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Wärme - und Stoffübertragung

, Volume 29, Issue 4, pp 243–249 | Cite as

Heat transfer and flow of a thermodependent and yield stress fluid

  • I. Moudachirou
  • M. Lebouche
  • R. Devienne
Originalarbeiten

Abstract

In this paper, we study the flow of a fluid possessing a yield stress, in a cylindrical pipe being the wall heated with a constant flux; experimental and numerical results being presented here. We are interested in the influence of the different parameters on the Nusselt number, and in the pressure variation. We propose a model which enables us to estimate the Nusselt number and pressure variation, which takes into account the variation of the physical properties due to temperature variations. The proposed correlations agree well with experimental measurement.

Keywords

Heat Transfer Temperature Variation Nusselt Number Experimental Measurement Apply Physic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a, b

K =a e −bT

C f

friction factor

C f*

reduced friction factor

Cp

specific heat capacity (J/Kg/°C)

D

internal diameter (m)

h

heat transfer coefficient (W/m2 °C)

H

free energy

Hb

Herschel-Bulkley number\(\frac{{\tau _0 }}{{k\left( {\frac{{U_0 }}{R}} \right)^n }}\)

K

fluid consistency (Pa · sn)

L

axial length (m)

\(\dot m\)

mass flow (Kg · m−3)

n

flow behaviour index

Nu

Nusselt number

p

pressure (Pa)

Pe

Peclet numberRe ·Pr=Re g ·Pr g

Pr

Prandtl numberPr g =kC p /λ

Prg

generalised Prandtl numberPr g =kC p /λ(U0/Dn−1

r

radial coordinate (m)

R

pipe radius (m)

Rc

plug radius

Re

Reynolds number

Re′

Metzner Reynolds number (Ostwald fluid)

Reg

generalised Reynolds number

Res

Metzner Reynolds number (Herschel-Bulkley fluid)

t

time (s)

T

temperature (°C)

Te

entrance temperature (°C)

Tm

mean temperature (°C)

Tp

wall temperature (°C)

U0

mean velocity (m/s)

u

axial velocity (m/s)

v

radial velocity (m/s)

X+

Cameron number

y, r

radial coordinate (m)

z

axial coordinate (m)

Greek symbols

α

R c /R

β

exponent used forNu

\(\dot \gamma \)

shear rate (s−1)

Δ

(3n + 1)/4n

Δ*

Δ/(ω(1 −a))

λ

thermal conductivity (W/m °C)

μa

apparent viscosity (Pa · s)

ϱ

density (kg/m3)

τ

shear stress (Pa)

τ0

wall shear stress (Pa)

φ

φ=b ψ p D/2λ

ψp

heat flux (W/m2)

ω

ω=1+2n/2n+1α+2n2/(2n+1)(n+1)α2

∂p*/∂z

∂p*/∂z=∂p/∂z/∂p/∂z (isothermal)

Indices

p

wall

i

axial index

j

radial index

Wärmeübertragungs- und Strömungsverhalten eines Fluids mit temperatur- und scherspannungsabhängigem Fließvermögen

Zusammenfassung

In dieser Arbeit wird das Strömungsverhalten eines Fluids mit temperatur- und scherspannungsabhängigem Fließvermögen in einem mit konstanter Wärmestromdichte beaufschlagten Kreisrohr untersucht. Hierbei fallen experimentell und numerisch gefundene Ergebnisse an. Besonders interessiert der Einfluß verschiedener Parameter auf die Nusselt-Zahl und den Druckverlust. Es wird ein Modell zur Berücksichtigung der Auswirkung temperaturabhängiger Stoffwerte auf beide Intensitätsparameter vorgeschlagen. Die hieraus resultierenden Korrelationen stimmen gut mit den experimentellen Befunden überein.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • I. Moudachirou
    • 1
  • M. Lebouche
    • 1
  • R. Devienne
    • 1
  1. 1.LEMTA, UA C.N.R.S. No. 875, Université Nancy IVandœuvre CedexFrance

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