Thermal Resistance

[Wing Hoe]

I have been working on selecting thermal pads recently and have found that thermal pads can be specified either with a thermal conductivity (W/mK) or thermal resistance. The thermal resistance often comes with the units, Km[sup]2[/sup]/W.

I have often been told that this means thermal resistance per unit area. However, looking at the units, since m[sup]2[/sup] is on the numerator, this does not seem to be the case. Also, a bigger area should mean less total resistance.

I have often struggled with wrapping my head around this. What is the correct way of understanding the units Km[sup]2[/sup]/W?

 

[IRstuff]

"The thermal resistance often comes with the units, Km2/W. "

This is technically incorrect. Thermal resistance is the inverse of thermal conductance, which is thermal conductivity (the inverse of thermal resistivity) multiplied by area/length. That makes thermal resistivity m*K/W, and thermal resistance K/W. Thermal resistance is the temperature rise incurred by the heat flow, so something that is more resistant must have a higher temperature rise.

m^2-K/W is more like the R-value of house insulation, and is typically used where thickness is not adjustable, as in the case of thermal pads. Therefore, thermal resistance = (m*K/W)(known_thickness/area) = (m^2-K/W)/area, which makes sense, since with all else being equal, a larger area pad of the same thickness must have a lower resistance (temperature) to heat flow.

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[Compositepro]

Did you read the thread on thermal resistance that was posted on April 9? Your question is very similar. You have to be aware that in any thermal problem there are length units used to represent thickness and area. Although the units used are the same (meters) they are not the same physical quantity. More area means less resistance while more thickness means more resistance. In math we simplify m[sup]2[/sup]/m to m. But in reality you cannot divide area by thickness and get a quantity that means anything.

In your example of thermal resistance you say the units are Km[sup]2[/sup]/W. This is a simplification of the actual units, which our brains can easily understand, K/(W/m[sup]2[/sup]). This is the temperature rise you will see, given in degrees K, for a heat flux, given in W/m[sup]2[/sup]. This is not a material property but rather a property of a particular thermal pad of a fixed thickness. If the area of the pad were also fixed, you could use units of K/W instead, to describe that part's properties.