However, if a material conducts heat differently in the x- and y- perpendicular directions (see Fig. 2 below), which both lie in-plane, the Hot Disk® Anisotropic tests return the geometrical average of thermal properties in these two directions. Carbon textiles are a common example of a material type which possesses three-dimensional (3D) anisotropy, another being devices produced by additive manufacturing (i.e. 3D printing). In order to obtain thermal properties in all three orthogonal directions for such materials, Hot Disk AB offers the so-called Hot Strip® method, which operates with special Hot Strip® sensors (see Fig. 1).
To achieve this, a Hot Strip sensor is carefully placed on the sample to control the direction of heat flow. This arrangement, displayed in Fig. 2, restrict heat propagation to one particular direction within the plane, while permitting free heat movement along the other in-plane direction. In Fig. 2, the sensor is slightly smaller than the sample in the y-direction. Hence, a heat wave generated by the sensor will reach the sample border in the y-direction after a short period of time during a transient recording. When this sample border is reached, an overwhelming portion of the heat will propagate only in the x-direction during the remaining measurement time. Thus, such an experiment allows us to obtain relevant thermal conductivity and thermal diffusivity in the x-direction.
In order to obtain the thermal properties in the y-direction, a sample is cut so that an applied heat wave is restricted to moving in the x- direction, and the measurement is repeated (see Fig. 3). As an alternative, if one wishes to avoid cutting, it is possible to use Hot Strip sensors whose length greatly exceeds their width (see Fig. 4). Then, the sensor is placed along the y-axis so that the thermal properties in the x-direction are obtained. Finally, the sensor is simply rotated by 90 degrees to align with the x-axis, and testing is repeated.
The examples above assume that the sample comprises a thin and fairly thermally conductive sheet (above 1 W/mK in thermal conductivity). Since it is thin, heat propagation is also restricted in the through-plane (z-) direction. So, when measuring such a sample, the obtained thermal properties are in a single direction in-plane only (x- or y-direction). If the sample is thick enough so that heat can propagate without reaching the sample boundaries in the z-direction, during the full transient recording, a modified approach can be applied: this in order to obtain thermal properties both in the through-plane direction and in one of the in-plane directions. A setup of this type of measurement is depicted in Fig. 5.
Similarly to thin samples, restricting the heat motion to a specific direction in-plane, allows us to obtain, from a single measurement, either the thermal conductivity and thermal diffusivity in the x- and z-directions or in the y- and z-directions.
Applying the Hot Strip method to a Carbon Nanotube (CNT) textile:
In this example, Carbon textile sheets were cut in two different ways: 1) to restrict heat moving in the y-direction, 2) to restrict heat moving in the x-direction (see Fig. 6). The sample parameters are presented in Table 1.
The results provided in Table 2 are average values of 5 consecutive measurements with 30 minutes interval between the measurements. The measurement time was 2 to 3 seconds and the heating power was 0.25 W.
The minor deviation in thermal conductivity values in the z-direction between the two setups is likely due to slight differences in applied pressure (thermal resistance between layers is less when greater pressure is applied).
The following equations were utilized to calculate the thermal conductivity in the x-, y-, and z-directions from the measured A and B parameters:
This application note introduces our unique technique for measuring the 3D thermal conductivity tensor of 3D anisotropic materials. By manipulating the geometry of the sample relative to the sensor, this method allows for precise control over the direction of heat flow. Demonstrated on a CNT textile, the findings in Table 2 are consistent with predictions, showing that the out-of-plane thermal conductivity is significantly lower, by an order of 102, than the in-plane values, due to thermal contact resistance between CNT textile layers. A comparison of in-plane conductivities indicates higher thermal conductivity in the x-direction, which is expected as the fibers are aligned along this direction.
Our in-house developed Hot Strip technique represents a significant advancement in the accurate determination of the directional thermal conductivity of both thin and thick 3D anisotropic samples.
