr
a
Prandtl number based on apparent viscosity at the wall, c
p/k
-
q
w
Heat flux at the wall, W · m–2
-
Re
a
Reynolds number based on apparent viscosity at the wall, Vd/
-
St
Stanton number, Nu/(Re
a
Pr
a)
-
T
Temperature, K
-
T
b
Bulk temperature of fluid, K
-
T
w
Inside-wall temperature, K
-
V
Average velocity, m · s–1
-
Ws
Weissenberg number, V/d
-
x
Axial coordinate, m
Greek symbols
g
Shear rate, s–1
-
Apparent viscosity evaluated at the wall, P5
-
0
Zero shear-rate viscosity, P5
-
Apparent viscosity at infinite shear rate, P5
-
Characteristic time of fluid, s
-
Density of fluid, kg · m–3
-
w
Wall shear stress, N · m–2
Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A. |
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Keywords: | non-Newtonian fluid polyacrylamide polymer rheology viscoelasticity |
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