Fin Efficiency Calculator

What this tool does

A fin is never as good as its own surface area suggests, because the metal has to conduct heat out to the tip before the air can take it away, and the tip is always cooler than the base. Fin efficiency is the honest ratio between what the fin actually does and what it would do if the whole of it stayed at base temperature. This uses the adiabatic-tip solution with the corrected length Lc = L + t/2, which is the standard way to account for the exposed tip.

Formula

m = √(2h/(k t)) ; Lc = L + t/2 ; efficiency = tanh(m Lc)/(m Lc)

Variables

Symbol	Meaning	Unit
`hc`	Overall heat transfer coefficient	W/(m²·K)
`kk`	Thermal conductivity	W/(m·K)
`tt`	Fin thickness	mm
`lf`	Fin length	mm
`wf`	Fin width	mm
`dt`	Temperature difference at one end	K
`EF`	Fin efficiency	%
`MM`	Fin parameter m	1/m
`LC`	Corrected fin length	mm
`QQ`	Heat dissipated	W
`QM`	Heat if the fin were isothermal	W

Worked example

Overall heat transfer coefficient50 W/(m²·K)
Thermal conductivity200 W/(m·K)
Fin thickness3 mm
Fin length50 mm
Fin width1000 mm
Temperature difference at one end60 K

Fin efficiency87.48 %
Fin parameter m12.910 1/m
Corrected fin length51.50 mm
Heat dissipated270.30 W
Heat if the fin were isothermal309.00 W

Limitations

Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.

Frequently asked questions

Why does a longer fin not give more heat?

It does give more, but with rapidly diminishing returns. The tip of a long fin has cooled almost to ambient, so the last centimetre contributes almost nothing while still costing material and weight. Efficiency falls as m·Lc grows, and past m·Lc of about 2 you are mostly adding metal. Thicker or more conductive fins raise efficiency; a higher air-side coefficient lowers it.

Results