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Wärme - und Stoffübertragung

, Volume 27, Issue 8, pp 489–497 | Cite as

Heating of non-Newtonian falling liquid film on a horizontal tube

  • P. K. Sarma
  • J. Saibabu
Article

Abstract

The problem of heat transfer to non-Newtonian laminar falling liquid films on horizontal tubes is investigated theoretically for constant heat flux and isothermal conditions imposed at the inner periphery of the tube. The local and average heat transfer coefficients are obtained as function of the system parameters by conjugating the convective transport of heat to the liquid film to the thermal conduction in the material of the tube in the peripheral direction. The results indicate that the average heat transfer coefficient can be described successfully by three dimensionless groups characterizing the dynamic flow characteristics of the film, modified Prandtl number and the index of the power law variation of the rate of angular shear deformation of the fluid with respect to the shear stress.

Keywords

Heat Transfer Shear Stress Heat Flux Heat Transfer Coefficient Prandtl Number 
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

Ar

Archimedes number,g R3/ν l 2

Arm

modified Archimedes number for non-Newtonian fluids, [g R(2+n)/(2−n)]/[ν l 2(2−)n ] (ϱvϱl)

Cp

specific heat of the film

g

acceleration due to gravity

G

dynamic flow characteristic, [Rem/Ar m (2n−1)(2n+2) ]

h

heat transfer coefficient

H

dimensionless heat transfer coefficient, [Nu/Ar m (2−n)/(2n+2) ]

H

dimensionless average heat transfer coefficient, [Nu/Ar m (2−n)/(2n+2) ]

k

thermal conductivity

K

coefficient of consistency (see Eq. (1))

m

mass flow rate of liquid per unit length of the tube

M

conduction ratio parameter, (klR/kwt)Ar m (2−n)/(2n+2)

n

power-law index

Nu

Nusselt number,h R/kl

Nu

average Nusselt number,h R/k1

Pr

Prandtl number,νl

Prm

modified Prandtl number, [ν l 2 g3(n−1)/2R(n−1)/2α−(n+1)]1/(n+1)

q

heat flux

qi

heat flux at wall-liquid interface

Q

dimensionless heat flux, [(qwR/klT0)Ar m (2−n)/(2n+2) ]

R

radius of the tube

Re

Reynolds number, 4m/μ1

Rem

modified Reynolds number, (m/03F1;1) [R2(n−1)/νl]1/(2−n)

t

thickness of the tube wall

T

temperature

u

velocity of the fluid (tangential)

y

distance normal to the direction of the film flow

Greek symbols

δ

boundary layer thickness

δl

thermal boundary layer thickness

Δ

(δ/R)Ar m (2−n)/(2n+2)

Δ0

1/Δ

ζ

δt

ϑ

dimensionless temperature, (Tw−T0)/T0

λ

parameter in Eq. (7)

μ

absolute viscosity

ν

kinematic viscosity, (K/ϱ)

τ

shear stress

ϱ

density

Subscripts

l

liquid

0

inlet

w

wall

Erwärmung des Fallfilms einer nicht-Newtonschen Flüssigkeit an einem horizontalen Rohr

Zusammenfassung

Das Problem des Wärmeübergangs an laminar ablaufende Fallfilme nicht-Newtonscher Flüssigkeiten an horizontalen Rohren wird unter Voraussetzungen konstanter Temperatur bzw. konstanten Wärmeflusses bezüglich des Rohrinnenumfangs theoretisch untersucht. Die örtlichen und gemittelten Wärmeübergangskoeffizienten erhält man als Funktion der Systemparameter unter gleichzeitiger Berücksichtigung des konvektiven Wärmetransportes an dem Flüssigkeitsfilm und der Wärmeleitung im Rohrmaterial in Umfangsrichtung. Die Ergebnisse zeigen, daß sich der gemittelte Wärmeübergangskoeffizient zufriedenstellend in Abhängigkeit von drei dimensionslosen Kenngrößen darstellen läßt. Diese charakterisieren das dynamische Fließverhalten des Films bzw. entsprechen einer modifizierten Prandtl-Zahl und dem Exponenten des Potenzgesetzes, welches die Abhängigkeit der Scherdeformation der Flüssigkeit von der Schubspannung wiedergibt.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • P. K. Sarma
    • 1
  • J. Saibabu
    • 1
  1. 1.Dept. of Mechanical Engineering College of EngineeringAndhra UniversityViaskhapatnamIndia

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