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Fin Design. T . T b. Total heat loss: q f =Mtanh(mL) for an adiabatic fin, or q f =Mtanh(mL C ) if there is convective heat transfer at the tip. Fin Effectiveness.

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fin design
Fin Design

T

Tb

Total heat loss: qf=Mtanh(mL) for an adiabatic fin, or qf=Mtanh(mLC) if there is convective heat transfer at the tip

fin effectiveness
Fin Effectiveness

How effective a fin can enhance heat transfer is characterized by the fin effectiveness f: Ratio of fin heat transfer and the heat transfer without the fin. For an adiabatic fin:

fin effectiveness cont
Fin Effectiveness (cont.)
  • To increase f, the fin’s material should have higher thermal conductivity, k.
  • It seems to be counterintuitive that the lower convection coefficient, h, the higher f. But it is not because if h is very high, it is not necessary to enhance heat transfer by adding heat fins. Therefore, heat fins are more effective if h is low. Observation: If fins are to be used on surfaces separating gas and liquid. Fins are usually placed on the gas side. (Why?)
  • P/AC should be as high as possible. Use a square fin with a dimension of W by W as an example: P=4W, AC=W2, P/AC=(4/W). The smaller W, the higher the P/AC, and the higher f.
  • Conclusion: It is preferred to use thin and closely spaced (to increase the total number) fins.
fin efficiency
Fin Efficiency

For infinite k

T(x)=Tb, the heattransfer

is maximum

T(x)<Tb for heat transfer

to take place

Tb

x

x

Total fin heat transfer qf

Ideal heat transfer qmax

Real situation

Ideal situation

fin efficiency cont
Fin Efficiency (cont.)

Use an adiabatic rectangular fin as an example:

Figures 8-59, 8-60

overall fin efficiency
Overall Fin Efficiency

Overall fin efficiency for an array of fins:

qf

Define terms: Ab: base area exposed to coolant

Af: surface area of a single fin

At: total area including base area and total finned surface, At=Ab+NAf

N: total number of fins

qb

thermal resistance concept
Thermal Resistance Concept

L1

A=Ab+NAb,f

t

Rb=t/(kbA)

T1

T

T1

Tb

T2

T

R1=L1/(k1A)

Tb

T2