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Two-dimensional performance of convecting-radiating fins of different profile shapes

Das zweidimensionale Verhalten von Rippen unterschiedlicher Profil-form bezüglich Wärmeabfuhr durch Konvektion und Strahlung

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Abstract

A finite element approach is used to investigate the two-dimensional performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The heat transfer rate depends on fin size parameter α, Biot numberBi, radiation-conduction parameterN r , and environment temperatures θ∞ and θ r . Numerical results for the heat transfer rate and the error due to one-dimensional assumption are presented and discussed for each geometry. The highest heat dissipation is achieved with the concave parabolic shape and the lowest with the rectangular shape with the trapezoidal and triangular shapes falling in between. The maximum error of +144 percent is noted for a short and thick rectangular fin (α=1) and −47 percent for a long thin triangular fin (α=20).

Zusammenfassung

Mit Hilfe der Methode der Finiten Elemente wird das zweidimensionale Übertragungsverhalten bezüglich Konvektion und Strahlung von Rippen mit rechteckigem, trapezförmigem, dreieckförmigem und konkav-parabolischem Querschnitt untersucht. Der übertragbare Wärmestrom hängt von dem Rippenparameter 2L/W, der BiotzahlBi, dem StrahlungskonvektionsparameterN r und von den Umgebungstemperaturen θ W und θ r ab. Für jede Geometrieform werden der übertragene Wärmestrom und der bei eindimensionaler Behandlung auftretende Fehler angegeben und diskutiert. Der höchste Wärmeübergang wird mit dem Parabelprofil, der niedrigste mit dem Rechteckprofil erzielt. Trapez- und Dreiecksform liegen dazwischen. Für eine kurze und dicke Rechtecksrippe (2L/W=1) erhält man einen Maximalfehler von +144% und für eine lange dünne Dreiecksrippe (2L/W=20) von −47%.

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Abbreviations

Bi :

=h w/2k, Biot number

F :

load vector

h :

convective heat transfer coefficient

J :

Jacobian

k :

thermal conductivity of fin

L :

fin length

m :

iteration number

N :

set of basis functions

N r :

=ε σ w T 3 b /2k, radiation-conduction parameter

q :

heat transfer rate per unit fin depth

Q :

=q/k T b , dimensionless heat transfer rate

T :

temperature

w :

fin base thickness

x :

axial coordinate

X :

=α x/L

y :

transverse coordinate

Y :

=y/(w/2)

α :

=L/(w/2)

ε :

emissivity of fin surface

θ :

=T/T b , dimensionless temperature

σ :

Stefan-Boltzmann constant

Ω :

domain of fin

Γ :

perimeter of fin

1:

one-dimensional conduction

2:

two-dimensional conduction

∞:

convective environment

b :

fin base

r :

radiative environment

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Authors and Affiliations

  1. Department of Mechanical Engineering, Gonzaga University, 99258, Spokane, WA, USA

    A. Aziz

  2. Idaho National Engineering Laboratory, EE & G Idaho, Inc., 83415, Idaho Falls, ID, USA

    H. Nguyen

Authors
  1. A. Aziz
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  2. H. Nguyen
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Aziz, A., Nguyen, H. Two-dimensional performance of convecting-radiating fins of different profile shapes. Wärme - und Stoffübertragung 28, 481–487 (1993). https://doi.org/10.1007/BF01539679

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  • DOI: https://doi.org/10.1007/BF01539679

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