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Heat Sink Fin Efficiency and Resistance Calculator

trafolo.eu / calculators / Heat sink fins

Adding fin height only helps while the fin can still carry heat to its tip. This computes the fin efficiency from the standard corrected-length solution and turns the array into a thermal resistance, so you can see the point where a taller fin is just more aluminium.

Straight rectangular fin array on a base plate base plateLtgaptb fin efficiency falls as the tip cools toward ambient
A fin only helps while it can still carry heat to its tip. Packing fins closer adds area but chokes the flow between them, which this model does not penalise - watch the gap.

Inputs — enter your values

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Take this from the natural or forced convection calculator rather than guessing.

Results — computed for you

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Below about 0.6 the fin tip is running near ambient and extra height is mostly wasted metal.

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Wetted area weighted by fin efficiency. This is what actually convects.

Below roughly 3 to 5 mm in still air the boundary layers merge and the real coefficient collapses.

Choosing something to solve for makes Total thermal resistance an editable target and computes the chosen input from it.

Formula

m = sqrt( 2h / (k t) ) Lc = L + t/2 (adiabatic tip, corrected length) eta_f = tanh(m Lc) / (m Lc) A_eff = A_base_exposed + eta_f A_fins R = 1/(h A_eff) + t_base/(k W D)
eta_f fin efficiency, 1 means the fin is isothermal
m fin parameter, sqrt(2h/kt) (1/m)
L, t fin height and thickness (m)
h convection coefficient over the wetted surface (W/m^2/K)
k thermal conductivity of the fin (W/m/K)

What this model assumes, and where it stops

Assumptions

  • Straight rectangular fins of uniform cross-section, all identical.
  • One-dimensional conduction along the fin, with an adiabatic tip handled by the corrected length.
  • A single uniform convection coefficient over every wetted surface.
  • Isothermal base, so no spreading resistance from the heat source into the base.
  • Steady state, no radiation.

Limitations

  • The single uniform coefficient is the weak assumption. In a real array the coefficient varies strongly along the fin and between channels, and closely spaced fins in still air perform far worse than an isolated-plate value suggests.
  • Spreading resistance is not included. A small die on a large base can add more resistance than the entire fin array, and this page will not see it.
  • Fin gap is reported but not acted on: the model does not reduce h when the fins crowd together, so packing more fins always looks beneficial here. It is not.
  • Radiation is ignored. On a black anodised sink in still air it can be a quarter of the total.
  • The corrected-length adiabatic tip is an approximation, though a good one while the tip area is small against the side area.
  • Interface resistance between the device and the base is not included.

When you need a 3D field solution instead

Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:

  • Fin spacing decisions, where the coefficient depends on the channel geometry the model treats as fixed.
  • Spreading resistance from a concentrated source into a wide base - often the dominant term, and invisible here.
  • Non-uniform airflow across the array, which is the normal case with a fan mounted on one end.
  • Pin-fin, folded-fin, skived or bonded-fin geometries that are not straight rectangular fins.
  • Cases where you need the base temperature distribution rather than a single resistance.
Try Trafolo 3D FEM Talk to us about your design

Common questions

What does fin efficiency actually mean?

The ratio of heat a real fin moves to what it would move if it were all at base temperature. The default array runs about 97%: aluminium fins of sensible proportions are nearly ideal, so adding area helps almost linearly. Efficiency collapses for long thin fins or poor conductors - a 60% fin is carrying dead weight at its tip.

When do more fins stop helping?

When the channels between them choke. This model adds area per fin but assumes the stated h still reaches every surface; in natural convection that fails once the gap drops below roughly 6 to 10 mm, because each fin’s boundary layer fills the channel. The default array’s gap is 4.1 mm - fine with a fan, already marginal in still air. Optimum fin count in natural convection is a genuine optimisation, not "as many as fit".

Why is my heat sink worse than its datasheet rating?

Datasheet Rth values are measured with a uniformly heated base and defined airflow. A small device heats only the middle of the base, adding spreading resistance this page does not model; duct bypass lets fan air escape around the fins instead of through them; and interface resistance adds on top. A 2 K/W sink cooling a 15 mm die can easily behave like 3 K/W at the junction.

References

  • Incropera & DeWitt - Fundamentals of Heat and Mass Transfer, 6th ed., ch. 3.6 on extended surfaces
  • Kraus, Aziz & Welty - Extended Surface Heat Transfer, Wiley 2001

Related calculators

  • Forced convection - Convection coefficient for air blown along a flat surface, from Reynolds and Nusselt, with the laminar to turbulent transition handled explicitly.
  • Natural convection - Convection coefficient for a plate in still air from Rayleigh and Nusselt, for vertical and horizontal surfaces, instead of guessing a value.
  • Thermal resistance - Junction-to-ambient thermal resistance through a conduction path to a surface losing heat by convection and radiation in parallel.
  • Thermal via array - Thermal resistance of a plated via array through a PCB, with the improvement over bare laminate and the effective through-plane conductivity.