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Comparison of performances of the various shapes of asymmetric fins

Abstract

A comparison between the heat loss of the asymmetric triangular fin and the asymmetric trapezoidal fins which have various slopes of the fin’s upper lateral side is performed. The relation between the slope factor of the fin and the non-dimensional fin length for equal amount of heat loss is shown. Further, the relation between the Biot number and the non-dimensional fin length for equal amount of heat loss is given. For these analyses, a forced analytic method is used. In particular, the same equation is used for both the asymmetric triangular fin and the asymmetric trapezoidal fins just by adjusting the value of the slope factor. It is shown that this equation can also be applied to a rectangular fin with very good accuracy. The base temperature, thermal conductivity of fin’s material and the heat transfer coefficient are assumed constant.

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Abbreviations

Bi :

Biot number (=hl/k)

h :

Coefficient of heat transfer

k :

Thermal conductivity

l :

Fin thickness at the base

L′:

Fin length

L :

Non-dimensional fin length (L′/l)

Q :

Heat loss from the various shapes of asymmetric fins

Q r :

Heat loss from a rectangular fin

T :

Fin temperature

T w :

Fin base temperature

T :

Fin’s surrounding temperature

x′:

Coordinate along the fin length (base to tip)

x :

Non-dimensional coordinate along the fin length (x′/l)

y′ :

Coordinate along the fin height

y :

Non-dimensional coordinate along the fin height (y′/l)

s :

Slope factor

θ:

Adjusted fin temperature (T–T )

θo 0:

Adjusted fin base temperature (T w–T)

λ n :

Eigenvalues

References

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Author information

Correspondence to Hyung Suk Kang.

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Kang, H.S. Comparison of performances of the various shapes of asymmetric fins. KSME International Journal 11, 311–318 (1997). https://doi.org/10.1007/BF02946323

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Key Words

  • Forced Analytic Method
  • Asymmetric Fin
  • Heat Loss
  • Slope Factor