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How do I calculate the airflow needed to cool a RPi2 / 3 / 4?

Assume "cool" means keeping the chip below a temperature where the Pi needs to throttle.

Assume the chip is being stress tested, ambient temp is 20°C, no heatsinks.

TIA

Boodysaspie
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2 Answers2

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Look at the data sheet, it will give you the thermal resistance from the die to the case. You need to know what the max temperature you will allow the die to reach. Stress testing without details is not a useful parameter without details of the test. Forced air cooling of electronic components results in a big improvement over natural convection cooling. This effectiveness of this is listed below: Reduction in the temperature of the air in the vicinity of the components being cooled. Improvement in the heat transfer coefficient of the components transferring heat to the air surrounding them. Although the best way to make an accurate determination of cooling requirements is by actual test of the equipment to be cooled; a good approximation of the amount of air required can be determined from the mass flow relationship:

q=wCpΔt (Eq. 1)

Where q = amount of heat absorbed by the air in BTU/hr w = mass flow of air in lb/hr Cp = specific heat of air in BTU/lb °F Δt = temperature rise of the air in °F

This equation yields the following formula, which is more directly applied to electronics forced air-cooling: Q = (178.4tikW)/(Δt*Pb) (Eq. 2)

Where Q = airflow required in cubic feet per minute ti = inlet temperature in R (R = °F + 460°) Δt = temperature rise across the equipment in °F kW = power to be dissipated in the equipment in kilowatts Pb = barometric pressure at the air inlet in inches of Hg Here it is assumed that all of the heat to be dissipated is picked up by the air; i.e. conduction and radiation as well as natural convection effects on the external surfaces of the equipment are ignored.

For standard conditions of 70°F and 29.92" Hg, equation 2 reduces to the familiar: Q = (3160*KW)/ Δt (Eq. 3)

Recognizing that a given cooling application has numerous design considerations, a temperature rise of 15°F will usually yield effective cooling without incurring penalties of over sizing of the air moving device.

For a general reference on the subject, consult the book Cooling of Electronic Equipment by Allen W. Scott, John Wiley & Sons, New York, NY, 1974. There are several modeling programs that will give you an accurate answer but you need to give it the necessary details.

Gil
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  • This is a good and reasonable answer to the OP's question, but one thing needs to be kept in mind: The RPi has a built-in closed-loop thermal control system that "changes things" - the RPi will "throttle" system performance when it reaches a preset temperature threshold (85℃ ). At this point, the "open-loop" system (fans, heat exchangers, etc) might seem to be having an outsize effect, when it may actually be the case that the closed-loop system has reduced the heat being generated. – Seamus Jul 03 '21 at 18:43
  • Thank you! I was a little surprised to see kW mixed in with BTUs and Fahrenheit :) – Boodysaspie Jul 06 '21 at 02:53
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    @Seamus I would say that if the RPi is throttling then the cooling needs upgrading. – Boodysaspie Jul 06 '21 at 02:54
  • @Boodysaspie: Not necessarily. – Seamus Jul 06 '21 at 06:01
  • @Seamus OK, so the cooling doesn't need upgrading yet the Pi still throttles. Please explain. – Boodysaspie Jul 08 '21 at 14:59
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    Slowing the clock will cool the CPU but it also reduces its performance. – Gil Jul 08 '21 at 15:24
  • @Boodysaspie: Imagine that your RPi is very lightly loaded on average, but in a high ambient environment (perhaps outdoors in Alabama). Imagine that whatever your RPi is doing, it can do in 10 seconds at "full speed" once every hour, but it takes 12 seconds if it's throttled. Would you add cooling to avoid throttling, and save 2 seconds once every hour? If you still don't understand, then by all means, turn on the fans. – Seamus Jul 08 '21 at 19:18
  • @Seamus I don't understand why you have changed my question. Pi under a stress test, not 10 secs every hour; and ambient 20℃, not the mid 40s of Alabama. – Boodysaspie Jul 08 '21 at 23:16
  • @Boodysaspie: I didn't change your question. I only wanted to make it clear that the in-built, closed-loop heat control system should be considered when doing thermal calculations - which is what you asked about. – Seamus Jul 08 '21 at 23:22
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There are several reasons why the CPU will throttle. A lot depends on the design and no one these is inclusive to all designs. One reason is that the CPU gets to warm. Why with CMOS designs they are capacitive and the more and or the faster they switch the more energy is required. This causes the CPU to get warmer. Typically this is held in check with a heat sink but they do not always do the job. They then generally slow the clock down causing it to dissipate less power causing it to cool down. CPUs can and many times do reach a point where the actual clock is controlled by the temperature. This keeps you from frying the CPU.

Adjusting the clock speed of the CPU. Also called "dynamic frequency scaling," CPU throttling is commonly used to automatically slow down the computer when possible to use less energy and conserve battery, especially in laptops. CPU throttling can also be adjusted manually to make the system quieter, because the fan can then run slower. Contrast with overclocking.

CPU throttling can also be caused by a power supply being too weak, or heating up and causing it to be less efficient, making it produce less power which can also affect performance when a Overclocked or high consumption CPU needs more power to hit higher speeds. This is generally compensated for by using a higher capacity power supply.

To summarize CPU throttling is a mechanism in which the performance of the CPU is reduced during high temperatures somewhere in the 80 degrees Celsius (176 degrees Fahrenheit) range. When the CPU detects this temperature the performance of the CPU is immediately reduced causing it to run cooler. This reduces CPU usage until the temperature drops to operating range and will then speed up, this prevents overheating and damage to the internal components.

Gil
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  • I don't want it to throttle. I want to find out how to calculate the airflow required to prevent reduced performance. – Boodysaspie Jul 08 '21 at 15:41
  • You need to keep the temperature below the throleting point if it is throttling on temperature. It is dependent on getting heat out of the chip, how it is heatsinked and from that you will can determine the thermal resistance and then calculate how much airflow you will need across the heat sinking device. Your heat sink can be as simple as the IC package and the thermal conductive to the PCB. It is possible you may not be able to do it. – Gil Jul 09 '21 at 00:32