Thermal Time Constant and Specific Heat, A Second Look - John Dunn, Consultant, Ambertec, P.E., P.C.

A while back, we looked at how the specific heat of a heat sink mass can be used to examine the thermal rise time of an eight pound mass. We will now rescale that to a one pound mass, just to make these numbers a little easier to deal with, as we examine one additional issue regarding thermal rise, the time.

There is no surprise in the statement that as thermal resistance is increased, the final temperature of the object rises. However, as the thermal resistance rises, so does the thermal time constant. The higher the thermal resistance goes, the longer it takes for the object to settle out to its final temperature.

Using this new one-pound mass case above as our example, here's what happens for four values of thermal resistance:   

You might think while watching a temperature rise test, that after three minutes, you've gotten a pretty good look at what the final temperature will be, but that might not be so!!

If the thermal resistance is higher than your expectation, so might the thermal time constant and the temperature rise time exceed your expectation.

Comments

[jws]

I would expect there to be some effect of the distributed thermal resistance inside the block as well. Especially in less conductive materials, this could dwarf the interface "R". I'd be interested to see how this is treated, it becomes even more of an interest when there's "something" on the other side of the main mass that is the real site of interest (like, say, a die on top of a Cu-W heat slug on top of that thermal plane).

[Rick Collins]

There are some assumptions missing in the above example. To get a temperature from a thermal resistance I believe there has to be a constant heat flow from the base plate through the mass. That means there has to be a thermal resistance from the mass into the environment, normally considered a type of "heat sink" at a constant temperature.

I suppose this is detailed in the previous article referred to here but not cited in a way I can find it.

[John Dunn]

It wasn't detailed in the previous item either. This is admittedly simplified in that sense, but temperature excursions do take time to happen. Thermal time constants are involved but often overlooked which is the point at hand.

[Nick Name]

In fact the problem is much more complex than described. The temperature rise time constant at the interface between source and heat sink is function of : thermal resistance at contact (as mentioned), diffusibility of heat in the sink material (not mentioned since conductivity is high) and thermal resistance at the sink-fluid surface. The assumption is made that the whole sink mass is at same temperature which is valid ONLY if the heat source has a quite low dynamics with respect to the heat diffusion, a fast changing source will lead to local higher temperatures since the heat cannot be diffused in the whole mass. From the other side the highest temperature depends on the possibility for the sink to transfer heat to environment. This last property is not only function of area and fluid velocity but also of the boundary layer thickness. This is the reason why profiles are designed so that a high turbulence occurs.