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A note on the free convection boundary layer on a horizontal circular cylinder with constant heat flux

Bemerkung über die freie Konvektionsgrenzschicht an einem horizontalen Kreiszylinder mit gleichförmigem Wärmestrom

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Abstract

The equations governing the free convection boundary-layer flow on a horizontal circular cylinder on which there is a prescribed surface heat flux are solved using a finite-difference scheme. This numerical solution is then used to compare the accuracy of two proposed series expansions, a Blasius expansion and a Görtler-type expansion. It is shown that the former method is better at estimating temperature profiles while the latter is better at estimating velocity profiles.

Zusammenfassung

Die Grenzschichtgleichungen für die freie Konvektion an einem horizontalen Kreiszylinder mit gleichförmigem Wärmestrom durch die Oberfläche wird mit Hilfe eines finiten Differenzverfahrens gelöst. Die numerisch ermittelten Ergebnisse werden nachher für den Vergleich der Genauigkeit von zwei Reihendarstellungen der Lösung der Grenzschichtsgleichungen benützt. Diese Reihen sind vom Blasiusbzw. Görtier-Typ. Es wird bemerkt, daß die Reihendarstellung von Blasius die Temperaturprofile besser beschreibt, während die Reihenentwicklung der Görtlerschen Art für die Geschwindigkeitsprofile eine gute Übereinstimmung mit der exakten Lösung zeigt.

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Abbreviations

a :

radius of the cylinder

g :

acceleration of gravity

P r :

Prandtl number

Q :

prescribed (constant) heat flux

T :

temperature of the fluid

t 0 :

temperature of the ambient fluid

u :

velocity in thex-direction

v :

velocity in they-direction

x :

co-ordinate measuring distance round the cylinder

y :

co-ordinate measuring distance normal to the cylinder

G r :

Grashof number=g β Q a 4/v2

β :

coefficient of thermal expansion

x :

thermal conductivity

v :

kinematic viscosity

τ w :

skin friction

References

  1. Merkin, J. H.: Free convection on an isothermal horizontal cylinder. Paper 76-HT-16 ASME. AIChE Heat Transfer Conference (St. Louis, 1976)

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  3. Saville, D. A.; Churchill, S. W.: Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies. J. Fluid Mech. 29 (1967) 391–399

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  4. Wilks, G.: External natural convection about two-dimensional bodies with constant heat flux. Int. J. Heat Mass Transfer 15 (1972) 351–354

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  5. Koh, J. C. Y.: Laminar free convection from a horizontal cylinder. Paper 76-HT-16 ASME-AIChE Heat Transfer Con-Transfer 7 (1964) 811–813

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Authors and Affiliations

  1. The University of Leeds, LS2 9JT, Leeds, Great Britain

    J. H. Merkin

  2. Faculty of Mathematics, University of Cluj, R-3400, Cluj, CP253, Romania

    I. Pop

Authors
  1. J. H. Merkin
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  2. I. Pop
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Merkin, J.H., Pop, I. A note on the free convection boundary layer on a horizontal circular cylinder with constant heat flux. Wärme- und Stoffübertragung 22, 79–81 (1988). https://doi.org/10.1007/BF01001575

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  • DOI: https://doi.org/10.1007/BF01001575

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