## 2 Technique Background  
The method determines the thermal conductivity of a sample using a reference material by a permanent state technique known as the concentric bar cut method [3]. The system consists of a bar with well-known properties, called reference bar, another bar with conductivity to be determined, called sample o test bar, and another reference bar. The composite metal bar is covered with an insulating material to prevent heat flow in the radial direction. At one end of the composite bar, a heat source is placed, and at the opposite end, there is a heat sink or cold source [4; 5]. Then, employing temperature and length measurements, the conductivity of the sample material can be determined. Figure 1 shows a diagram of the composite bar system. The arrangement diagram of the bars for the method used in this work is shown in Figure 1a. The reference bars are located at the ends and the test bar in the center of both. At one end of the bar array, a heat sink or cold source is located; at the other end, a heater that allows generating a temperature gradient, necessary for the determination of the thermal conductivity value. Marked with \(x\) in Figure 1a is where the thermocouples indicated at a certain height in mm and designated according to the letter \(z\) are located; the thermocouples type T were a fine wire of 0.6 mm diameter from OMEGA brand, calibrated by CENAM. \(r_{A}\) indicates the radius of the bars used for the test and \(r_{B}\) the radius of the insulation used in the test. A force is applied axially to improve the contact between the bars axially. A brief description of the process performed to carry out the test is named in Figure 1b. Before starting the test the bars to be used need to meet the necessary diameter and height, as well as some flatness on the flat faces of the bars, after these perforations are made on the cylindrical face a few millimeters deep to house the thermocouples later. After finishing the bars, they are placed one above the other in the order, as appear in Figure 1a. Then the thermocouples are placed in each one of the sweepers made in the bars, then it is surrounded with the insulating material, and the guard is added; the axial force is applied to improve the contact. The next step is to adjust the operating temperature of the hot and cold source according to the measurement temperature at which the test is required to reach the operating temperature was used as a power supply, which supplies the necessary voltage to an electrical heater until it reaches temperature operation, which is registered by the thermocouple located in the hot source. For example, if a test temperature of 100 \({}^{\circ}\)C is required, the average temperature of the hot and cold source must be sought to be 100 \({}^{\circ}\)C. For example, the temperature of the hot source at 150 \({}^{\circ}\)C and the cold source at 50 \({}^{\circ}\)C, so the average temperature is 100 \({}^{\circ}\)C. In this way, several combinations can be generated. Once the operating temperatures have been adjusted, data acquisition begins, by a program in LabView developed by CENAM, where the signal of thermocouples are read by a multimeter and send to a PC to register its values. The values will be adequate when a the steady-state regime has been reached, it is known, because charts of temperature from thermocouples do not change, reach a constant temperature throw experiment in time. With the acquired data, Equation (1) is used to calculate the thermal conductivity value. From the work in [2] it was found that the thermal conductivity of the sample is given by  
\[\lambda_{M}=\frac{Z_{4}-Z_{3}}{T_{4}-T_{3}}\left[\frac{\lambda_{R_{1}}}{2} \left(\frac{T_{2}-T_{1}}{Z_{2}-Z_{1}}\right)+\frac{\lambda_{R_{2}}}{2}\left( \frac{T_{6}-T_{5}}{Z_{6}-Z_{5}}\right)\right] \tag{1}\]  
where \(\lambda_{M}\) is the thermal conductivity of the sample. \(\lambda_{R1}\), and \(\lambda_{R2}\) are the thermal conductivity of reference materials 1 and 2.