Capstone · Heat Transfer + Numerical Methods

Design a Cooling Fin Array — Meet the Spec, Then Beat It

This isn't a "verify the known answer" lab — it's a design brief. You're given a target, a footprint, and a material catalog. Everything underneath is the same single-fin physics already verified in the Circular Fin lab; what's new is the search for a design that actually works.

▶ Play the capstone 📖 Fin theory background

The design brief

An electronics module dissipates heat into a 8 cm × 8 cm footprint and needs a pin-fin heat sink to keep its base near 75°C in a 25°C room — a 50°C rise. Your job: choose a fin diameter, fin length, and material that reject at least 50 W, using as little material as you can.

Footprint
8 cm × 8 cm
Base temp.
75°C
Ambient
25°C
Target heat duty
≥ 50 W
Fin spacing rule
2.5 × diameter, center-to-center

Fin array, top-down view (footprint to scale)

Fins in the array
—
Heat rejected
—
Thermal resistance
—
Fin material used
—

Fin diameter

4.0 mm

Fin length

40 mm

Material

Cooling

Verdict

—

A design capstone built on the verified single-fin physics from the Circular Fin lab — the array logic and material/geometry tradeoffs here are original to this exercise, not transcribed from any source notes.

Why thin, long fins keep winning

Push the diameter down and the length up, and the heat rejected per cubic centimeter of material climbs steadily. The reason: a thinner fin lets you pack many more of them into the same footprint (count scales like 1/D²), and the per-fin heat loss doesn't fall nearly as fast as the per-fin volume does. Total surface area is what dominates here — not how much metal you're using.

The catch: thin, long fins are conduction-sensitive

Switch the material from aluminum to steel and try a thick, short fin first — barely any change. Now try a thin, long one — steel falls noticeably behind copper and aluminum. A thicker, shorter fin is already so efficient (heat barely has to travel before it reaches air) that the material almost doesn't matter. A thinner, longer fin makes the heat travel farther through a smaller cross-section, so how well that metal actually conducts starts to matter a lot. Material choice and geometry choice aren't independent decisions — they trade against each other.

When no aluminum geometry is enough

At natural convection, some combinations of diameter and length simply can't reach 50 W within this footprint — there isn't enough fin area physically achievable with believable dimensions. That's not a bug in the calculator; it's the same conclusion a real designer would reach: when natural convection can't do the job within the geometry you're allowed, you switch to forced air. Toggle to forced convection and watch the same geometries that fell short suddenly clear the bar.

EngineeringCandy · Capstone · single-fin physics verified in the Circular Fin lab, array logic original to this exercise · design it, test it, beat it