*5.2. Conclusions*

Thermal conductivity is important in several applications to different temperatures, i.e., aerospace industry; nuclear industry; nuclear control rods; radioactive waste containment; the phase change material; or items such as bearings, piston parts, pumps, compressor plate valves, cable insulation and medical implants used in different applications. Therefore, it is essential to measure this thermal property with the most accurate as possible.

The percentage error obtained by ANSYS was 13.5% for the robust model, averaging the 4 volumes (2 copper bars, 1 aluminium bar, and the fibreglass insulator).

The union of elements that interact between the interfaces of the materials is essential and considerably affects the results. In spite of this, it is possible to know with a 13.5% error the temperature distribution inside the system of cut bars [35].

The values near the borders are very far from the experiment; however, the values near the sample bar are too close to those obtained experimentally.

The temperature deviation obtained through simulation and experimental work of the cold source is affected by the contact between it and the copper bar. On the other hand, the same is valid for hot source contact. In the simulation, losses due to bad contact or heat leakage to the environment are not considered. Other methods proposed in the literature to characterise materials have allowed us to verify experimental results [36,37].

The bars cut in CENAM must be designed to prevent radial heat leakage because, according to the simulation results, there is heat leakage in this direction. With the results obtained, a guard can be proposed that balances the gradients generated in the system. Because three distinct sections are noted for the latter case, it would be 213.33 ◦C, 277.77 ◦C, and 342.22 ◦C. As a proposal for improving the design of the CENAM cut bar system.

According to the analysis of the results and the simulations obtained, the following design criteria are proposed. Improve the thermal contact between the hot source and the cold source with the reference bars, which can be achieved by a system that compresses the three bars. Implement a guard with a control system in the hot source and in the cold source, which, although it does not eliminate the radial temperature gradient, reduces it to a minimum. From simulation realised, it is possible to obtain the location of the temperature sensor for the control guard system.

## **6. Future Work**

ASTM standard E1225-99 establishes that the measuring equipment by the cut-car method can operate at 1000 ◦C with a fairly acceptable uncertainty of less than 2%. Then the equipment used by CENAM needs major adjustments and, most likely, a redesign because other critical heat transfer phenomena such as radiation have to be considered. Therefore, with the support of the finite element method, it is intended to analyse the behaviour of a new system, but at an operating temperature of 1000 ◦C to develop a measuring device that operates at that temperature and can perform measurements of thermal conductivity at temperatures of 500 ◦C.

There is another problem that affects the accuracy of the results obtained for thermal conductivity value by the method presented in this work, and they are the radial heat leaks. With the use of the finite element method, we will try to minimise these heat leaks to increase accuracy. Another future work is to try to calculate the heat losses by comparing the experimental method and the simulation to obtain an estimate of the heat losses in the experimental system and to find the cause of them. It will serve to make corrections when calculating the uncertainty and implement improvements to the system to reduce these heat leaks.

**Author Contributions:** Conceptualization, J.E.E.G.D. and O.J.G.-R.; Methodology, M.A.Z.-A. and J.R.-R.; Writing–original draft preparation, N.M.-L., R.G.G. and J.R.-R.; Writing–review and editing, M.A.Z.-A., J.E.E.G.D., J.R.-R. and O.J.G.-R.; Supervision, J.R.-R. and J.E.E.G.D.; Data curation, D.J.G.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partial funded by CONACYT and PRODEP.

**Acknowledgments:** The authors appreciate the support of Centro Nacional de Metrología (CENAM). The authors appreciate Master César Javier Ortiz Echeverria for his support during the revision of the project.

**Conflicts of Interest:** The authors declare no conflicts of interest.
