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Optimization of a 3-D thermally asymmetric rectangular fin

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

The non-dimensional fin length for optimum heat loss from a thermally asymmetric rectangular fin is represented as a function of the ratio of the bottom surface Biot number to the top surface Biot number, fin tip surface Biot number and the non-dimensional fin width. Optimum heat loss is taken as 98% of the maximum heat loss. For this analysis, three dimensional separation of variables method is used. Also, the relation between the ratio of the bottom surface Biot number to the top surface Biot number and the ratio of the right surface Biot number to the left surface Biot number is presented.

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Abbreviations

Bi1:

Fin top Biot number,h 1 l/k

Bi2:

Fin bottom Biot number,h 2 l/k

Bi3:

Fin left side Biot number,h 3 l/k

Bi4:

Fin right side Biot number,h 4 l/k

Bi5:

Fin tip side Biot number,h 5 l/k

h 1 :

Fin top heat transfer coefficient [W/ m2 °C]

h 2 :

Fin bottom heat transfer coefficient [W/ m2 °C]

h 3 :

Fin left side heat transfer coefficient [W/ m2 °C]

h 4 :

Fin right side heat transfer coefficient [W/ m2°C]

h 5 :

Fin tip heat transfer coefficient [W/m2 °C ]

k :

Thermal conductivity [W/m °C]

l :

One half fin height at the base [m]

L′ :

Fin length (base to tip) [m]

L :

Non-dimensional fin length,L′/l

T :

Fin temperature [°C]

T w :

Fin base temperature [°C]

T∞ :

Ambient temperature [°C]

w′ :

One half fm width [m]

w :

Non-dimensional a half fm width,w′/1

x′ :

Length directional variable [m]

x :

Non-dimensional length directional variable,x′/1

y′ :

Height directional variable [m]

y :

Non-dimensional height directional variable

z′ :

Width directional variable [m]

z :

Non-dimensional width directional variable,z′/l

θ 0 :

Adjusted temperature, (T w -T∞)

θ:

Non-dimensional temperature, (T-T∞)/(T w -T∞)

λ n :

Eigenvalues (n=l, 2, 3, …)

μ m :

Eigenvalues (m=l, 2, 3, …)

ρ πm :

Eigenvalues (\(\sqrt {\lambda _n ^2 + \mu _m ^2 } \))

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Authors and Affiliations

  1. Division of Mechanical and Mechatronics Engineering, Kangwon National University, 200-701, Kangwon-do, Korea

    Hyuag Suk Kang

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  1. Hyuag Suk Kang
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Correspondence to Hyuag Suk Kang.

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Kang, H.S. Optimization of a 3-D thermally asymmetric rectangular fin. KSME International Journal 15, 1541–1547 (2001). https://doi.org/10.1007/BF03185744

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  • DOI: https://doi.org/10.1007/BF03185744

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