Library / Heat transfer and thermal systems / HTS-15
Heat transfer and thermal systems
Overall efficiency of a finned surface
Effectiveness of a whole finned surface, from the total fin area Af, the total exposed area At (fins plus unfinned base) and the single-fin efficiency ηf of identical fins.
- Ref
- HTS-15
- Rev
- v1
- Field
- Heat transfer and thermal systems
- Result
- ηo
For a finned surface made of identical fins on a uniform base, the overall efficiency is ηo = 1 − (Af/At)(1 − ηf), where Af is the total fin area and At is the total exposed area including the unfinned base. It makes the whole finned surface behave like a single surface at the base temperature with a single, reduced effective area. Exclude areas covered by fin footprints.
Effectiveness of a whole finned surface, from the total fin area Af, the total exposed area At (fins plus unfinned base) and the single-fin efficiency ηf of identical fins. Uniform base temperature and a common coefficient.
Calculator
- Fin share of the exposed area, Af/At0.8
- Loss of efficiency against a perfect surface, 1 − ηo0.2
- Heat rate per kelvin with h = 50 W/(m² K), ηo h At40 W/K
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With 80 % of the area on fins of efficiency 0.75, the whole surface is 80 % efficient.
- The unfinned base counts as 100 % efficient, which is why finned surfaces always do better overall than their fins alone.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| ηf Single-fin efficiency | 0 to 1 | 0.2 | 1 | 0.8 | +10% | +7.5 % |
| At Total exposed area (fins plus base) | 0.8 to 10 m² | 0.75 | 0.98 | 0.23 | +10% | +2.27 % |
| Af Total exposed fin area | 0 to 0.8 m² | 0.8 | 1 | 0.2 | +10% | −2.5 % |
Sweep of Single-fin efficiency
| Single-fin efficiency | Overall surface efficiency |
|---|---|
| 0 | 0.2 |
| 0.125 | 0.3 |
| 0.25 | 0.4 |
| 0.375 | 0.5 |
| 0.5 | 0.6 |
| 0.625 | 0.7 |
| 0.75 | 0.8 |
| 0.875 | 0.9 |
| 1 | 1 |
Sweep one variable
Variables and how each one contributes
Overall surface efficiency
What the equation gives you. Everything else feeds it.
Total exposed fin area
The total exposed fin area, in m². More fin area with ηf below 1 lowers the overall efficiency. Raising it by 10 % (to 0.88) moves the result by −2.5 %, from 0.8 to 0.78.
Total exposed area (fins plus base)
The total exposed area (fins plus unfinned base), in m². A larger total area relative to the fins raises the overall efficiency. Raising it by 10 % (to 1.1) moves the result by +2.27 %, from 0.8 to 0.8182.
Single-fin efficiency
The single-fin efficiency, between 0 and 1. A higher fin efficiency raises the overall efficiency. Raising it by 10 % (to 0.825) moves the result by +7.5 %, from 0.8 to 0.86.
Worked example with the values above
- Fin area share: Af/At = 0.8 / 1 = 0.8.
- Fin shortfall: 1 − ηf = 0.25.
- ηo = 1 − 0.8 × 0.25 = 0.8.
Assumptions and limits
- Uniform cross-section, constant k and h, and one-dimensional conduction along the fin.
- Negligible radiation, with the base held at a uniform temperature.
Common mistakes
- Using the cross-section perimeter wrongly when finding m.
- Mixing absolute temperatures and excess temperatures above ambient.
- Using an insulated-tip formula when the tip convects, which matters for short fins.
Statistics and uncertainty
Fin results depend strongly on the heat-transfer coefficient h, which is usually known to only 20 % to 30 %. Because m varies as √h, the temperature and heat-rate errors are somewhat smaller, but still significant.
Where it is used
- Pin, rib and rod fins on heat sinks, engines and pipes.
- Rating finned tubes and checking tip temperatures.
Maths you need
- Fin parameter: m = √(hP/(kAc))
- Excess temperature: θ = T − T∞
- Fin efficiency: actual heat rate divided by the rate if the whole fin were at the base temperature