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Wärme - und Stoffübertragung

, Volume 22, Issue 3–4, pp 129–139 | Cite as

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

  • J. Stasiek
Article

Abstract

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO2) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.

Keywords

Heat Transfer Coefficient Constant Heat Flux Convective Heat Exchange Flow Inside Radiative Energy Transfer 
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

area

ap

apparent absorptivity of gas surface

cp

specific heat of fluid

D

tube diameter

E

energy or direction energy of gas per unit time

e

emissive power, emissivity per unit area

F

geometric configuration factor

H

dimensionless heat — transfer coefficient

Hexp

heat-transfer coefficient which includes both convection and radiation area and gas

h

convective heat — transfer coefficient

K

geometric configuration factor between elements on inside of tube wall

k

dimensionless gas absorption coefficient,a·D

L

length of tube

l

dimensionless length,L/D

Q

energy flux

q

heat added per unit area at tube wall

qi*

total incoming radiation per unit area to surface element

qo

total outgoing radiation per unit area from surface element

N

radiation heat-transfer coefficient

n

number surfaces of gas body

R

dimensionless radiation heat-transfer coefficient

Re

Reynolds number

S

Stanton number

T

temperature

t

dimensionless temperature

um

mean gas velocity

V

volume

X

axial length co-ordinate measured from tube entrance

x

dimensionless co-ordinate,X/D

Y

dummy integration variable

α

absorption coefficient

ɛ

emissivity of surface

ɛp,ɛp,i

apparent emissivity of gas surface

\(\bar \varepsilon \)

relation of absorptivity and apparent emissivity of gas

ɛz

substitute emissivity factor

ɛe

effective emissivity factor

ɛg,ij

irectional emissivity of gas

ξ

dimensionless variable,Y/D

g9

density of gas

x

optical thickness or extinction coefficient

σ

Stefan-Boltzmann constant

Subscripts

b

blackbody

e

exit end of tube

g

gas

i

inlet end of tube (except in symbol qi)

i, j

index of gas body surface

p

apparent surface

r

reservoir

w

inside surface of tube wall

Zonen-Übertragungs-Verfahren zur Berechnung des komplexen Wärmeaustausches bei Strömung einer optisch aktiven Umgebung im Inneren eines Rohres mit grau-diffusen Eigenschaften

Zusammenfassung

Im Artikel werden analytisch-experimentale Untersuchungen zum Einfluß der radiativen Energieübertragungsform auf den komplexen Wärmeaustausch bei Strömung eines optisch aktiven Gases im Inneren eines Rohres mit grau-diffusen Eigenschaften dargestellt. Es wird vorausgesetzt, daß das Rohr von außen mit ständigem Wärmestrahl beheizt ist, und das innen fließende Gas hat emittierende und absorbierende Eigenschaften mit geringer optischer Dichte. Analytisch wurde der Einfluß von Länge und Strahlungseigenschaften der Rohroberfläche sowie des Gases auf den Temperaturverlauf an Wand und im Gas untersucht. Der Einfluß der Strahlungsübertragung der übertragenen Energie auf den Gesamt-Wärmekoeffizienten wurde schätzungsweise angenommen. Gestützt auf das Prinzip der Zonenaufteilung nach Hottel und der Oberflächenübertragung wurde ein mathematisches Modell der Strahlungs-Konvektionsübertragung von Wärme in einem System mit eindimensionalem Temperaturfeld erarbeitet und der numerisch-experimentellen Überprüfung unterzogen. Die numerischen Rechenergebnisse wurden mit den experimentellen, bei Strömung von CO2 im Inneren eines elektrisch beheizten (keramischen) Rohres erhaltenen, verglichen. Ein System von nichtlinearen Differentialgleichungen wurde nach dem Runge-Kutta-Verfahren mit Modifikationen nach Hamming gelöst, wobei die Separable-Kernel-Methode zur Anwendung kam.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. Stasiek
    • 1
  1. 1.Department of Heat TechnologyTechnical University of GdańskGdańskPoland

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