Large Diameter Hot Disk® Sensors Enabling Thermal Conductivity Measurements of Aggregates and Particulates

Larger Sensors for Representative Bulk Measurements

Sampling a larger portion of a heterogeneous material can help the measured thermal properties represent the bulk material rather than an individual pore, particle, inclusion, or local region. The 180 mm Hot Disk® sensor has a sensor-to-sample contact area of 254 cm², which is 36 times the area of a 30 mm sensor, nine times that of a 60 mm sensor, and 2.25 times that of a 120 mm sensor. Using the maximum targeted probing depth within the Hot Disk® measurement-sensitive region, the 180 mm sensor can probe sample volumes of up to 55.0 L.

Why Sensor Size Matters

The Hot Disk® technique determines thermal conductivity, thermal diffusivity, and volumetric heat capacity from the temperature response of a plane double-spiral element that acts as both a transient heat source and a resistance thermometer¹. For homogeneous materials, different sensor diameters can provide comparable results when the experimental conditions satisfy the Hot Disk® model. In coarse or heterogeneous materials, however, a small-diameter sensor may sample too few structural features to represent the component as a whole. A larger sensor samples more particles, pores, flakes, or aggregates and can therefore improve the representativeness of the effective bulk properties.

In a double-sided Hot Disk® measurement, heat from the double-spiral element propagates into both sample halves. The thermally probed region can be approximated by an oblate spheroid. Here, r is the sensor radius and p_r is the thermal probing depth measured from the sensor plane into each sample half and radially beyond the sensor edge. The equatorial and polar semi-axes are a = r + p_r and c = p_r, respectively, giving an estimated probed volume of V = 4π(r + p_r)²p_r/3.

For particulates and strongly heterogeneous materials, a sensor-radius rule of thumb of r ≥ 10 d_max provides a guide to sensor selection, where d_max is the largest relevant particle or structural-feature dimension. The thermal probing depth should also remain within the specimen or loose-material assembly. Larger-radius sensors increase the range of feature sizes and sample volumes that can be investigated.

Materials such as lightweight concrete construction blocks and expanded clay pellets contain pores, particles, and interparticle voids. A larger measurement region includes more of these features and can reduce sensitivity to sensor position, providing a more representative bulk value.

Materials and Measurement Configuration

Test set 1: Comparing measurements made with different sensor diameters. Expanded polystyrene (EPS), expanded glass beads, and compressed graphite were measured with Hot Disk® sensors of 30, 60, and 120 mm diameter. The tests compared Hot Disk Instruments’ newly introduced 120 mm diameter sensor with established smaller-diameter sensors across a thermal-conductivity range spanning more than three orders of magnitude. The purpose was to verify the performance of the new 120 mm sensor.

Test set 2: Measurements of aggregate and particulate samples with large particle features. A lightweight concrete construction block measuring 580 × 240 × 180 mm and expanded clay pellets with particle sizes of 8–12 mm were measured using the newly introduced 120 and 180 mm Hot Disk® sensors. The clay pellets were filled into a cylindrical container with a diameter of 280 mm and height of 240 mm, with the sensor positioned at the midpoint along its height.

Table 1. Samples, sensor diameters, heating powers, and measurement durations. The tests were performed using a Hot Disk® instrument model TPS 1000 at ambient laboratory temperature. Heating power and measurement duration were selected for each sensor–sample combination to provide a sufficient temperature rise while limiting thermal penetration through the specimen.

Sample	Material form and dimensions	Hot Disk® sensor diameter (mm)	Measurement power (mW)	Measurement duration (s)
Expanded polystyrene (EPS)	Porous cellular solid	30	25	80
		60	50	160
		120	150	320
Expanded-glass beads	Loose beads; particle size ≈1 mm	30	30	640
		60	70	1280
		120	200	2560
Compressed graphite	Compacted flakes	30	7500	2.5
		60	7500	3
		120	7500	3
Lightweight concrete construction block	Porous block; 580 × 240 × 180 mm	120	800	640
		180	800	640
Expanded clay pellets	Pellets: 8–12 mm; holder: Ø280 × 240 mm	120	600	640
		180	800	1256

For the test set 1 measurements, a double-sided measurement setup was used. For test set 2, the expanded clay pellets surrounded the sensor in a loose-material assembly, whereas the lightweight concrete construction block was tested in a single-sided configuration, with the sensor against one face of the block and insulation on the opposite side of the sensor.

Measurement Results

Temperature-rise transients and thermal-property results are presented below.

Table 2. Measurement results of test set 1, i.e. comparing Hot Disk® sensors of different diameter sizes.

Sample	Sensor diameter (mm)	Thermal conductivity (W·m−1·K−1)	Thermal diffusivity (mm2·s−1)	Volumetric heat capacity (MJ·m−3·K−1)
EPS	30	0.030 ± 0.0004	1.30	0.023
	60	0.033 ± 0.0005	1.68	0.020
	120	0.034 ± 0.0004	1.69	0.020
Expanded-glass beads	30	0.080 ± 0.001	0.34 ± 0.025	0.23
	60	0.080 ± 0.004	0.34 ± 0.011	0.24 ± 0.07
	120	0.090 ± 0.006	0.39 ± 0.078	0.25 ± 0.05
Compressed graphite	30	188.8 ± 1.7	119.5 ± 2.9	1.58 ± 0.05
	60	184.0 ± 1.2	133.4 ± 10.9	1.39
	120	181.0 ± 4.8	147.8 ± 11.3	1.23

Table 3. Thermal-conductivity measurements on the construction block and expanded clay pellets using the 120 and 180 mm Hot Disk® sensors.

Sample	Configuration	Sensor diameter (mm)	Thermal conductivity (W·m−1·K−1)
Lightweight concrete construction block	Single-sided	120	0.46 ± 0.003
	Single-sided	180	0.459 ± 0.08
Expanded clay pellets	Loose-material assembly (double- sided)	120	0.21 ± 0.007
	Loose-material assembly (double- sided)	180	0.23 ± 0.001

Conclusions

The newly introduced 120 and 180 mm diameter Hot Disk® sensors extend thermal-property measurements to larger sample areas and volumes, enabling characterization of materials with coarse particles and structural features. The 180 mm sensor provides a contact area of 254 cm² and, in a double-sided configuration, can probe volumes of up to 55 L.

Measurements on three materials spanning more than three orders of magnitude in thermal conductivity confirmed the performance of the 120 mm sensor compared with smaller Hot Disk® sensors. Further measurements on lightweight concrete blocks and expanded clay pellets demonstrated the benefits of the larger sensors for porous bulk and granular materials.

For the lightweight concrete blocks, the thermal-conductivity values obtained with the 120 and 180 mm sensors differed by only 0.22%, demonstrating excellent agreement. This also indicates that both sensors fulfil the rule of thumb of having a radius more than ten times larger than the structural features in the porous block sample. For the expanded clay pellets, the 180 mm sensor gave a 9.5% higher thermal conductivity than the 120 mm sensor. This difference reflects the influence of local particle packing and interparticle voids when relatively large 8–12 mm particles are measured. By sampling a larger number of particles, the 180 mm sensor can provide a more representative estimate of bulk thermal conductivity.

Overall, the results demonstrate the practical value of large Hot Disk® sensors for characterizing porous solids and coarse granular materials.

References

1. S. E. Gustafsson, “Transient Plane Source Techniques for Thermal Conductivity and Thermal Diffusivity Measurements of Solid Materials,” Review of Scientific Instruments 62(3), 797–804 (1991).↩︎
2. B. M. Mihiretie, D. Cederkrantz, A. Rosén, H. Otterberg, M. Sundin, S. E. Gustafsson, and M. Karlsteen, “Finite Element Modeling of the Hot Disk Method,” International Journal of Heat and Mass Transfer 115, 216–223 (2017).↩︎