A heatsink without airflow is decoration
Why the fins do almost nothing in still air.
A heatsink's fins only work by handing heat to the air passing across them, and in genuinely still air, where nothing is actually moving that air along, most of a finned heatsink's carefully increased surface area sits behind a thin layer of warm, stagnant air that barely gets replaced at all, which means the same finned block that performs impressively next to a fan can do only a fraction of that job once the fan is taken away.
The mechanism behind a heatsink's real job
A heatsink's whole purpose is to spread a hot component's heat across a much larger surface area than the component itself has, on the reasonable assumption that a larger surface hands its heat to the surrounding air faster than a small one does. That assumption only holds if the air actually touching each part of that larger surface is genuinely being replaced by cooler air from further away, because the moment air sits against a hot surface without moving, it warms up, and once it has warmed up close to the surface's own temperature, it stops being able to absorb much more heat from that surface at all, regardless of how much surface area is technically still in contact with it. In still air, the only thing moving that warmed layer away is natural convection, the same buoyancy that makes warm air rise on its own, and natural convection is a comparatively gentle, slow process next to a fan actively pushing fresh air across the same surface, which is why a heatsink relying on it alone spends most of its theoretical surface area doing far less work than the same surface area would do with even a modest breeze crossing it.
The wet-towels-on-a-rail comparison
Wet towels hung on a rail with a real gap left between each one dry noticeably faster than the same towels hung pressed close together, because a towel with open space on either side keeps meeting drier air from the room as it evaporates, while a towel squeezed tightly against its neighbours is mostly exchanging moisture with the humid air trapped in the narrow gap between them, air that has nowhere useful to go and simply gets more saturated the longer it sits there. Hanging more towels on the same rail by packing them closer together looks, at a glance, like it should dry more washing overall, since more towels are technically hanging on the same rail doing the same job, but past a certain point the closer spacing actually slows every individual towel down, the trapped humid air between neighbours doing more to prevent drying than the extra towel count does to help it. A heatsink's fins behave the same way in still air: packing more fins into the same footprint increases the theoretical surface area on paper, but if the gaps between those fins are narrow enough that the warm air sitting in them barely gets exchanged with the room, the extra fins are contributing much less real cooling than their added surface area would suggest, for exactly the same reason a tightly packed row of towels dries more slowly than a well-spaced one.
Why closely packed fins can trap the very air they are meant to shed heat into
The physical detail behind both the towels and the fins is the same: air, like the water vapour leaving a wet towel, has to actually leave the immediate vicinity of the surface it picked up heat or moisture from before that surface can go on giving up any more, and a narrow gap between two closely spaced surfaces restricts exactly how easily that exchange can happen. In still air, a heatsink fin's own boundary layer, the thin film of air clinging closest to its surface, can grow thick enough relative to a tight fin spacing that neighbouring fins are effectively sharing the same stagnant pocket of warmed air rather than each one drawing on genuinely fresh air of its own, and once that happens, adding still more fins into the same tight spacing no longer buys proportionally more cooling, since each new fin is competing with its neighbours for access to the same limited, slow-moving air rather than reaching any new air at all.
The one number worth remembering
Past a certain point, packing more fins into a heatsink relying on natural convection alone can actually reduce the total heat it manages to shed rather than increase it, since tightly spaced fins trap a layer of warm, stagnant air between them that a forced draught would otherwise sweep away, meaning more surface area stops translating into more cooling the moment the gaps between fins become narrower than the still air actually needs to circulate through them.
What this does not explain
None of this means a finned heatsink is pointless without a fan, since a well-spaced set of fins still meaningfully outperforms a plain flat surface even under natural convection alone, and the earlier article in this set on sealed enclosures already showed that a sealed box's own conduction path to its outer case is doing real work of its own regardless of whether any fins or fans are involved at all. What natural convection through fins cannot do is scale up cheaply, since chasing more cooling by adding ever more fins into the same footprint quickly runs into the stagnant-air limit this article has described, which is exactly the point at which the next article in this set follows the same problem into what actually happens once real airflow is finally added back in. A specification sheet quoting a heatsink's total surface area in isolation, without also stating whether that figure was measured under still air or under a stated forced airflow, is quoting a number that can mean two very different things depending on which condition the finished product will actually sit in, and a design that copies a promising-looking heatsink from a data sheet tested with a fan into an enclosure that has no fan at all has quietly inherited a much weaker cooling path than the data sheet's own number implied.