Rapid Determination of the Relative Thermal Conductivity Coefficient of Insulating Materials

 View Online  Export Citation RESEARCH ARTICLE | SEPTEMBER 04 2025 Rapid determination of the relative thermal conductivity coefficient of insulating materials  Marek Velička ; Jiří Burda; Jozef Vlček; Mario Machů; Jiří Fiedor; David Rigo; Milan Raclavský; Ivan Priesol AIP Conf. Proc. 3355, 020018 (2025) https://doi.org/10.1063/5.0292177 Articles You May Be Interested In Research of the sintering process of no cement refractory castable with dead burned magnesia filler AIP Conf. Proc. (September 2025) 08 October 2025 13:57:04 Rapid Determination of the Relative Thermal Conductivity Coefficient of Insulating Materials Marek Velička1, a), Jiří Burda1, b), Jozef Vlček1,2 c), Mario Machů1, d), Jiří Fiedor1, e), David Rigo1, f), Milan Raclavský 1, 3, g) and Ivan Priesol 4, h) 1Department of Thermal Engineering, Faculty of Materials Science and Technology, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00, Czech Republic 2Material and Metallurgical Research s.r.o.., Pohraniční 693/31, 703 00 Ostrava, Czech Republic 3Ecofer s.r.o. Oldřichovice 914, 739 61 Třinec, Czech Republic 4I.P.C. Refractories, spol. s r.o., Magnezitárska 11, 040 13, Košice, Slovakia a) Corresponding author: m[email protected] b) [email protected] c) [email protected] d) mario.mac[email protected]z e) [email protected] f) [email protected] g) [email protected] h) [email protected] Abstract. Currently, there is intensive development in the field of renewable energy sources, especially photovoltaics, whose share is growing by tens of percent on an annual average. These trends will cause dramatic changes in the energy sector, and one of the ways to address this situation is high-temperature heat storage. The aim of this research was to find materials suitable for high-temperature technologies in energy industry. Attention was paid to two directions: insulation materials for high-temperature applications and storage materials. The article describes the original methodology for quickly determining the thermal conductivity coefficient and the application of this method to a series of samples. From the results obtained, it is clear that the most suitable in terms of maintaining the largest thermal content (sensible heat, enthalpy) appears to be the use of insulation with a minimum value of the thermal conductivity coefficient and at the same time, the lowest value of the temperature conductivity coefficient, which ensures slower temperature equalization between the reservoir and the insulation, because the primary goal is to maintain the thermal potential of the reservoir at a usable value. The article also shows that there are possible material modifications to improve both insulating and mechanical properties of materials. INTRODUCTION Renewable energy sources (RES), and in particular photovoltaics, are currently undergoing a rapid development, with their share growing by tens of percent year-on-year on average. The limiting element of these sources is the ability to accumulate the energy produced, which renewable sources provide unequally over time. High-temperature heat storage is one way of addressing this situation. [1]. This concept is the subject of this research, which aims to study and prepare suitable materials for high-temperature power generation technologies (HPTE). The attention is paid to two directions: insulating materials for high-temperature applications and storage materials for hightemperature applications [2, 3]. Several approaches to energy storage technology in the form of heat have been developed so far. By comparing the properties and applicability of commonly available materials (corundum, SIC, concrete, graphite, cast iron, steel) Thermophysics 2024 AIP Conf. Proc. 3355, 020018-1–020018-7; https://doi.org/10.1063/5.0292177 Published under an exclusive license by AIP Publishing. 978-0-7354-5242-8/$30.00 020018-1 08 October 2025 13:57:04 for storing of HPTE, a temperature of 750 °C can be considered as the upper limit of applicability [4]. Potential materials for HPTE applications include magnesite bricks with potential of operating temperatures up to 1200 °C, materials with high latent heat of fusion and so called phase-change materials (molten salts, metal melts) [5]. A study [6] investigated the potential of recycled waste materials from the mining and metallurgical industries for HPTE. Thermal and mechanical properties of slag-based materials with different cementitious binders in the temperature range up to 750 °C. Properties of natural rocks (e.g. quartz sands, granite, limestone) for use in HPTE applications where the heat transfer medium is warm air and the maximum upper temperature in the charge and discharge cycle is 650 °C [7]. Long-term stability of the properties under cyclic heat load (250 cycles - over 3000 operating hours) up to 675 °C in an experimental 1 MWh heat storage tank heated by resistance wires was demonstrated in diabase [8]. The work led to the design of a partially underground rock heat reservoir with a heat content of 450 kWh [9]. The heatbearing mass was heated to 600 °C electrically and the heat was extracted by air. Diabase, magnetite and basalt were identified as materials with potential for such applications. Simulations verified by measurements and further parametric studies aimed at optimising the heat extraction from the reservoir have demonstrated the possibilities of using these materials [10]. In terms of the parameters of thermal insulation materials, the coefficient of thermal conductivity is decisive [11]. This specified quantity generally depends on temperature, density, chemical composition, structure of the mass, pressure and humidity. The parameter is defined as the heat that passes per unit time through a unit area of an isothermal surface with a unit temperature gradient in the body. The value of the thermal conductivity coefficient is practically specific for each type of material [12]. In terms of high temperature applications, the increase of this coefficient with temperature is significant but undesirable. METHODOLOGY FOR DETERMINING THE THERMAL CONDUCTIVITY COEFFICIENT For some common types of materials such as steel, glass, etc., there are a number of empirical relationships for determining thermal conductivity. These procedures take into account the chemical composition of the materials and even determine the thermal conductivity value as a function of temperature [13]. For heterogeneous materials, such simplifying procedures cannot be applied. The thermal conductivity value of materials can be reliably determined by experimental measurement. Measurements are particularly important for materials where the conductivity is very low or high. The specific determination of such materials creates a requirement for precise knowledge of the physical parameter to be analysed [14]. The thermal conductivity coefficient can be measured by different types of methods. One possibility is the heating wire method, which is one of the recognised methods used for ceramic materials. There are two variants of this method in so-called cross or parallel arrangement. The advantage of this method is that the thermal conductivity value can be obtained as a function of temperature, the ambient temperature can be up to 1250 °C [15], which is problematic for materials with thermal conductivity values below 1 W⋅m-1⋅K-1. Dr. Bock's method is one of the so-called direct methods. Direct methods refer to procedures where the heat that passes through the measured material is measured directly and the value of the thermal conductivity coefficient can then be derived directly. Different procedures are applied for this group of methods. These are based on the differential principle, where the heat flux through a standard whose thermal conductivity value is known is monitored and subsequently the heat flux through the material under test is monitored [16]. The Light Flash Analysis (LFA) method is an indirect method for determination of thermal conductivity coefficients [17]. The technique measures the thermal conductivity coefficient and the value of the thermal conductivity coefficient is then determined from the known formula (1): 𝑎=𝜆 𝑐⋅𝜚 (m2.s-1) (1) where λ is the thermal conductivity coefficient (W⋅m-1⋅K-1), c is the specific heat capacity (J⋅kg-1⋅K-1), ρ is the density (kg⋅m-3) In the case of the LFA method, the source of the required heat is a laser discharge, which is applied to the sample to be measured, and then the temperature change of the sample is monitored at specified time intervals. The test procedure is not regulated by the standard. The method is used by leading manufacturers of techniques for thermal conductivity determination and this method is perceived by the professional community as reliable [18]. The 020018-2 08 October 2025 13:57:04 advantages of the method are that it is possible to measure solid and liquid samples, compact and powder samples, electrically conductive and non-conductive samples, etc., and the method allows the measurement of a parameter as a function of temperature, with measurements possible at temperatures exceeding 2000 °C [19]. There are also numerical models that use various types of empirical models and a large database of already determined thermal conductivity values. For specific physical parameters, the model then calculates the required values [20], that can be used as boundary conditions for modelling the temperature distribution in the material [21]. The disadvantage of all methods is the time and experimental complexity, especially at high temperatures. For material development purposes, these methods are unsuitable in terms of time and experimental complexity. Therefore, an original method for the determination of thermal conductivity was developed. PRINCIPLE OF EQUIPMENT FOR RAPID ANALYSIS OF THERMAL PROPERTIES OF MATERIALS A new method of comparing the thermal conductivity coefficient was designed and tested for the prototype device. The method consists of comparing the surface temperatures between a known reference material and an unknown material by measuring the bottom surface temperature in the heating plate and on the other hand the surface of the material is measured with a FLUKE TiS45 thermal imager. Once the temperature conditions have stabilised, it is possible to determine which of the two materials has the higher thermal conductivity coefficient. Assuming the same temperature on the underside of the measured materials and approximately the same conditions for heat dissipation by convection on the topside, and after including the different losses by radiation, the mean thermal conductivity coefficient can be calculated quite accurately (see figure 1). In the development of the new method, it was assumed that in the development of materials it is not necessary to know the exact value of the thermal conductivity coefficient, but knowledge of the relative values is sufficient, i.e. whether the new material has better or worse properties relative to the reference material. The proposed method is suitable for high temperature measurements and is based on the assumptions that: • The lower part of the device is a closed heated chamber in which the temperature is homogenised by all heat transfer mechanisms, but especially by radiation • The temperature in the heated chamber is measured on a homogenising heating metal plate with a pair of thermocouples • The upper surface of the measuring plate loses heat to the space by all heat transfer mechanisms, but mainly by radiation • The measured insulating materials have similar emissivities • The material with the higher thermal conductivity therefore has a higher temperature on the upper surface • The material with the lowest surface temperature is the best insulator and the worst conductor FIGURE 1. Model concept diagram FIGURE 2. Measurement scheme 020018-3 08 October 2025 13:57:04 After modifying the measuring plate with a high quality insulating brick type HBU (see Table 1), several samples could be measured and compared simultaneously. One sample was always taken as the standard reference material (S1), the other samples had different "modifier" concentrations (S2 - S5) (see Figure 2). TABLE 1. Properties of HBU insulation bricks Chemical composition (%) Volumetric mass (kg.m -3 ) Temperature expansion (%) Pressure strength (MPa) Porosity (%) Coefficient of thermal conductivity (W.m -1 .K -1 ) Al2O3 Fe2O3 1000°C 1200°C 500°C 800°C 1200°C 36.0 1.9 500 0.46 0.55 1.2 82 0.23 0.30 0.45 Five equally sized and equally deep holes were milled in the HBU brick into which the tested materials were successively poured. The surface was aligned so that the thickness of each layer was always the same (see Figure 3). For the materials tested, perlite and Refrasil GIA material (sample 1) were used as the reference sample, to which an increased volume of reflective substances was gradually added. The aim of the development was to create materials with fine granulometry and with the best possible thermal insulation properties, which were modified in 4 different ways: - by trapping imperfect combustion products on the surface of the powdered perlite (sample 2). - by mixing of powdery and finely granulometric perlite with fine-grained particles with a mean granulometry of 5 µm (sample 3). - by calcination of perlite with various salts. Two types of salts were selected, one nickel salt (sample 4) and one clay salt (sample 5). FIGURE 3. Sample set prepared FIGURE 4. Fluke camera measurement demonstration Subsequently, a measuring device with continuous power control was used for the measurements. Images were taken by a thermal imaging camera at each time point and then evaluated (see Figure 4). In Fluke Connect programme, the measurement fields of each sample were plotted on the temperature recording image and the average maximum and minimum temperatures at a given time were evaluated while the temperature of the base material was measured for comparison (see Figures 5 and 6). 020018-4 08 October 2025 13:57:04 FIGURE 5. Screenshot at the beginning of the measurement FIGURE 6. Screenshot at the end of the measurement If the thermal conductivity coefficient of the base material is not known, only the ratios of the two coefficients are determined. The heat flux densities of the measured and reference material can be written according to equations: 𝑄1=𝜀𝜀𝑇1 4= λ 1 ℎ(𝑇HP − 𝑇1) (2) 𝑄2=𝜀𝜀𝑇2 4= λ 2 ℎ(𝑇HP − 𝑇2) (3) If we put these two heat fluxes in proportion, we can express the thermal conductivity coefficient: 𝑄2 𝑄1 =𝜆2.(𝑇HP−𝑇 2) 𝜆1.(𝑇HP−𝑇 1)=𝜎.𝜀.𝑇 2 4 𝜎.𝜀.𝑇 1 4 (4) λ 2= λ 1.(𝑇HP−𝑇 1).𝑇 2 4 (𝑇HP−𝑇 2).𝑇 1 4 (5) where λ is the coefficient of thermal conductivity (W⋅m-1⋅K-1), ε is the emissivity (1), σ is the Stefan-Boltzmann constant (W⋅m-2⋅K-4), Q is the heat flux density (W⋅m-2), T is the absolute temperature (K), h s the sample thickness (m), Indexes: HP heating plate, 1 reference material, 2 measured material. The measured average temperatures of the samples and the surroundings are given in Table 2, the calculated relative ratios of the measured materials in Table 3 and the calculated approximate values of the thermal conductivity coefficient in Table 4. A series of three measurements were made in which the heated plate temperature was increased to 208 °C, 384 °C and 406 °C. TABLE 2. Measured average temperatures Measurement Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Surrounding 1 Surrounding 2 (°C) (°C) (°C) (°C) (°C) (°C) (°C) 1 40.62 42.33 41.78 41.74 39.32 46.24 47.91 2 178.30 183.47 184.06 178.08 168.69 243.57 239.15 3 197.30 198.16 196.70 194.61 187.65 250.56 244.96 TABLE 3. Relative ratios of measured materials Measurement Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Surrounding 1 Surrounding 2 (1) (1) (1) (1) (1) (1) (1) 020018-5 08 October 2025 13:57:04 1 1 1.0220 1.0149 1.0144 0.9835 1.0736 1.0963 2 1 1.0466 1.0520 0.9981 0.9175 1.7165 1.6585 3 1 1.0073 0.9949 0.9773 0.9204 1.5359 1.4712 TABLE 4. Approximate values of the thermal conductivity coefficient Measurement Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 HBU (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) 1 0.1185 0.1241 0.1247 0.1173 0.1088 0.1500 2 0.1383 0.1413 0.1403 0.1372 0.1360 0.2000 3 0.1530 0.1541 0.1522 0.1495 0.1408 0.2300 FIGURE 7. Comparison of achieved results The experiments performed (see Figure 7) show that for sample 2, in which the products of imperfect combustion were trapped on the surface of the powdered perlite, the measurements lead to ambiguous results in which an increase in the value of the thermal conductivity coefficient was observed. For sample 3 into which the powdered perlite with fine particles was mixed, better results were obtained when the mixing time was extended and the best results were obtained when the perlite was ground together with the fine particles. The best results were obtained for samples 4 and 5 in which calcination of perlite with two types of salts was carried out at 700°C. The calcination results show that this method could be the easiest to implement on an industrial scale and also the trends of improvement in the relative thermal conductivity coefficient are significant. CONCLUSION In this paper, a new benchmark method for the rapid determination of the thermal conductivity coefficient is presented, which is based on comparing the surface temperatures between a known reference and an unknown material, by measuring the bottom surface temperature in a heating plate and, on the other hand, measuring the surface of the material using a thermal imaging camera. Under steady-state temperature conditions, the mean thermal conductivity coefficient of the material under test can be determined fairly accurately and quickly for the entire set of samples in a single measurement. This methodology was tested on four samples for which suitable 020018-6 08 October 2025 13:57:04 thermal insulation properties were determined. It is clear from the results that, as expected, the use of insulation with the lowest thermal conductivity coefficient value appears to be the most appropriate in terms of maintaining the highest heat content (sensible heat, enthalpy), thus ensuring a slower temperature equilibration between the storage tank and the insulation, as the primary objective is to maintain the thermal potential of the storage tank at a usable value. The experiments carried out show that the lowest values were obtained for the material with the highest addition of reflective material, where the thermal conductivity coefficient was reduced by 8 %. These results are very promising for the continuation of this research. ACKNOWLEDGMENTS This paper was created as part of the project No. CZ.02.01.01/00/22_008/0004631 Materials and technologies for sustainable development within the Jan Amos Komensky Operational Program financed by the European Union and from the state budget of the Czech Republic and was supported under Project No. SP2024/025 - Advanced materials and technologies for decarbonization. REFERENCES 1. D. Wang. B. Chu. P. Li. W. Han. Y. Kong. P. Fu. Y. Li. J. Hao and W. Li. Ceramics International. 49. pp. 37486-37493 (2023). 2. C. Ma. R. Zhang. G. Zhang. H. Du. J. Liu. R. Liang and Z. Wang. Journal of Energy Storage. 72. art. no. 108374 (2023). 3. V. Becattini, T. Motmans, A. Zappone, C. Madonna, A. Haselbacher and A. Steinfeld. Applied Energy. 203, pp. 373-389 (2017). 4. S. Khare, M. Dell'Amico, C. Knight, S. McGarry. Solar Energy Materials and Solar Cells. 115, pp. 114-122 (2013). 5. B. Cárdenas and N. León. Renewable and Sustainable Energy Reviews. 27, pp. 724-737 (2013). 6. M. E. 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