Fin Efficiency Calculator
Fin efficiency compares actual heat flow with that of a fin at base temperature: a 5 mm, 50 mm aluminium pin with mL = 0.5 has η = 92.4234 %.
92.423431452002 %
Full answer, then cut to fewer decimals (not rounded):
- 92.423431452002 %
- 92.42343145200 %
- 92.4234314520 %
- 92.423431452 %
- 92.42343145 %
- 92.4234314 %
- 92.423431 %
- 92.42343 %
- 92.4234 %
- 92.423 %
- 92.42 %
- 92.4 %
- Fin heat transfer Q
- 1.36105 W
- Fin effectiveness ε = Q/(hAcθb)
- 36.9694
- Fin parameter m = √(hP/kAc)
- 10 1/m
- mL
- 0.5
Step-by-step solution
- m = √(hP/kAc) = √(25 × 0.015708 ÷ (200 × 0.000019635)) = 10 1/m
- η = tanh(mL) ÷ mL = 0.924234
- Q = √(hPkAc) θb tanh(mL) = 1.36105 W
Fin Efficiency Formula
η = tanh(mL)/mL, m = √(hP/kAc)
P perimeter, Ac cross-section, Q = √(hPkAc) θb tanh(mL)
Worked Example
A 5 mm aluminium pin fin (k = 200), 50 mm long, h = 25 W/m²·K, base 100 °C in 25 °C air:
- m = √(hP/kAc) = √(25 × 0.015708 ÷ (200 × 0.000019635)) = 10 1/m
- η = tanh(mL) ÷ mL = 0.924234
- Q = √(hPkAc) θb tanh(mL) = 1.36105 W
Fin effectiveness ε = Q/(hAcθb): 36.9694 · Fin parameter m = √(hP/kAc): 10 1/m · mL: 0.5
More Heat Transfer Calculators
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Heat Conduction Calculator
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composite: R = 1/hᵢA + Σ L/kA + 1/hₒA
Example: A 200 mm wall (k = 0.8 W/m·K, 10 m²) with faces at 40 °C and 10 °C: Heat transfer rate Q = 1200 W.
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Lumped Capacitance Calculator
(T − T∞)/(Tᵢ − T∞) = e^(−t/τ), τ = ρcLc/h
Lc = V/As (D/6 sphere, D/4 cylinder), valid when Bi = hLc/k < 0.1
Example: A 1 mm thermocouple bead (ρ = 8500, c = 400, k = 20) at 25 °C plunged into gas at 200 °C with h = 400 W/m²·K, reaching 199 °C: Time to reach T, t = 7.31678 s.
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LMTD Calculator
LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂)
counter-flow ΔT₁ = Th,i − Tc,o, ΔT₂ = Th,o − Tc,i
Example: Counter-flow: hot 150 → 100 °C, cold 30 → 70 °C, Q = 200 kW, U = 500 W/m²·K: LMTD = 74.8888 °C.
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NTU Effectiveness Calculator
ε = [1 − e^(−NTU(1 − Cr))] ÷ [1 − Cr e^(−NTU(1 − Cr))]
NTU = UA/Cmin, Cr = Cmin/Cmax (counter-flow)
Example: UA = 3000 W/K, Ch = 4000 W/K, Cc = 2000 W/K, hot in at 120 °C, cold in at 20 °C: Effectiveness ε = 0.690785.
Frequently asked questions
When is a fin worth adding?
When its effectiveness Q/(hAcθb) is well above 1, usually above 2; fins help most with low h, as in gases.
What is the corrected length?
Lc = L + Ac/P (L + d/4 for a pin) lets the insulated-tip formula account for convection from the tip.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Fin Efficiency Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/fin-efficiency-calculator/
IEEE
Scientific Converters, "Fin Efficiency Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/fin-efficiency-calculator/