Fans and cooling. CFM vs. LFM and the significance of heatsinks

In my (limited) experience, a fan’s airflow is rated in CFM (Cubic feet per minute). When I read application notes for certain devices, however, they tend to talk about airflow in terms of LFM (linear feet per minute). LFM is apparently equivalent to CFM divided by the cross-sectional area of interest. The larger the cross-sectional area, the smaller the LFM for a given CFM.

So, why do ribbed surfaces act as heatsinks then? Ribbing a surface effectively increases the cross-sectional area, right? If that’s true, then adding ribs to a metallic surface would increase the area over which the air passes, which, if I’m interpreting the above relation correctly, actually reduces the LFM figure. In the app notes I’ve been reading, lower LFM means less cooling. So, adding a heatsink reduces cooling? That doesn’t make sense. I must be interpreting something incorrectly. Does anyone know which aspect I’m misinterpreting?

That, or I’m forgetting to account for the fact that increasing the surface area will also increases the amount of material the heat can conduct to.

Either way, I’m new to the specifics of cooling, and I’d like to get my facts straight. Any help would be appreciated.

I think you have hit the nail o the head right there.

No, it increases the surface area, but not necessarily the cross-sectional area.

But that’s not the point. The trick is that the “cross-sectional area of interest” is not the surface of the heatsink. Let’s call CFM air flow and LFM air speed. (I don’t get all these three-letter acronyms. m³/s might be too much to wish for, but what’s wrong with ft³/min?)

Let’s say you have a pipe in dire need of cooling with a fan sealed to one end. In this case it’s the cross-section of this pipe that is divided from the air flow to give the air speed. If the fan give a constant airflow, increasing the diameter of the pipe will make the air flow more slowly. Given constant inner surface of the pipe (yes, it’s possible - i can’t adjust its length at will, haha), one could imagine the wider pipe getting worse cooling. But a long pipe would make the air warm up and then there’s temperature-deltas and heat conductivities and whatnot, delta-Qs over deltatimes in some advanced formula I will not attempt or pretend I understand.

I hope you get what I’m trying to say.

If all you do is adjust the air speed over some fixed geometrical shape, then you want higher air speed to get more cooling.

But if instead you hold the air speed fixed, and change the geometry, then you want more area.

It would be something like area times speed. This could get weird, because for example at a speed where the flow is just beginning to get turbulent, a small increase in speed would make a big increase in cooling. So area times the square of the speed might be a better rule of thumb. Actually, in different setups, different rules of thumb will come closer. But I don’t think the heat transfer will ever change less than proportionally to the speed, or more than speed to the power 2 or maybe 2.5.

One way to look at this is to think of the air your fan moves. If it floats past a flat surface, it will be heated up somewhat. Now, if it has to wander through the close fins of a heat sink, so no part of the air is more than a tiny distance from hot metal, then the air will be heated up more.

If you like, use this rule of thumb: the watts of heat transferred per square meter of area per kelvin temperature difference (AKA the heat transfer coefficient) will typically be some constant times the Reynolds number to some power near 1. This is a Nusselt correlation.

From Wiki: (energy per unit area per unit time) divided by a temperature gradient (temperature difference per unit length)
The thermal resistance of the two materials (theta) when one is a fluid is just that above.

That means surface area times LFM. The higher the LFM or the higher the surface area means lower theta. The CFM can be a factor in the case where the air is replaced as is flows along the surface are due to the heat rise in the air that remains in contact along the way.

Heat sinks are rated by their still ambient theta and de-rated with air flow in LFM.

I think this is what I needed. I guess I was confusing cross-sectional area and surface area.

I do understand your pipe analogy, as well.

That is in keeping with the app notes I was reading. I had just confused cross-sectional area with surface area and while the correlation you describe made sense to me, it seemed to be at odds with the CFM/LFM correlation.

Fluid dynamics is hard. Thanks, guys!

One thing that will help you grok the difference is thinking about the flow in terms of a cross-section being dragged perpendicular to its direction. For a pipe, picture an infintely-thin, coin-shaped chunk of air being moved down the pipe; for a duct, the shape would be a square or rectangle.

For surface area, consider the perimeter of those shapes times the total length of the volume of interest – instead of a coin shape, now imagine a wire loop of constant circumference tracing out a hollow pipe. You can imagine someone bending the loop into a square or rectangle, tracing out a duct, and ending up with a shape of the same surface area. Hopefully, you can see that identical surface area doesn’t mean identical cross-sectional area from this.

Conversely, there are many many cross-sections with identical cross-sectional areas but very different perimeters. You can conceive of the coin-shaped section from above being turned into a gear-shaped section by going around the rim and doing identical additions and subtractions of semicircular bits. The cross-sectional area would be the same as the circular pipe above, but the surface area would be much much greater.