if heat dissipation from heatsink surface area is less than the heat generated by IC, then the mass temperature will keep increasing until they find their equilibrium
Right. However, here we do not have a simple case of equilibrium thermodynamics, but something much more complicated.
The energy dissipated in the chip is converted to heat. This heat is not generated uniformly in time and space, it depends on the activity. In many cases with computers, especially SBCs, this activity is not steady, but sporadic; pulse-like.
Let's do some math. These small (14mm by 14mm by 9mm) aluminium heatsinks typically have about 5g of aluminium. The specific heat capacity of aluminium is about 0.9 J/(g·K), so the heat capacity of such heatsinks is about 4.5 J/K. Since [J] = [W·s], this means that 4.5 watts in one second (of thermal energy) increases the temperature of the heatsink one Kelvin (or equivalently, by one degree Celsius centigrade). If you think of this as a low-pass filter, and the typical amounts of energy dissipated in these chips, this is very significant.
There are two mechanisms the heatsink can dissipate energy to the ambient environment: via thermal radiation, and via thermal conduction. At these temperatures (say, 20°C to 60°C, or roughly equivalently 68°F to 140°F) and thermal energies (on the order of watt or two), the majority is via thermal conduction. (This is why the manufacturer charts, like Enzotech BCC9 copper heatsink chart
here (PDF), do not start from zero airflow; without airflow, there is no thermal conduction – the surrounding stand-still air just heats up as the heatsink heats up – and the thermal radiation is usually insignificant. Do note that this does not mean forced air circulation is always necessary; hot air is lighter than cold air, and rises up, and such natural air convection often suffices.)
It is obvious that heatsinks can dissipate the extra heat to the ambient environment, and allow the chips to turn more energy into heat – to do more "calculation" or "work". This is not in question here, in my opinion. The question is, can these small heatsinks make a difference on top of memory chips and bus controllers and such, that only get up to say 60°C when used without any heatsinks.
As I've mentioned, practical experiments and anecdotal evidence suggests they do on small single-board computers.
There are two different situations we should consider separately: 1) when long-term stress tests (say, 15 minutes or longer duration) causes the board to become unreliable (crashing occasionally), and 2) when specific workloads cause the board to become unreliable.
The first one is a problem in heat dissipation. You need more airflow (a fan, for example), larger heatsinks (with fins), or both. The heatsink simply cannot dissipate enough energy to the ambient environment, and both the heatsink and the chip get too hot to operate reliably. (This is why e.g. Odroid XU4 with a fan outperforms Odroid XU4Q with a passive heatsink: the CPU must be throttled more often with a passive heatsink, in order not to overheat the CPU.)
The second one is the more interesting, more hand-wavy, complex case. For simplicity, let's assume the thermal mass of the plastic/epoxy encapsulating the chip is insignificant, less than 0.1 J/K. The thermal energy generated in the chip is not steady state, but more pulse-train-like. Let's assume the chip encapsulation temperature is a steady 50°C at some point in time (due to work done in the past), when a surge of activity in it generates say five joules of thermal energy. Because of the minuscule heat capacity in the un-heatsinked chip, this will cause a local hot spot where the temperature reaches 100°C. It will rapidly dissipate to the ambient environment, but during the temperature spike, the operation of the chip can be unreliable. Or at least, this is what I think happens.
(This definitely depends on the internal structure of the ICs, too. For example, Trinamic stepper drivers should be heatsinked on the bottom, through the PCB. I've never looked at the datasheets of bridge chips or high-capacity dynamic RAM modules, so I don't know if they describe that sort of stuff, but these stepper drivers, and DC-DC converter chips with integrated MOSFETs and/or inductors definitely do.)
If we consider both of these cases together, then finned heatsinks in an enclosure with either natural convection airflow or forced airflow via a fan makes a lot of sense, even if small; no question here.
The heatsinks are not needed for all chips, only those that can generate the kind of thermal spikes as I mentioned above – the more complex ones, in other words.
However, manufacturers prefer not to include heatsinks, if they are not needed in most typical situations. SBCs like Raspberry Pis and Pi clones do not usually run heavy computation/IO loads, the sort of loads where the heatsinks would make a difference. Those who do run maximal loads on their boards, tend to find that adding these small heatsinks does make them run more stably. Adding forced airflow and/or larger heatsinks reduces thermal throttling (because the CPU is typically the main source of heat); but adding that for the CPU only – omitting heatsinks for the bridge/IO/RAM chips – often leads to an unstable machine. All this varies depending on SBC, of course.
Compare to a DC-DC converter chip that is rated for 3A without heatsinking, 5A with proper heatsinking; with a load that pulses once a second between 1A and 4A. Do you need a heatsink or not? The average current is only 2.5A. Yet, heatsinking may still be necessary, because this is not steady-state operation.
As to memory heat spreaders, there is a
reason why many are made of copper and not aluminium. I do happen to have a set of Scythe Kama Wing Copper heat spreaders (in a package, never installed), and these are rather massive. (Then again, they have a "wing" that extends in a 45° angle about the width of the DIMM card.) A lot of "overclocked" DIMM sticks already have heat spreaders installed at the factory; and I do not believe it is
just for heat dissipation (case 1 above), but also for thermal capacitance reasons (case 2 above).
(Copper heatsinks are worth the extra cost, in my opinion, only if you have forced airflow but no room for a bigger aluminium heatsink.)
I'll happily agree that heat dissipation is the primary reason. I'd even say that the secondary case is quite specific to SBC-type devices, because they basically turn electricity into heat in a very spiky, pulsed way, in a very small volume. I cannot claim my belief is true, though, because I haven't verified it. I could simulate it to find out, but with the practical experience and anecdotal "evidence" on the matter, I don't think it is worth the effort.
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