Fins and Extended Surfaces

In Q = hA·ΔT, the temperature difference is usually set by the process, and raising h costs continuous fan or pump power. Area is the remaining variable, and it costs nothing to run — a passive solution with nothing to fail.

Heat must conduct along the fin while simultaneously being lost from its sides, so the temperature falls with distance from the base. A fin is extra area at a reduced temperature, which is why the arithmetic is not a simple multiplication.

A fin can be 40% efficient and 8 times effective — an excellent fin by the only measure relevant to the decision to fit it. Conflating the two is a standard error.

• Many short fins beat a few long ones with the same metal, because each runs closer to base temperature — until the spacing chokes the airflow between them.
• High conductivity raises efficiency; a high h lowers it, by pulling heat off before it reaches the tip.
• Fins go on the worse side. Water-side coefficients run around 3000 W/m²K and air-side around 30, so a car radiator is finned on the air side only.
• Rule of thumb: fins are worthwhile when kP/hA_c exceeds about 5.

Two solid surfaces touch only at a few high points, with air filling the rest — and air conducts at 0.026 W/mK. That contact resistance can dominate everything else.

Which is why an extruded one-piece heatsink beats a bolted assembly, and why thermal interface compound is mandatory. A perfect fin bolted on badly performs worse than a mediocre fin made in one piece.

Fins reduce whichever resistance they are attached to, so they do almost nothing where h is already high — a fin in boiling water is wasted metal. And if the spreading resistance in the base is the constraint, fins cannot help at all, because the heat never reaches them.

That is why a modern processor cooler puts a vapour chamber or heat pipes underneath before any fin appears: spread the heat first, then present it to the air.