Fins and the Heat Sink: A Fin That Is Too Long Does Nothing

Take a 10 W power resistor. Run it from the bench power supply at a known power — for example 5 W: set the voltage to √(5 × R) — and read the current to confirm. Tape a waterproof temperature probe to the resistor body and log its temperature until it stops rising, for four arrangements: 1. bare, lying on a wooden block; 2. clipped to a small heat sink with a thin layer of thermal paste; 3. on the largest heat sink in the assortment; 4. on the same large sink with a small fan blowing across it. For each, **thermal resistance = (resistor temperature − air temperature) ÷ power**, in K/W. Expect the bare resistor to be many times worse than the fan-cooled sink. Try the large sink without paste: the rise shows how much a dry contact adds.

Look at the heat sinks you just measured. The fins are short, closely spaced and made of aluminium — exactly what the notebook's tables recommend. Closer spacing adds surface, but in still air the fins' own warm boundary layers merge and choke each other; with a fan they can be closer. That is why sinks designed for fans have many thin fins, and passive sinks have fewer, wider-spaced ones, standing vertically so the warm air can rise out between them. The thick base spreads the heat from a small hot component across all the fins. Where the source is far from the fins, a heat pipe (the previous rung) carries it there.

A practice rung: extended surfaces appear in this catalogue on the steam engine's cylinder, the Seebeck thermocouple's cold junction and every air-cooled machine. The fin equation used in the notebook is standard heat-transfer theory. **Honest limits of the numbers.** The convection coefficients are assumed round values; real ones depend on spacing, orientation and air speed, which is why step 2 measures rather than calculates. The fin model assumes a uniform coefficient and an insulated tip, both simplifications.