Simple Temperature Rise question

Using direct temperature (vs watts/current/voltage) as input from a heat plate @ 100C - simple conduction - with a disparity of area - Heat plate is 25in sq, as it ratchets down to a 10 mil copper conductor (actually a cupper plated via) through a 100 mil PCB.

Will the temperature rise when it reaches conductor peak (via surface) as opposed to remain steady state?

For the theoretical - resistances are too negligible to factor but if it need a value, the inverse would assume Cu to be 400 w/m-k

So Im trying to solve for for t2

T1=100C.... Along - Dia=.010/Distance = .100 Cu.... With k = 400w/m-k.... T2=( ? )

• Sadly, there's no simple answer and it will depend on things like how much air is blowing past the upper surface of the board. Mar 8 '20 at 6:13
• Really - Assume there is no air. None whatsoever. Vacuum.
– tim
Mar 8 '20 at 6:20
• Then assuming the hot plate is well-regulated, it will be damn near 100 C. If you need it to the nearest 0.1 C, then it depends on what kind of radiation heat sources are surrounding it. Mar 8 '20 at 6:21
• No that's the question would it stay fairly steady state, or could there be a temperature rise. Reason= I have solder joints that have been compromised, but the liquidus is 217C, makes no sense...unless there is a rise, even a short spike before gaining equilibrium
– tim
Mar 8 '20 at 6:29
• It won't be higher than 100 C unless it's sitting under a broiler element or something. Maybe if it's in direct sunlight. Mar 8 '20 at 6:31

standard copper foil --- 1 ounce per square foot 35 microns thick, or 1.4 mils thick --- has 70 degree C per watt thermal resistance per square of foil, the heat flowing from edge to opposite edge.

A via, with height/periphery of 1:1, if plated to 35 micron thickness, will also be 70 degree C per watt

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If there is no heat flow off the top of the via, the will be no temperature difference.

• Thank You for responding. Its 1/2 Oz Cu both sides so yes, resistance or conductivity follows proportionately. BUT the question remains, lets assume for argument sake the Via is a solid Copper conductor. Would the temperature rise at the T2 point, as the heat has nowhere to go. So far it would appear that it will remain steady state, no rise whatsoever. The answer would be the same Yes/No whether 1/2 Oz or 1 Oz although the specific rise (if it were applicable) would vary proportionately.
– tim
Mar 8 '20 at 19:36

Assuming your heat source is really controlled at 100 deg C, and there are no other sources of heat impinging on the top surface (such as direct sunlight or reflected sunlight from the earth), the maximum temperature of the top surface cannot be greater than 100 deg C - your controlled heat source.

In most cases, in a vacuum and facing deep space, the top surface will be cooler than 100 deg C because of radiative cooling.

There are thermal analysis tools out there that do a good job analyzing such problems.