# Heat disipation required to keep below a temp threshold

## Main Question or Discussion Point

This question is easier to explain with an example.

A silicon microprocessor consumes 100W of real power. If the surrounding air has a temperature of 22°C, and the temperature of the microprocessor must stay below 60°C, how much heat must the microprocessor dissipate?

This isn’t a homework or coursework question. I just want to know the formulas and relationships involved.

Thanks!

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berkeman
Mentor
This question is easier to explain with an example.

A silicon microprocessor consumes 100W of real power. If the surrounding air has a temperature of 22°C, and the temperature of the microprocessor must stay below 60°C, how much heat must the microprocessor dissipate?

This isn’t a homework or coursework question. I just want to know the formulas and relationships involved.

Thanks!
Seems like in the steady state, it would have to dissipate all 100W to keep from heating up more...

A more precise question would be what the thermal resistance θja would have to be to keep the IC junction temperature below 60C. Do you know how to calculate that?

Seems like in the steady state, it would have to dissipate all 100W to keep from heating up more...
Ahh of course. Thanks. I'm going to delete this question and ask a better one in the morning.

berkeman
Mentor
Ahh of course. Thanks. I'm going to delete this question and ask a better one in the morning.
No, please don't delete or alter your OP. That is against the PF rules. Just add your new question later here, or you could start a new thread if the question is different enough. :-)

A silicon microprocessor consumes 100W of real power. If the surrounding air has a temperature of 22°C, and the temperature of the microprocessor must stay below 60°C, how much heat must the microprocessor dissipate?
You probably want to ask how much heat should it dissipate if it has to stay below 60°C for a certain amount of time.

jh0
As berkeman pointed out, the heat that the processor has to dissipate is 100W. Due to the temperatures involved, almost all the heat transfer will be through convection:

Q=hc·A·ΔT

You know the power you have to dissipate (Q). Depending on the conditions (mainly the shape and position of the surface and whether it is induced or forced convection) you can estimate the convective heat transfer coefficient (hc).

If the heat is directly dissipated through the microprocessor's surface, and we can consider it to be at 60°C, we would already know the difference of temperatures, therefore we could calculate the required surface you need (A) in order to get rid of the heat.

But I'm afraid you will get a much bigger surface than the microprocessor's, that's why they put heat sinks (the aluminium plates with fins) so there is a much bigger surface. And also they put fans on top of that: forced conductivity with a significant air velocity through the fins means the convective heat transfer coefficient (hc) is much higher.