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Turbulent heat transfer in circular tube flows of viscoelastic fluids

Turbulenter Wärmetransport bei Strömung in kreisrunden Rohren von viskoelastischen Medien

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Abstract

The effects of thermal entrance length, polymer degradation and solvent chemistry were found to be critically important in the determination of the drag and heat transfer behavior of viscoelastic fluids in turbulent pipe flow.

The minimum heat transfer asymptotic values in the thermally developing and in the fully developed regions were experimentally determined for relatively high concentration solutions of heat transfer resulting in the following correlations:

$$\begin{gathered} j_H = 0.13\left( {\frac{x}{d}} \right)^{ - 0.24} \operatorname{Re} _a^{ - 0.45} thermally developing region \hfill \\ x/d< 450 \hfill \\ j_H = 0.03 \operatorname{Re} _a^{ - 0.45} thermally developed region \hfill \\ x/d< 450 \hfill \\ \end{gathered} $$

For dilute polymer solutions the heat transfer is a function ofx/d, the Reynolds number and the polymer concentration.

The Reynolds analogy between momentum and heat transfer which has been widely used in the literature for Newtonian fluids is found not to apply in the case of drag-reducing viscoelastic fluids.

Zusammenfassung

Der Einfluß der thermischen Einlauflänge, die polymere Zersetzung und die Lösungsmittelchemie wurden als wichtige Einflußgrößen bei der Bestimmung des Widerstandes und Wärmeüberganges bei turbulenter Rohrströmung von viskoelastischen Fluiden erkannt.

Für Lösungen mit relativ hoher Konzentration wurden die minimalen asymptotischen Wärmeübergangszahlen in der thermischen Einlaufstrecke und der voll ausgebildeten Strömung experimentell ermittelt. Folgende Gleichungen beschreiben den Wärmeübergang:

$$\begin{gathered} j_H = 0.13\left( {\frac{x}{d}} \right)^{ - 0.24} \operatorname{Re} _a^{ - 0.45} f\ddot ur das thermische Einlaufgebiet \hfill \\ x/d< 450 \hfill \\ j_H = 0.03 \operatorname{Re} _a^{ - 0.45} f\ddot ur die ausgebildete Str\ddot omung \hfill \\ x/d< 450 \hfill \\ \end{gathered} $$

Bei verdünnten Polymerlösungen ist der Wärmeübergang eine Funktion vonx/d, der Re-Zahl und der Polymerkonzentration. Die Reynolds-Analogie zwischen Impuls- und Wärmetransport, die in der Literatur häufig auf Newtonsche Fluide angewendet wird, ist nicht anwendbar bei widerstandsreduzierenden, viskoelastischen Fluiden.

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Abbreviations

c :

concentration (wppm)

d :

tube diameter (cm)

De:

Deborah number

h :

convective heat transfer coefficient (w/m2‡C)

jH :

heat transferj factor, StPr2/3

k :

thermal conductivity of fluid (w/m ‡C)

K′, n :

power-law constant in Τw=K′ (8V/d) n

l :

total tube length (cm)

Nu:

Nusselt number,h d/K

Pra :

Prandtl number based on the viscosity at wall,η C p/K

Rea :

Reynolds number based on the viscosity at wall,ϱ Vd/η

Re′:

Reynolds number defined asV 2−n dn/(K′ 8n−n)

St:

Stanton number, Nu/(Rea Pra)

T b :

bulk temperature of fluid

T w :

inside wall temperature

¯T :

characteristic time of the flow

V :

average velocity

x :

axial distance (cm)

\(\dot \gamma \) :

shear rate (l/sec)

η :

apparent viscosity evaluated at wall (poise)

ϱ :

density of fluid (g/cm3)

Τ w :

wall shear stress (dyne/cm2)

λ :

characteristic time of fluid

%DR:

percentage drag reduction defined as (fNewtonian f)/fNewtonian

%HTR:

percentage heat transfer reduction defined as (j H,Newtonian-j)/j H.Newtonian

exit:

data collected at the tube exit

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Authors and Affiliations

  1. Energy Resources Center, University of Illinois at Chicago Circle, P.O. Box 4348, 60680, Chicago, Illinois, USA

    E. Y. Kwack,  J. P. Hartnett (Director) & Y. I. Cho

Authors
  1. E. Y. Kwack
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  2. J. P. Hartnett
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  3. Y. I. Cho
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Dedicated to Prof. Grigull on his 70th Birthday.

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Kwack, E.Y., Hartnett, J.P. & Cho, Y.I. Turbulent heat transfer in circular tube flows of viscoelastic fluids. Wärme- und Stoffubertragung 16, 35–44 (1982). https://doi.org/10.1007/BF01322804

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