# Melting of Paraffin Waves Embedded in a Porous Matrix Made by Additive Manufacturing
## 4 Measurements of Thermal Conductivities and Thermal Diffusivities  
The thermal conductivities and thermal diffusivities of the three paraffins in the solid state, as well as of the AlSi\({}_{10}\)Mg alloy sample, have been experimentally measured. Moreover, the knowledge of the density, \(\rho\), permitted to calculate the specific heat, \(c\), as:  
\[c=\frac{k}{\rho\cdot a} \tag{1}\]  
where \(k\) is the thermal conductivity and \(a\) is the thermal diffusivity. The hot disk transient plane source (TPS) method was applied to measure thermal conductivity and thermal diffusivity. This is a transient type technique for the measurement of thermal conductivity. The measuring equipment was the commercial thermal constants analyzer model TPS 2500 HOT DISK AB. The hot disk method uses a flat sensor element in the shape of a double spiral that has been etched out of a thin nickel foil. The sensor is covered on both sides with two layers of electrically insulating film (kapton or mica). The kapton sensor provides an accuracy of 3 \(\div\) 5%, while the mica sensor provides lower accuracy (about 8 \(\div\) 10%) when measuring the thermal conductivity. During the measurements, the hot disk sensor is sandwiched between two sample halves of the specimen to be investigated, each one with a plane surface facing the sensor, as illustrated in Figure 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **RT42** & **RT55** & **RT64 HC** & \\ \hline Melting temperature range & 38–43 & 51–57 & 63–65 & [\({}^{\circ}\)C] \\ Heat storage capacity 1  & 165 & 170 & 250 & [k] kg\({}^{-1}\)] \\ Density solid 2  & 0.88 & 0.88 & 0.88 & [kg dm\({}^{-3}\)] \\ Density liquid 3  & 0.76 & 0.77 & 0.78 & [kg dm\({}^{-3}\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thermophysical characteristics of the tested paraffins. Data by the manufacturer [25]. The sensor acts both as a heat source for increasing the temperature of the sample and a resistance thermometer for recording the time-dependent temperature increase. During the experiment, constant electric power is supplied to the hot disk sensor. This causes the temperature to rise and an increase in the resistance of the spiral while the heat is absorbed by the test sample. This temperature increase is dependent on the thermal transport properties of the material surrounding the sensor. By monitoring this temperature increase over a short period of time after the start of the experiment, it is possible to evaluate the thermal properties of the material. The ideal model of the heat conduction equation assumes that the sample can be considered as a semi-infinite medium during the time \(t\) of measurement. However, being the samples of finite dimensions, this entails that the time of transient recording has to be chosen so that the outer boundaries of the sample do not influence the temperature increase detected by the sensor. In practice, by choosing short time intervals and proper sensor and sample sizes, the measurement can still be analyzed as if it was performed in an infinite medium. In this case, by fitting the theoretical solution of the variations of temperature of the specimen active surfaces to the experimental recorded temperature variations, using least-squares analysis, it is possible to calculate the thermal conductivity and the diffusivity of the tested material in an independent way. More details about this technique can be found in the references [26; 27]. Four different materials were studied: three paraffins and an AlSi\({}_{10}\)Mg alloy sample. Table 2 lists the materials and experimental results. The thermal conductivities of all samples were measured at room temperature (23 \({}^{\circ}\)C). The presented values are the mean of at least five repeated measurements with the same test setup and boundary conditions. The relative standard deviation of repeated thermal conductivity measurements has been less than 1.2% for all samples.