Fin Efficiency
Efficiency of a straight fin of uniform cross-section: η_fin = tanh(m·L) / (m·L).
m·L
0.474 -
Fin efficiency η_fin
0.931 -
Formula, assumptions, and limits
$$m = \sqrt{\frac{2 h}{k \cdot t}}, \quad \eta_\text{fin} = \frac{\tanh(m L)}{m L}$$
Valid for rectangular straight fins with insulated tip. Well-designed fins target m·L ≈ 1 (η ≈ 0.76). Larger m·L wastes material; smaller m·L has poor heat spreading.
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $h$ | External film coefficient | W/(m²·K) | convection |
| $k$ | Fin conductivity | W/(m·K) | material property |
| $t$ | Fin thickness | m | geometry |
| $L$ | Fin length from base | m | geometry |
| $m·L$ | Dimensionless fin parameter | - | derived |
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