Heat Transfer Fin Efficiency Calculator
Calculate fin efficiency and heat transfer rate for rectangular fins using the hyperbolic tangent method.
Enter fin geometry, thermal conductivity, and convection coefficient.
Fins (also called extended surfaces) increase the area available for convective heat transfer. Fins on a CPU heatsink, a motorcycle engine, a refrigerator condenser, or a radiator all work on the same principle: more surface area means more heat removed per unit time.
The fin parameter m:
m = sqrt(h x P / (k x A_c))
where h is the convective heat transfer coefficient in W/m2 K, P is the fin perimeter in m, k is the fin thermal conductivity in W/m K, and A_c is the fin cross-sectional area in m2.
For a thin rectangular fin of width W and thickness t (assuming W » t): P = 2W, A_c = W x t, which gives m = sqrt(2h / (k x t))
Fin efficiency (insulated tip approximation):
eta = tanh(m x L) / (m x L)
where L is the fin length. Efficiency runs from 1.0 (a perfect conductor where every point is at base temperature) down toward zero for very long or poorly conducting fins.
Heat transfer from the fin:
Q_fin = eta x h x P x L x delta_T
where delta_T is the temperature difference between the base and the ambient fluid.
Design rule of thumb. Making fins longer always increases total heat transfer, but efficiency drops and returns diminish. Most practical fins target 60-80% efficiency. Below 50%, the extra material is not earning its weight. The chart below shows how efficiency falls as fin length increases for your geometry.