Analysis and improvement of the hot disk transient plane source method for low thermal conductivity materials

The hot disk transient plane source (TPS) method is a widely used standard technique (ISO 22007–2) for characterizing the thermal properties of materials, especially the thermal conductivity, k. Despite its well-established reliability for a wide variety of common materials, the hot disk TPS method is also known to suffer from substantial systematic errors when applied to low-k thermal insulation materials, because of the discrepancies between the idealized model used for data analysis and the actual heat transfer process. Here, we present a combined numerical and experimental study of the influence of the geometry of the hot disk sensor on the measured k value of low-k materials. We demonstrate that the error is strongly affected by the finite thickness and thermal mass of the sensor's insulation layer as well as the corresponding increase of the effective heater size beyond the radius of the embedded metal heater itself. We further numerically investigate the dependence of the error on the sample thermal properties, confirming that the errors are worse in low-k samples. A simple polynomial correction function is provided based on the numerical error analysis, which converts the apparent (erroneous) result from a standard hot disk TPS measurement to a more accurate value of k. To experimentally validate the conclusions from numerical simulations, standard polyimide (Kapton) sensors are systematically optimized (thinned) by etching and used to measure low-k materials, including a standard polystyrene foam, a commercial Airloy® x56 aerogel, and a commercial Hydrophobic Silica Disk aerogel from Aerogel Technologies, LLC. The experimental results clearly demonstrate the strong influence of the sensor thickness. The k results of these samples obtained using either the optimized sensor or the pristine sensor then corrected with the corresponding polynomial correction functions are in good agreement with the values measured independently using a steady-state heat flowmeter (HFM) method: whereas the raw values measured with the pristine sensor are in error by 35% and 40% compared to the HFM reference values for the Airloy® x56 and the hydrophobic aerogel, respectively, the correction function greatly reduces those errors to <2% and <4%. This study reveals the detailed mechanisms of the systematic error in the hot disk TPS method for low-k samples, and shows that both the numerical correction to a pristine sensor and/or using an optimized (thinned) sensor are capable of providing highly accurate values of thermal conductivity for such materials.