Fin Efficiency Calculator

η_f = tanh(mL) / (mL) — uniform straight fin with adiabatic or corrected tip. Computes fin parameter m, dimensionless mL, efficiency η_f, and optionally overall surface efficiency η_o for an array of fins.

Heat Transfer · Extended Surfaces

Inputs

Fin cross-section geometry:

Tip boundary condition:

Assumes no heat loss from the fin tip — slightly over-predicts efficiency.

Fin width w (mm)

Fin thickness t (mm)

P = 2(w + t) · A_c = w × t (computed automatically)

Fin length L (mm)

Convection coefficient h (W/(m²·K))

Fin thermal conductivity k (W/(m·K))

Also compute overall surface efficiency η_o = 1 − (N·A_f/A_t)·(1−η_f)

Theory

Fin parameter and efficiency:

m = √(h × P / (k × A_c)) [m⁻¹]

η_f = tanh(mL) / (mL) [adiabatic/corrected tip]

L_c = L + A_c / P [corrected length — accounts for tip convection]

Rectangular fin shortcuts:

P = 2(w + t) [m] — cross-section perimeter

A_c = w × t [m²] — cross-section area

L_c = L + t/2 [m] — corrected length for rectangular fin

Overall surface efficiency for a finned array:

η_o = 1 − (N × A_f / A_t) × (1 − η_f)

A_f = P × L_c [m²] fin surface area (one fin)

A_t = total area including fins and unfinned base

η_o is used in Q = η_o × h × A_t × (T_base − T_∞) to find the total heat transfer rate from a finned surface.

Design guidelines:

mL	η_f	Assessment
0.2	99%	Essentially ideal — fin surface at base temperature
0.5	92%	Excellent — practical design target
1.0	76%	Good — common in practice
1.5	60%	Moderate — consider shortening fin
2.0	48%	Poor — fin length exceeds optimum
3.0	33%	Very poor — additional length adds little heat transfer