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A lumped study of laminar forced convection in pipes with circular transverse fins at the outer surface

Eine Studie der laminaren Zwangskonvektion an Rohren mit runden Querrippen an der Außenfläche

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Abstract

A simplified analysis of laminar forced convection heat transfer in an externally finned horizontal pipe was performed using a lumped energy balance formulation. Local values for both the internal and external Nusselt numbers via correlations have been employed, leading to a simple ordinary differential equation which is solved numerically by a standard Runge-Kutta method. Results are presented for the distribution of the dimensionless total heat transferQ T/Q max plotted against the dimensionless axial stationX in the region of thermal development of the pipe. A sample of typical cases covering a wide variety of combinations of geometrical and thermal parameters in the finned pipe are discussed at length. It is found that results for all cases tested compared favorably with other more laborious numerically and analytically-oriented papers published recently in the open literature.

Zusammenfassung

Eine vereinfachte Analyse von laminarer erzwungener konvektiver Wärmeübertragung in einem Rohr mit Rippen an der Außenfläche wurde unter Benutzung einer Energiebilanz erstellt. Lokale Größen für innere und äußere Nusselt-Zahlen wurden in den Gleichungen verwendet, was zu einer einfachen Differentialgleichung führt, die numerisch mit einer Standard-Runge-Kutta-Methode gelöst werden kann. Die Verteilung der dimensionslosen GesamtwärmeübertragungQ T/Q max, aufgetragen über der dimensionslosen axialen Koordinatex wird im Bereich des thermischen Einlaufes des Rohres dargestellt. Ein Beispiel für typische Kombinationen der geometrischen und thermischen Parameter des gerippten Rohres wird ausführlich diskutiert. Es wird festgestellt, daß die Ergebnisse der getesteten Fälle, verglichen mit anderen aufwendigeren numerischen und analytischen Veröffentlichungen gut übereinstimmen.

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Abbreviations

Bi :

Biot number,h e R/k

Bi 1 :

Biot number for unfinned surface,h 1 R/k

Bi 2 :

Biot number for finned surface,h 2 R/k

c p :

specific heat

D :

pipe diameter

h e :

external convective coefficient

h i :

internal convective coefficient

h 1 :

convective coefficient for unfinned surface

h 2 :

convective coefficient for finned surface

k :

thermal conductivity

\(\dot m\) :

mass flow rate

Nu i :

internal Nusselt number,h i D/k

Nu eq :

equivalent Nusselt number, eq. (5)

Pe :

Peclet number,u D/α

Q T :

total heat transfer

Qmax :

maximum heat transfer

R :

pipe radius

T b :

mean bulk temperature

T 0 :

inlet fluid temperature

T ∞ :

ambient temperature

u :

mean velocity

x :

axial coordinate

x 1 :

interfin spacing

x 2 :

fin thickness

X :

dimensionless axial coordinate,x/R Pe

X 1 :

dimensionless value ofx 1

X 2 :

dimensionless value ofx 2

α :

thermal diffusivity

θ :

dimensionless value ofT b, (T b −T 0)/(T ∞ −T 0)

Ω :

heat transfer efficiency,Q T/Q max

References

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  3. Patankar, S. V.; Spalding, D. B.: Heat and mass transfer in boundary layers. London: Intertext 1970

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  4. Campo, A.; Lacoa, U.: The simplest approach to forced convection in horizontal pipes exposed to natural convection and thermal radiation. Int. Comm. Heat Mass Transfer 14 (1987) 551–560

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  5. Shah, R. K.; London, A. L.: Laminar flow forced convection in ducts. New York: Academic 1978

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  6. Tolpadi, A. K.; Kuehn, T. H.: Numerical study of three-dimensional natural convection from a horizontal cylinder with transverse circular fins. Int. Heat Transfer Conference 3 (1986) 1305–1310

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Author notes

  1. A. Campo

    Present address: Mechanical Engineering Dept., Florida International University, 33142, Miami, Fla., USA

Authors and Affiliations

  1. Departamento de Termodinámica, Universidad Simón Bolívar, Caracas, Venezuela

    A. Campo & F. Miralles-Wilhelm

Authors
  1. A. Campo
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  2. F. Miralles-Wilhelm
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Campo, A., Miralles-Wilhelm, F. A lumped study of laminar forced convection in pipes with circular transverse fins at the outer surface. Wärme- und Stoffübertragung 24, 47–51 (1989). https://doi.org/10.1007/BF01599505

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  • DOI: https://doi.org/10.1007/BF01599505

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