A numerical study on the influence of insulating layer of the hot disk sensor on the thermal conductivity measuring accuracy

The hot disk TPS method suffers from substantial systematic errors when applied to low-k thermal insulation materials.

“Despite its well-established reliability for a wide variety of common materials, the hot disk TPS method is also known to suffer from a substantial systematic errors when applied to lowk thermal insulation materials, because of the discrepancies between the idealized model used for data analysis and the actual heat transfer process.”

For aerogel samples, TPS measurements using mica-insulated sensors showed a k result 54% higher than polyimide-insulated sensors for the same sample.

“For aerogel samples, there is also a report on the discrepancy in the k result obtained with TPS measurements using different types of sensors insulated with mica and polyimide, where the former type showed a result 54% higher than the later for the same sample. 20”

Error in TPS measurement comes from two sources: (1) uncertainty in experimental data and selection of time interval for analysis, and (2) deviation of the original idealized analytical heat transfer model from the practical measurement scenario.

“Error in the TPS measurement 20-31 comes from two sources: (1) uncertainty in the experimental data and the selection of time interval for analysis, and (2) deviation of the original idealized analytical heat transfer model 3, 32 from the practical measurement scenario.”

For a thin insulating layer under constant heating power, the average temperature drop between the metal heater and the sample-sensor interface becomes almost constant after a short time, a few multiples of the diffusion time hi^2/αi.

“under constant heating power it is well known 20 that ( ) i T t  becomes almost constant after a short time, a few multiples of the diffusion time hi 2 / α i”

The bifilar spiral metal heater together with the dielectric insulation layer are usually approximated by several concentric and equally spaced circular rings with constant power in both analytical and numerical prior models.

“The bifilar spiral metal heater together with the dielectric insulation layer are usually approximated by several concentric and equally spaced circular rings with constant power in both analytical 3, 32 and numerical 20, 27-31 prior models.”

There is a lack of a clear understanding and quantitatively useful solution to the problem of relating the measurement error for thermal insulation materials to the sensor parameters in a definitive way.

“Although it was mentioned that the finite thermal mass of the sensor can lead to error in some lowk materials, 17, 20 there is still a lack of a clear understanding and quantitatively useful solution to this problem which relates the measurement error for TI materials to the sensor parameters in a definitive way.”

Several publications investigated the accuracy and performance of commercial TPS devices based on numerical simulations to study the effect of sensors on TPS measurement for bulk or thin film and the error due to thermal radiation in semitransparent sample.

“In the latter aspect, several publications investigated the accuracy and performance of commercial TPS devices based on numerical simulations to study the effect of the sensors on the TPS measurement for bulk or thin film 20, 27-31 and the error due to thermal radiation in semitransparent sample. 17, 33”

Detailed information about the specific fitting and optimization procedure is rarely given in the literature, being typically either described simply as a least square method or not clearly mentioned.

“Detailed information about the specific fitting and optimization procedure is rarely given in the literature, being typically either described simply as a least square method (often without specifying the fitting parameters) 20, 27, 28 or not clearly mentioned. 29”