# How would a change in ambient temp affect a radiator?

I'm curious if you have a radiator or say a block of metal (lets say it's copper since it has the highest thermal conductivity) and on one side is a processor producing heat.

At idle the processor heats the block to 50°C, and the block is 120mm x 120mm. The ambient room temp is 22.2°C. You put a fan on the block (120mm x 120mm @ 1000RPM) and it cools the block to 40°C. Now drop the ambient temp 2 degrees C to 20.2°C.

Would the full change in ambient temp take effect upon the aluminum block? Would it have less effect due to the blocks efficiency? The processor's heat is constant and the fan blowing on the block is constant.

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Let's assume there is excellent thermal conductivity from the heater to the block, and from the block to the inner surface of the radiator.

This is a convective radiator. The rate of transfer of heat energy depends linearly on the difference in temperature between the block and the air (since you're holding other things fixed). The whole system will reach an equilibrium where the total rate of heat transfer to the air equals the power of the heater. The block's temperature will rise high enough above the air temperature to achieve the necessary heat flow.

So, long and short, yes, if you make the air two degrees cooler, you will make the block two degrees cooler.

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Hey Mike, thanks for answering the question! If you don't mind I'd like to clarify a few things - To simplify the layout say you just have the processors [P] directly contacted with the block [B] then the fan right on the block [F] - [P][B][F] - you're saying that a change in ambient temperature (air being blown from the fan) would result in a equal change in the blocks temperature? No change in temperature would be loss to the blocks efficiency in conducting the change? Wouldn't air velocity play a part? Thanks again Mike, appreciate the response and hope I haven't made this more confusing. – Gk3Biz May 20 '13 at 20:25
@Gk3Biz: Think of it like an electrical resistor being fed a constant current (heat power). Then a constant voltage (temperature difference) will appear across it. If you up your fan speed, that's like reducing the resistance, giving you less voltage (temperature) difference. Generally, electric equipment like motors have a rated temperature rise above ambient, in order to shed the heat they produce. – Mike Dunlavey May 20 '13 at 20:51
@Gk3Biz: the airflow inducted by the fan affects the convection (Which is affected by the Nusselt number). – fibonatic May 20 '13 at 21:15

The air flow, the block's efficiency, etc. do have an effect. If you assume 100% efficiency, infinite supply of 2 degree cooler air, etc. then a 2 degree drop in cooling air, would result in a 2 degree drop in the block temperature. However, most likely it would be a 1 degree drop (assuming 50% efficiency).

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