I might actually follow you there, but I'm already "over budget" for 2014 after my server re-build project.

Oy, I hear you there.

The AP-30 fan is really not something you want hanging on any cooler, D14 or D15, unless you plan to control it with a ceiling around 3,000 RPM. But the acoustic-padded duct mod I posted really worked with the fan as case exhaust ported to the cooler.

Reports of fan whistle/whine at 4250 rpm aside, 50.5 dBA is probably less noise than my 2-fan combo puts out right now. I forget exactly what they are, but one of them is a Delta, and I think together it's around 55-56 dBA using simple logarithmic addition.

It is a tantalizing possibility, though. How much air could you pull through a wider -- perhaps taller spin-off of the D14? At what point would enhanced airflow cease to matter? And as I said -- if I could squeeze another 10C improvement out of the D14, what would it be like starting with the few C degrees advantage D15 shows over D14?

Oh, goody. Someone asked this question. Time for grossly-oversimplified pseudo-analysis!

There are two ways in which increased airflow improves performance of a heat sink, provided that the heat sink fins are spaced closely enough that additional airflow doesn't pass through the fin stack in a thermally isolated air channel (which can happen in wide fin stacks . . . has to do with the effects of velocity on the thermal boundary layer, blah blah blah). If the air isn't making contact with the fin surface and/or mixing with air that does make contact with the fin surface, then it isn't picking up any heat from the heat sink.

The first (and probably most relevant) way is to examine the total heat capacity of the air passing through the heat sink every second, again making the assumption that all of the air is picking up heat from the fins (we are talking about the D15 which has a really tight fin stack). If we also make the assumption that you're operating in a "best case" scenario in which your CPU/IHS temperature is only rising a few degrees above ambient and that ambient happens to be 27C/300K, we can somewhat-accurately assume that the heat capacity of the air will be around 1006 J/kg * K. Let's say that we want to keep the average fin temperature (again, only marginally relevant due to actual temperature distribution within the fins, but this makes things easier to process) within 1K of ambient.

We have two known quantities: Cp = ~1006 J/kg *K, and delta T = 1. Next we need to know the expected heat flux (in Watts) and the air flow required to maintain the mandated delta T. We can probably calculate the heat flux from tech specs on the processor. For example, if we were cooling an FX 9590 with a TDP of 220W, we could safely assume that it would produce a heat flux of 220W at load.

So (1 / (Cp * delta T)) * heat flux should yield the required mass per second of air flow. In this case, we get ~.219 kg/s. Assuming air density of around 1.1774 kg/cubic meter, we can calculate the cubic meters per second by taking the inverse of the density and multiplying it by the mass flow, giving us a volume flow of ~.186 meters cubed per second, which translates into ~394 cfm.

Of course, some would point out that it's the film temperature that's relevant here, forcing us to use delta T = .5, which would effectively double the required air flow to ~788 cfm.

So, assuming the fin stack can still maintain any kind of temperature differential (1K or higher) over ambient and that that you have no boundary layer separation (which you may) or air flow completely independent of the thermal boundary layer (which you also may), if you want your fin stack to remain within 1K of ambient with a heat flux of 220W, you need around 788 cfm of air flow. Scary. Anything beyond that brings the fin temperatures even closer to ambient at a rate that suffers fairly significant diminishing returns: if we wanted to get the fins within .5K of ambient, it would require around 1576 cfm of airflow, which is so much air that you will probably produce so much extra heat from the fan motors and/or friction between the air and the fin surface that you'd offset the additional benefits of extra coolant flow (assuming we haven't already reached that point @ 788 cfm, which we probably have).

We can also look at the convective heat transfer coefficient, a.k.a. 'h'. In turbulent (or laminar, but our situation is most certainly turbulent) convective heat flow regimes, h tracks upwards as air flow velocity increases. For a situation where you've got heat transfer from a flat plate (which is somewhat approximated by the fins of the D15, but not really . . . ), the average value of h over the plate is ((Pr ^ 1 / 3) * (.036(Re(L) ^ .8) - 836) * k) / L, where:

L = distance from the edge of the fin from its base

Re(L) = (V * L) / v

v = kinematic viscosity

V = Velocity

k = thermal conductivity of the cooling fluid (in this case, air)

Pr = Prandtl number (don't ask)

Without breaking out my ruler and doing some measurements on the D14 in my case (or without doing some research to find the dimensions of the D15), it would be impossible to even approximate the velocity of air flowing through the D14 or D15 @ 394 cfm (or 788 cfm). However, we can see that h tracks upward exponentially with velocity at a rate of V ^ .8 .

The effect that h has on actual heat transfer can be seen either in a simple analysis where you multiply the total fin surface area, A, by your average h value (havg or h(avg)) and the difference between the fin temperature and the film temperature of the air (film temperature = (Tambient + Tfin)/ 2) OR in a more complex analysis where we allow for differences in fin temperature at fin points further and further away from the base, which is messier than I want to get into right now (especially since the fin "base" for the D14 and D15 happens to be six heat pipes, so the fins are more like annular fins than fins extending straight out of a flat base, AND they connect with multiple heat pipes at different points. So messy).

Anyway, in simple analysis, heat flux (I'm just going to call this 'q') = havg * A * (Tfilm - Tfin). So, you can see that there is a linear relationship between h and q: if you double your value of h, you double your value for q. By logical extension, the relationship between q and V (velocity) is also exponential at a rate of V ^ .8.

If you double your velocity, you should see an increase in q of about 140% under ideal conditions where your fins are all of uniform temperature Tfin, which is totally not going to happen, ever. In reality, you'll see less than 140% increase in q.

And, to disambiguate, the value of q I'm specifying here is the expected heat flux that the heat sink can handle given the desired Tfilm and Tfin temperatures.

So, what's the theoretical maximum air flow that could benefit the D15? The answer is "a lot". But really, notable performance increases probably top out at around 300-350 cfm of useful airflow (anything beyond that, and you'll see temp drops of maybe 1K or less). Any airflow that is deflected somehow (ducts prevent this) will obviously be of no use.