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Research Papers: Heat Transfer Enhancement

# The Flat Plate Fin of Constant Thickness, Straight Base, and Symmetrical Shape

[+] Author and Article Information
Alejandro Rivera-Alvarez

Department of Mechanical Engineering
and Center for Advanced Power Systems,
Florida State University,
2000 Levy Avenue,
Tallahassee, FL 32310
e-mail: rivera@caps.fsu.edu

Juan C. Ordonez

Mem. ASME
Department of Mechanical Engineering
and Center for Advanced Power Systems,
Florida State University,
2000 Levy Avenue,
Tallahassee, FL 32310
e-mail: ordonez@caps.fsu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 29, 2013; final manuscript received December 3, 2013; published online March 6, 2014. Assoc. Editor: W. Q. Tao.

J. Heat Transfer 136(5), 051903 (Mar 06, 2014) (9 pages) Paper No: HT-13-1170; doi: 10.1115/1.4026187 History: Received March 29, 2013; Revised December 03, 2013

## Abstract

A plate fin is an extended surface made from a plate. Classical longitudinal and radial fins are particular cases of plate fins with very simple shapes and no curvature. In this paper, the problem of a flat plate fin of constant thickness, straight base, and symmetrical shape given by a proposed power law is considered. Particular attention is paid to some basic shapes: rectangular, triangular, convex parabolic, concave parabolic, convergent trapezoidal, and divergent trapezoidal. One- and two-dimensional analyses are conducted for every shape and comparison of results is carried through the usage of a proposed shape factor. Beyond shape, temperature fields and performance for the considered plate fins are shown to be dependent on a set of three Biot numbers characterizing the ratio between conduction resistances through every direction and convection resistance at the fin surface. Effectiveness and shape factor are found to be hierarchically organized by an including-figure rule. For the rectangular, zero-tip, and convergent trapezoidal cases, effectiveness is limited by a maximum possible value of $Bit-1/2$, and two-dimensional effects are very small. For the divergent trapezoidal case instead, effectiveness can be larger than $Bit-1/2$, and one-dimensional over-estimation of the actual heat transfer can be substantially large.

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Topics: Fins , Shapes , Flat plates

## References

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## Figures

Fig. 1

Plate fin examples. (a) Flat plate fin with straight base and constant thickness. (b) Flat plate fin with curved base and constant thickness. (c) Curved plate fin with straight base and constant thickness. (d) Curved plate fin with curved base and variable thickness.

Fig. 2

Flat plate fin of constant thickness, straight base, and arbitrary symmetrical shape

Fig. 3

εBit1/2 versus BiH1/2 for rectangular and zero-tip plate fins. One-dimensional model

Fig. 4

εBit1/2 versus BiA1/2 for rectangular and zero-tip plate fins. One-dimensional model.

Fig. 5

εBit1/2 versus BiH1/2 for trapezoidal plate fins. One-dimensional model.

Fig. 6

Two-dimensional temperature fields for triangular fins with BiH1/2= 2 and three different BiW values

Fig. 7

εBit1/2 versus BiH1/2 for triangular fins. Two-dimensional model.

Fig. 8

Shape factor for triangular fins

Fig. 9

Shape factor for concave parabolic fins

Fig. 10

Shape factor for convex parabolic fins

Fig. 11

Two-dimensional temperature fields for divergent trapezoidal fins with BiH1/2= 2, M˜ = −0.25 and three different BiW values

Fig. 12

Shape factor for convergent trapezoidal fins with M˜ = 0.5

Fig. 13

Shape factor for divergent trapezoidal fins with M˜ = −0.5

Fig. 14

Shape factor for divergent trapezoidal fins with M˜ = −2.0

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