How to use the Fin Efficiency Calculator
- 1. Pick the finStraight rectangular (thickness and width) or circular pin (diameter).
- 2. Enter the dataLength, k, h, base temperature and fluid temperature.
- 3. Choose the tipCorrected length, exact convective tip, insulated tip or infinitely long.
Fin equations
For a fin of constant cross-section, m = √(hP / kAc) and M = √(hPkAc)·θb, where θb = Tb − T∞.
- Infinitely long fin: Q = M
- Insulated tip: Q = M tanh(mL)
- Convective tip: Q = M [sinh mL + (h/mk) cosh mL] / [cosh mL + (h/mk) sinh mL]
- Corrected length: Q = M tanh(mLc), with Lc = L + t/2 (rectangle) or L + D/4 (pin)
Fin efficiency η = Q / (h·Afin·θb) compares the fin with one held at the base temperature everywhere. Effectiveness ε = Q / (h·Ac·θb) compares it with no fin at all.
Worked example and exam tips
An aluminium fin (k = 200 W/mK) is 3 mm thick and 75 mm long, with its base at 300 °C in air at 50 °C and h = 10 W/m²K. Per metre of width, m = 5.77 m⁻¹ and Lc = 76.5 mm, so mLc = 0.442. Q = √(10 × 2 × 200 × 0.003) × 250 × tanh(0.442) ≈ 359 W per metre, and the fin efficiency is about 94%.
- A fin is worth adding only when its effectiveness is above about 2.
- Fins help most on the side with the low h (gas side), not the liquid side.
- When mL is above about 2.5, the fin behaves as infinitely long; extra length adds almost nothing.
Frequently asked questions
What is the difference between fin efficiency and effectiveness?
Efficiency compares the fin with an ideal fin at the base temperature everywhere. Effectiveness compares the heat loss with fin to the loss from the bare base area.
When can I use the corrected length?
When the tip loses heat by convection. Adding Ac/P to the length and treating the tip as insulated gives almost the same answer as the exact formula.
Why check the Biot number?
One-dimensional fin theory assumes the temperature is uniform across the fin thickness. That holds when h(t/2)/k is well below 0.1.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.