Application Notes

Thermal Contact Resistance

Thermal contact resistance is always present in the interface between two solid surfaces. In this example, we look at contact resistance between layers in a stack of copper sheets and its impact on the apparent thermal conductivity across the layers.

Interfaces slow the propagation of heat in a structure. This can be illustrated as a temperature drop across the boundary region, as depicted in the image to the right. As a result, powders hava a low apparent thermal conductivity, even if the intrinsic conductivity of the material is high. Contact resistance is important in any structures with a large number of interfaces, eg. laminates, powders, composites etc.

In this application, a stack of polished 0.2 mm thick copper sheets was tested. The stack was exposed to mechanical pressure in the axial direction. For comparison, measurements were repeated at two different pressures, the higher pressure being more than four times higher than the initial pressure.

The anisotropic measurements performed show that the thermal conductivity in the radial direction (in the plane of the sheets) is in the expected range for bulk copper, just below 400 W/m/K. However, in the direction perpendicular to the sheets, the value is dramatically lower. In the case of 1.8 kPa pressure, the conductivity is 650 times lower in the axial direction, across the interfaces, as compared to the in-plane conductivity. When pressure increases, the conductivity in the direction of the pressure vector rises somewhat, but the anisotropy is still monumental with a 460 times higher conductivity in the plane.

As no medium is present between the layers, the conductivity drop can be attributed to contact resistance. This clearly illustrates the significance of thermal contact resistance between solid surfaces.

 

1. Thermal conductivity of copper, stack of 0.2 mm thick sheets. Axial pressure 1.8 kPa.
Measurement λradial
[W/m/K]		 λaxial
[W/m/K]		 κradial
[mm2/s]		 κaxial
[mm2/s]
1 384.6 0.5963 111.8 0.1734
2 388.3 0.5862 112.9 0.1704
3 389.0 0.5884 113.1 0.1710
4 383.7 0.5999 111.5 0.1744
Avg. 386.4 0.5927 112.3 0.1723

 

2. Thermal conductivity of copper, same stack of 0.2 mm thick sheets. Axial pressure now 7.5 kPa.
Measurement λradial
[W/m/K]		 λaxial
[W/m/K]		 κradial
[mm2/s]		 κaxial
[mm2/s]
1 386.2 0.8483 112.3 0.2466
2 390.1 0.8328 113.4 0.2421
3 385.5 0.8534 112.1 0.2481
4 387.7 0.8458 112.7 0.2459
Avg. 387.4 0.8458 112.6 0.2457