[owenversteeg]

Did you even read my comment? I have designed cooling systems professionally and I can assure you that is how things work :) Not trying to be rude, but your comment is incorrect in several ways.

I'll make this very simple: The hot chip is warmer than the ambient air because the rate of heat transfer from the chip to the air is low. A fan will increase the rate of heat transfer, thus decreasing the temperature of the chip and increasing the temperature of the air in the backpack. It will also increase the rate of heat transfer from the backpack air to the backpack, which will increase the rate of heat transfer from the backpack to the environment.

Notably, the fan would help even if the backpack was a magic closed system (which it is not; put a 100W computer and a 1kWh battery into it, open ten hours later, and you will not have anywhere near 1kWh of heat.) But why would it help in a closed system? Because the chip does not care about the total energy in the system, the chip cares about the peak chip temperature. The chip will always be the hottest thing in the backpack, but the delta in temperature between the chip and the air can be quite large. Indeed, in practice, for "natural convection" (no fan), this dT between the chip and the air is considerable. When you add a fan ("forced convection") you shrink that dT substantially.

[ddingus]

Thank you. I learned something fundamental from your comment that I did not know prior. Well, maybe I did, but how I think about it makes it harder to reason about.

Whatever, it is easier to see for me now. Lol

Seeing the benefit of the fan in terms of increased heat transfer to everything the air touches is easy. Full stop.

[owenversteeg]

You're very welcome!

Heat is a fascinating thing. I can really recommend trying to visualize it and "playing around" with it in your daily life to get a stronger intuition for things. Pay attention to the thermal conductivity of the things around you and how that "feels": aluminum or copper extremely high, other metals high, plastics and woods low, fabrics and foams very low. Notice how evaporating water is very powerful at cooling things down, and how condensing water can warm things up. Notice how a small hot object cools slowly but a larger one can reject the same amount of heat very fast. Inspect the back of your fridge, or the inside of an A/C, and understand what's going on and where the energy is.

[ddingus]

Well, your comment is timely. I am part of a project about to embark on some highly specialized thermal simulation.

I will be doing exactly what you suggested to me here.

[ElFitz]

Very interesting, thanks!

Same thing for fans in a desktop case, a laptop case, or on a graphics card. They cool down the CPU / GPU / desk to case even when said computer is in a closed room.

Hadn’t thought of it this way, but it’s kind of obvious when you think of it. Would most likely have helped.