Measurement 182 (2021) 109713 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement Analysis of the characteristics of bimetallic and semiconductor heat flux sensors for in-situ measurements of envelope element thermal resistance Oleksandra Hotra a, *, Svitlana Kovtun b, Oleg Dekusha b a b Department of Electronics and Information Technology, Lublin University of Technology, Nadbystrzycka Str 38D, 20-618 Lublin, Poland Monitoring and Optimization of Thermal Processes Department, Institute of Engineering Thermophysics of NAS of Ukraine, M Kapnist Str 2a, 03057 Kyiv, Ukraine A R T I C L E I N F O A B S T R A C T Keywords: Heat flux sensor Metrological characteristics In-situ method Thermal resistance measurement Monitoring of the thermal resistance of building envelopes for assessing their energy efficiency is carried out through in-situ measurements of the heat flux It is therefore necessary to take into account not only the heat transfer conditions of the studied object but also the characteristics of the measuring instruments, which may depend on these conditions This paper presents the results of a study of the characteristics of heat flux sensors of two types —bimetallic and semiconductor — which are the most common in the control of building envelopes The case studies were focused on the characteristics of the sensors, such as the conversion coefficient (inversely proportional to sensitivity to the heat flux), the temperature dependence of the conversion coefficient, the response time of the sensors, and the emissivity of the sensor surface The conversion coefficient of a bimetallic sensor was determined under the conditions of conduction and radiation supply of heat energy, which revealed the dependence of the conversion coefficient on the heat transfer conditions of the sensor surface The value of the emissivity of the semiconductor sensor surface is lower than that of bimetallic sensors, and the time constant of bi-metallic sensors is two times less than that of semiconductor sensors Verification of the obtained results was carried out by studying the metrological characteristics of the multi-channel thermal resistance control system, which included bimetallic heat flux sensors as sensitive elements Thus, we suppose that the results of our study could be used to improve the accuracy in measuring the thermal resistance of building envelopes by the correct selection of heat flow sensors, or by making corrections to the measurement results that take into account the influence of experimental conditions on the characteristics of the sensors Introduction Thermal resistance is one of the main informative characteristics when monitoring the quality of insulating materials and the thermal stability of envelope elements The thermal resistance is a measure of how well an envelope element resists heat losses The actual values of thermal resistance, as a key indicator used in the assessment of the en ergy efficiency of a building, are required to ensure compliance with energy performance strategies and with energy use The thermal resistance of building envelope elements in the design phase is estimated according to ISO 6946 [1] or ISO 10211 [2] by direct measurement of the thermal conductivity of each material [3], and calculations using the guarded hot plate method according to ISO 8301 [4] or by a heat flux meter according to ISO 8302 [5] However, the real thermal resistance of building envelope elements does not always agree with the calculated value, for various reasons [6] Thus, it is important to measure and analyze the building envelope thermal resistance in-situ Common measurement methods for thermal resistance estimation in existing buildings are methods based on ISO 9869 [7] and ASTM C 1155 [8] These standards differ from the methods of in-situ measurement data analysis of the thermal building envelope The ISO 9869 standard introduces the Average method and Dynamic method, while the ASTM C 1155 standard introduces the Summation method and Least Square method All these methods require the measurement of the internal and external surface temperature and the internal heat flux for at least three days There are many factors which have a significant impact on the heat flux measurements at the realization of an in-situ method [9–11] Therefore, researchers have studied the factors of thermal mass [12], variations of daily outside temperature, direct sun radiation [13], pre cipitation and other outside climatic conditions which not allow establishment of stationary heat conditions, different heating systems * Corresponding author E-mail address: o.hotra@pollub.pl (O Hotra) https://doi.org/10.1016/j.measurement.2021.109713 Received March 2021; Received in revised form 30 April 2021; Accepted June 2021 Available online June 2021 0263-2241/© 2021 The Author(s) Published by Elsevier Ltd This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) O Hotra et al Measurement 182 (2021) 109713 influence on the physical parameters of relative humidity [14], and heat capacity of the element [15] Another factor is the complex shape of the building envelope ele ments, including such heterogeneous zones as brickwork, translucent elements (in particular windows), a reinforcing belt, and so forth In many research works, data are included to determine the thermal resistance of separate homogeneous areas, most often windows [16–18] The results of the theoretical study of the methodological errors in measuring the heat flow when the heat flux sensor is located on the surface of the enclosing structure are discussed in a previous paper [19] In this case, heat exchange with the environment occurs under boundary conditions of the third type It was found that the main factors affecting the methodological measurement error are the following: heat transfer coefficient, radius of the sensor, thermal conductivity of the envelope structure, and thermal resistance of the sensor Researchers have shown that in order to reduce the methodological error, it is necessary to use the sensor with the minimum thermal resistance, which can be obtained by reducing the thickness of the sensor or increasing the geometric di mensions of the sensor, with the maximum emissivity of the sensor surface and the shortest response time Thus, measuring instruments used for in-situ thermal resistance experiments also affect the mea surement results of heat flux [20] The development of systems for measuring the thermal characteris tics of buildings and construction elements is carried out by such wellknown companies as Hukseflux (TRSYS01 high-accuracy building thermal resistance measuring system with two measurement locations); Green TEG AG (gO measurement system for the assessment of the Uvalue, humidity and further parameters); and FluxTeq (FluxTeq R-value measurement system) The disadvantage of the Hukseflux and Green TEG AG measuring systems is the use of heat flux sensors of one type and size, which makes it impossible to conduct studies of various elements of the building, in particular windows and window frames The FluxTeq system provides such an opportunity, but a small number of measuring channels, which limits the number of control zones to two and does not allow monitoring of complex shaped building envelopes From the above, it follows that when measuring the heat flux by the in-situ method for determination of envelope element thermal resis tance, it is necessary to take into account the characteristics of the measuring instruments, which depend on the conditions of the experi ment The aim of this article was to study such characteristics of heat flux sensors as temperature dependence of the conversion coefficient, emissivity of the sensor surface, and influence of heat transfer conditions on the conversion coefficient of sensors This paper focuses on the comparison of the main characteristics of the sensors developed by us with sensors from other manufacturers, which are actively being used by researchers for measuring the thermal properties of building envelopes by the in-situ method Due to the fact that heat flux sensors are part of the measurement systems, it is also advisable to study the metrological characteristics of a multichannel thermal resistance control system The main novelty of this work resides in the use of a complex approach for determining the characteristics of heat flux sensors, taking into account the influence of the conditions of their subsequent use for in-situ mea surements of envelope element thermal resistance 2.1.1 Bimetallic heat flux sensors The sensor is a spiral structure of thermoelements, which are placed in a special matrix and filled with an insulating epoxy compound with a heat-conducting filler to give it the shape of a monolithic plate (see Fig 1) Such a sensor is a so-called “additional wall”, on the opposite sides of which are placed the junctions of thermocouples Under the influence of heat flux passing through the additional wall and, accord ingly, in parallel through all elements of the thermocouple, a tempera ture difference occurs between the junctions, which results in an electric signal being generated in each of the thermocouples in the series The total output signal of the sensor is proportional to the amount of heat flux That is, when measuring a stationary heat flux using such a sensor, its density is determined in accordance with the Fourier law, by the temperature difference on the outer surfaces of the sensor Features of the manufacturing technology of such sensors allow the design of a sensor of any configuration with a predetermined sensitivity The sensitivity of the sensor varies due to the thickness of the thermo couple material deposition on the wire The temperature dependencies of the conversion coefficient for sensors made of a constantan spiral with different percentages of galvanically deposited nickel are graphed in Fig As one can see, changing the percentage of galvanically deposited nickel, we can not only vary the conversion coefficient of the sensor, but also reduce the temperature dependence of the conversion coefficient 2.1.2 Semiconductor heat flux sensors Semiconductor sensors based on the Peltier effect, which are designed to work as thermoelectric current generators or refrigerators, have become widespread However, they can also operate in heat flux measurement mode, acting as a sensor in measurement systems The structure of the semiconductor sensor is depicted in Fig It consists of p- and n-type semiconductor elements connected in pairs by copper buses (switching plates) into a single electrical circuit, located between the ceramic boards Semiconductor elements are manufactured using alloys of telluride and selenides of bismuth and antimony The ceramic plate of the semiconductor sensor, to which the output wires are attached, is called the “hot side”, and the other ceramic plate is called the “cold side” The following semiconductor sensors in the mode of heat flux sensors and bimetallic sensors were studied: a) Thermoelectric semiconductor generator module PGM-15–250, which has standard dimensions of 40 × 40 × 3.4 mm and contains 200 BiTe thermoelements, with a thermocouple size of 1.45 × 1.45 × 0.83 mm; b) Cooling module TEC1-12703, which has standard dimensions of 30 × 30 × 3.5 mm and contains 127 thermocouples; c) Thermoelectric semiconductor Peltier (three pieces) cooling modules TEC1-12706, which have standard dimensions of 40 × 40 × 3.8 mm and contain 127 BiSn thermocouples; d) Disc-shaped thermoelectric bimetallic heat flux sensors, which are 30 mm in diameter and mm thick, with a constant-cell coil of NiConst coated wire (Ni-Const); these sensors are of our own production; e) Rectangular-shaped thermoelectric bimetallic heat flux sensors with dimensions of 20 × 80 × mm and a constant-cell coil of Ni-Const coated wire (Ni-Const); these sensors are of our own production; f) Disc-shaped thermoelectric heat flux sensor, 50 mm in diameter and mm thick, PU 22 series by Hukseflux Materials and methods 2.1 Heat flux sensors used in the monitoring of thermal resistance of the envelope structure This paper describes a study of semiconductor sensors and developed-by-us bimetallic heat flux sensors for measuring the thermal resistance of building envelopes using conductive and radiation methods In this study, we investigated the characteristics of heat flux sensors, which are most commonly used for in-situ measurements of envelope elements [20–24] Below is a description of the designs and the principle of operation of these two types of sensors Fig shows photos of the investigated sensors indicated above, under items “a”, “b”, “c”, “d”, “e”, “f” All semiconductor sensors have ceramic housings (Al2O3), and bimetallic sensors “d” and “e” are filled with a UP-610 epoxy resin compound The operating temperature ranges for sensor “a” is up to 230 ◦ C, for sensors “b” and “c” is up to 138 ◦ C, for sensors “d” and “e” is O Hotra et al Measurement 182 (2021) 109713 Fig The structure of the bimetallic heat flux sensor up to 200 ◦ C, and for sensor “f” is up to 90 ◦ C Technical specifications of the studied sensors are given in Table 2.2 Experimental equipment and methods In order to measure the surface heat flux density using the above mentioned sensors, the following metrological and operational charac teristics should be determined: the conversion coefficient, the dependence of the conversion coefficient on temperature, the inertia of the sensor, and the emissivity of the sensor surface The conversion coefficient of the sensor is determined by passing the thermal energy of a fixed value through the heat-sensitive surface of the investigated sensor, and measuring the output signal This study was conducted using the conduction and radiation methods of heat energy supply, which correspond to different conditions of heat exchange during the operation of sensors In order to determine the emissivity of the sensor surface, we used a heat metric method for calculating the thermal radiation characteristics of the surface [25,26] This method consists of determination of the ratio of the infrared radiation power absorbed by the surface to the incident radiation power from the heat source The radiation method for determining the conversion coefficient of the sensor lies in the fact that thermal radiation of a fixed density from a source of thermal radiation is simultaneously supplied to the reference and the studied sensors, which are located on a thermostated heat sink At the same time, equidistance of both sensors from the source of thermal radiation and the same values of the emissivity of their heatsensing surfaces are provided The sensor conversion coefficient is calculated by the following formula: ( )/ K = Kref ∙Eref Esens , (1) Fig Temperature dependencies of the conversion coefficient for bimetallic heat flux sensors with variation of the percentages of galvanically depos ited nickel Fig The structure of semiconductor sensor Fig Photos of the investigated sensors: “a”, “b”, “c” are semiconductor sensors and “d”, “e”, “f” are bimetallic sensors O Hotra et al Measurement 182 (2021) 109713 Table Technical specifications of sensors Sensor Model PGM-15–250 “a” TES1-12703 “b” TES1-12706 “c” bimetallic sensor “d” bimetallic sensor “e” PU 22 “f” Thermoelements Thickness [mm] Dimensions [mm] Filling material Heat flux density range [W/m2] Temperature range [◦ C]: Min Max Accuracy [%] 200 BiTe 3.4 40 × 40 Al2O3 ±2000 127 BiSn 3.5 30 × 30 Al2O3 ±2000 127 BiSn 3.8 40 × 40 Al2O3 ±2000 Ni-Const 30 epoxy resin ±2000 Ni-Const 20 × 80 epoxy resin ±2000 Not specify 50 PU ±2000 − 20 +230 Not specified − 20 +138 Not specified − 20 +138 Not specified − 20 +200 ±3 − 20 +200 ±3 − 20 +90 ±5 where E is the signal parameter (voltage) generated by the sensor (in dexes ref and sens are used for the reference and studied sensor, respectively), and Kref is the conversion coefficient of the reference sensor Determination of the sensor emissivity of the sensor surface was achieved using the thermometric method for determining the thermor adiation characteristics of selective coatings, which consists of deter mining the ratio of the power of the particle of infrared radiation absorbed by the surface to the power of incident radiation from the heat source [25,26] The value of the emissivity of the sensor surface was calculated by the following formula [26]: ) ( [ ( ) ]− − q∙Seqv ε−h − εsens = q∙ σ Th4 − Tsens , (2) K(t) = (W∙Ssens )/Esens , where W is the electrical power supplied to the main heater, Ssens is the area of the sensor, and Esens is the signal parameter (voltage) generated by sensor A conductive system was used for method implementation [27] It consisted of a heat block in which the studied sensor was placed and the required temperature and thermal conditions were provided, and an electronic block containing the means for regulating the thermal con ditions, and receiving and processing primary measurement information (Fig 5) The main elements of the heat block were an electric heater for setting a heat flux of a fixed value, which was structurally combined with a heat-shielding side screen, a heat-absorbing flat metal platform combined with a finned radiator, and a clamping device The heater body was made of a high thermal conductivity metal that contributes to the creation of isothermal conditions along its heat-transfer surface in contact with the heat-absorbing surface of the sensor under study An electronic block provided the setting of the experimental conditions and regulation and control of the temperature conditions, and obtained the primary measurement information The main characteristics of the system are shown in Table The main advantage of the conductive system is its ability to supply heat flux of low density, starting from W/m2, which is very important in the case of in-situ measurements of envelope elements with high thermal resistance or in the case of a low temperature difference where q is the radiation heat flux from the heat source, σ is the StefanBoltzmann constant, Th is the temperature of the heat source, Tsens is the temperature of the sensor surface, Seqv is the area ratio of the heat source to the sensor area, and εh is the emissivity of the heat source The studies of sensor characteristics in radiation conditions were performed using a radiation comparator for calibrating the heat flux sensors and measuring the emissivity of coatings and material surfaces [27] The radiation comparator consisted of the emitter as the heat source in the form of a flat blackbody model, the protective screen with a mirror-reflecting surface, and the water-cooled heat sink where the sensors were placed for the research The investigated sensor was compared with the reference heat flux sensor The flow of thermal ra diation of a fixed density from the emitter was simultaneously supplied to the investigated and reference sensors located on a water-cooled heat sink In this case, the heat-absorbing surfaces of both sensors were equidistant from the source of thermal radiation, and had the same emissivity The design of the emitter, in combination with the mirror-reflecting screen, thermostatically controlled at the same temperature as the heat sink, provided an almost complete absence of convective heat flux in the sensor location zone, with satisfactory uniformity in the distribution of heat flux density The technical specifications of the radiation comparator are pre sented in Table A conduction method of thermal energy supply provided a unidi rectional stationary heat flow through a sensor at a certain temperature value, to determine its density by measuring the electrical power sup plied to the main heater and the signal generated by the sensor This made it possible to determine the individual conversion coefficient by the absolute method of direct measurement The conversion coefficient at a fixed temperature was calculated by the following formula: Table Technical Specifications of radiation comparator Heat flux density range Range of operating temperature values Emissivity (3) 100 … 104 W/m2 10…80 ◦ C 0.040…0.99 Fig Block-diagram of the conductive system O Hotra et al Measurement 182 (2021) 109713 Table Technical Specifications of conductive system Heat flux density range Range of operating temperature values … 2.104 W/m2 25…250 ◦ C 2.3 Running of experiments In order to conduct the research in a radiation comparator, it was necessary to ensure the same emissivity of the heat-sensing surfaces of the investigated and reference sensors, for example by applying the same coating to their surfaces After that, the sensors were placed on the thermostatically controlled heat sink as shown in Fig with use of the contact greases [29], which allowed us to reduce the influence of contact thermal resistance between the sensor and the heat sink The results were obtained by comparison of the output signals of the investigated sensors with the signal of the reference sensor The disc-shaped ther moelectric bimetallic heat flux sensor, of 27 mm in diameter and 1.5 mm thickness and with a constant-cell coil of Ni-Const coated wire, was used as the reference sensor Its metrological characteristics were determined at the State Enterprise “Ukrmetrteststandart”, certified by ISO 17025 According to the sensor calibration results, the expanded uncertainty of heat flux measurement did not exceed 1.5% with an interval having a 95% level of confidence assuming a normal distribution In the experi ments, a constant temperature of the radiator of the installation was set to 120 ◦ C and the temperature of the water-cooled refrigerating plate varied in the range from room temperature up to 50 ◦ C The radiation heat flux ranged from 420 to 530 W/m2 In the conductive method, the sensor is installed on the surface of the heat sink as shown in Fig 7, and is covered by a heater combined with a heat shield In order to improve the thermal contact between the working surfaces of the installation and the investigated sensor, a clamping device is used Under such conditions of sensor installation the maximum value of contact thermal resistance in the investigated range of temperature does not exceed 0,0005 m2⋅K/W [30] According to the results of the calcu lations given in [30], the influence of contact thermal resistance on the measurement result does not exceed 0.2% Measurement of the sensor output signals was carried out after the onset of the stationary thermal regime In order to determine the con version coefficient with high accuracy, the contacting surfaces of the conductive system and investigated sensor should have the same diameter The measurement result is the average value of the output signal (voltage) of the heat flux sensor obtained by processing of the readings taken within 20 The studies were carried out with varying the temperature of the heat sink, from 25 to 50 ◦ C, while the heat flux density was set at 1000 W/m2 Fig Bimetallic sensor PU 22 series indicated as “f”, mounted on the cooling plate of the conductive system Results of sensors experimental studies The results of the experimental studies of the emissivity of the sensor surface ε are given in Table In order to reduce the random component of the uncertainty, five cycles of measurements were conducted, and the average value of the emissivity was taken as the measurement result According to the results of previous studies [28], when measuring the heat flux under unsteady conditions an important characteristic of sensors is the time constant The time constant is determined as the time from the beginning of the stepwise change of the heat flux until the output signal reaches a certain preset level of the steady-state value It is proportional to the square of its thickness and is inversely proportional to the temperature conductivity [28] Therefore, information on the time constant of sensors at the levels of 0.63 (τ 0.63) and 0.95 (τ 0.95) of the sensor signal is also given in Table In Fig 8, the test results of the sensitivity of heat flux sensors PGM15–250 “a”, TES1-12703 “b” and TES1-12706 “c” (the three lines graphed for “c” correspond to three sensors) are shown as the temper ature dependence of their conversion coefficients obtained at five points from the range of temperature values Each point in the graph depen dence is the average result of the measurement series at the given temperature The combined standard uncertainty of determining the conversion coefficients of the sensors with a 95% level of confidence does not exceed 3%.The test results of the bimetallic sensors “d” and “e” are presented in Fig The analysis of the obtained characteristics of the sensors shows that each of them has its advantages and disadvantages For example, the advantages of the TEC1-12706 “c” module are the low cost and high sensitivity (the lowest value of the conversion coefficient), and the Fig Heat flux sensors mounted on the heat sink of the radiation comparator (a) From left to right: semiconductor sensor PGM-15–250 indicated as “a”, reference sensor indicated as “ref”, semiconductor sensor TEC1-12703 indicated as “b”; (b) reference sensor (left), bimetallic sensor PU 22 series indicated as “f” (right) O Hotra et al Measurement 182 (2021) 109713 Table The experimental results of the emissivity of sensor surface ε and the response time of the sensors ε τ0.63 [s] τ0.95 [s] PGM-15–250 “a” TES1-12703 “b” TES1-12706 “c” Bimetallic sensor “d” Bimetallic sensor “e” PU 22 “f” 0.71 15 44 0.71 16 47 0.71 20 57 0.88 27 0.89 27 0.91 27 heat flux density measurement in the corresponding channels of the developed system was determined as the standard uncertainty of the heat flux measurement at two values of normalized surface density of heat flux: (250 ± 10) W/m2 and (500 ± 20) W/m2 The uncertainty of temperature measurement was determined by comparing of the tem perature values obtained by the corresponding channels of the devel oped system with the working standard: RTD thermocouple Pt-100 in U2C ultra thermostat The standard uncertainty of the temperature measurement was performed at two temperature values: ◦ C and +50 ◦ C The standard uncertainty of the heat flux density measurement was expressed as a relative standard deviation of experimental data under the assumption of a normal distribution The results of metrological experimental studies for the heat flux measurement channels of the developed system are given in Fig 12 The standard uncertainty of the temperature measurement in 22 channels of the developed system was expressed as an absolute standard deviation of experimental data under the assumption of a normal dis tribution The results of metrological experimental studies for the tem perature measurement channel of the developed system are given in Fig 13 The expanded uncertainty of the surface heat flux density measure ment of the developed system does not exceed 3% It was obtained by multiplying the combined standard uncertainty by a coverage factor that produces an interval having a 95% level of confidence assuming a normal distribution The expanded uncertainty of the temperature measurement does not exceed ◦ C with an interval having a 95% level of confidence assuming a normal distribution Measurements of the surface heat flux density are in the range from to 500 W⋅m− and temperatures in the range from − 40 to +50 ◦ C advantages of the bimetallic sensors “d” and “e” are their relatively small response time, the smallest thickness and thermal resistance, and the ability to produce the desired shape and size In order to carry out a comparative analysis to determine the con version coefficient of the sensors, depending on the method of supplying thermal energy, after the research in a radiation comparator studies were carried out in a conductive system Due to the fact that with a conductive heat energy supply, as mentioned in Section 2.3, an impor tant factor affecting the accuracy of measurement results is the corre spondence of the diameters of the sensor and the working surface of the conductive system, only the PU22 sensor was subjected to these studies Fig 10 shows the results of the study of the conversion coefficient of sensor PU 22 “f” under supply of conduction and radiation thermal energy As we can see, the difference in the values of the conversion coefficient is more than 14% This indicates that heat transfer conditions can have a significant effect on the results of the heat flux measurement Verification of metrological characteristics and comparison test For the purpose of in-situ measurements of thermal resistance ac cording to ISO 9869–1 [7], the multichannel control system was created [31] The system was constructed using a set of temperature and bimetal heat flux sensors (Ni-Const) (see Fig 11), that allow us to take into ac count the peculiarities of the envelope elements and ensure the ability to conduct research on a large number of representative zones 4.1 Metrological characteristics of the system The multichannel information-measuring system was calibrated to monitor the thermal resistance of the envelope elements It consists of eight heat flux sensors and 22 thermoelectric temperature sensors (thermocouples) The verification of metrological characteristics was carried out by laboratory certified according to ISO 17025 “Ukrmetr testStandard”, jointly with the Institute of Engineering Thermophysics of NAS of Ukraine (in further text: IET) According to the test report of the certified laboratory, to confirm the measuring capabilities of the system (measurement of heat flux and temperature in the range of declared values), the tests were carried out at two points of the declared range Therefore, the uncertainty of the 4.2 Experimental study of the system with bimetallic heat flux sensors For experimental studies of the developed monitoring system, comparative tests were carried out using equipment of the certified laboratory “Ukrmetrteststandart” The experiment was carried out on the window assembly with twochamber glazed system SPD 4i-14Ar-4 M1-12Ar-4i and PVC frame (70 mm width) in the climatic chamber The window assembly was mounted in the climatic chamber with cold section (as imitation of the Fig Temperature dependencies of the conversion coefficient of semi conductor sensors: PGM-15–250 “a”, TES1-12703 “b”, TEC1-12706 “c” Fig Temperature dependencies of the conversion coefficient for bimetallic sensors “d” and “e” O Hotra et al Measurement 182 (2021) 109713 contact greases [29] were used, which allowed us to reduce the influ ence of contact thermal resistance Theoretical thermal resistance values were calculated according to standard EN ISO 10077–2 [37] (for the opaque parts of the window) and according to standard EN 673 [38] (for translucent parts of the window) Calculated values of the thermal resistance (R) and the area of homo geneous zones (F) are follows: R1-10 = 0.76 m2⋅◦ C/W and F1-10 = 1.669 m2 for the glazed system, taking into account homogeneous zones (zones F1…F10 are marked with white in Fig 14); R11-14 = 0.68 m2⋅◦ C/W and F11-14 = 0.324 m2 for the opaque part of the glazed system sash, taking into account homogeneous zones (zones F11…F14 are marked with green in Fig 14); R15-19 = 0.68 m2⋅◦ C/W and F15-19 = 0.339 m2 for the opaque part of the glazed system frame, taking into account homogeneous zones (zones F15…F19 are marked with blue in Fig 14); Rassembly = 0.73 m2⋅◦ C/W and Fassembly = 2.332 m2 for the window assembly Fig 10 Temperature dependencies of the conversion coefficient for sensors PU 22 “f” outer side) and warm section (as imitation of the inner side) It should be noted that the investigation of thermal characteristics of building en velope fragments in laboratory conditions is carried out using a Hotbox apparatus The Hotbox design features and the corresponding mea surement methods are regulated by ASTM C1363 [32], ISO 8990 [33] and EN 12412 [34] However, in our research we have used recom mendations of the local standard DSTU B V.2.6–17 [35], which regulates the procedure of the windows assembly thermal resistance measurement in a climatic chamber with application of heat flux sensors This stan dard specifies the location of the sensors The same layout of sensors can be applied for in-situ measurements The measurement systems of the certified laboratory “Ukrmetrtest standart” and monitoring system developed in the IET with different types of heat flux sensors were used simultaneously for performing the tests For the cold-junction compensation of thermocouples the temperature-dependent bridge-type compensation circuit with constant voltage was used [36] Layout of homogeneous temperature zones on a window assembly with a two-chamber glazed system SPD 4i-14Ar-4 M1-12Ar-4i and PVC frame (width 70 mm) according to the test report of the certified labo ratory is given in Fig 14, a The sensors were mounted on the envelope elements marked by F1-19 (Fig 14, b) according to recommendations of standards ISO 9869 [7], ASTM C 1155–95 [8], and DSTU B V.2.6–17 [35] suggesting the installation of the sensors in the centers of uniform temperature zones on the inner surface In the case of a combination of sashes and frames, the sensors should be installed on the surfaces of the sashes and frames For measurements on sashes and frames, the sensor’s width should be not more than half of the profile width [35] To meet this requirement, sensors with di mensions of 20 mm × 80 mm were used For installation of the sensors The stationary operating regime in the climatic chamber was set over 48 h The ambient temperature in the cold and warm chambers at the distance of 0.15 m from the window assembly was in the range of 20.74 and 18.98 ◦ C and between 24.26 and 26.48 ◦ C, respectively The mea surements were carried out over 24 h after stationary operating regime setting Results obtained with the measurement system of the certified lab oratory “Ukrmetrteststandart” and monitoring system developed in the IET are given in Table Data from the sensors of the developed monitoring system were recorded with intervals of min, and then averaged accordingly [8] In order to evaluate the results, a comparative analysis of the calculated and measured values was carried out according to ISO 9869 [7] For the glazed system the difference between results of comparison is equal to 1.3%, exhibiting good agreement between the calculated and measured values In the case of the opaque part (frame) the difference between results is equal to 11.7%, which is acceptable For the opaque part (sash) the difference between results equals to 19.1%, which is the boundary permissible value It is probably connected with convective air flows in the sash, which influence the R-value measurements but are not taken into account in the calculation of the theoretical value of the thermal resistance of the envelope element due to good agreement of the measured values of both systems Thus, the results obtained indicate the correct operation of the multichannel system with bimetal heat flux sensors, which allows us to apply it for in-situ monitoring of the thermal resistance Conclusions In this paper, a complex approach for determining the characteristics of bimetallic and semiconductor heat flux sensors most commonly used for monitoring the thermal resistance of building envelopes was intro duced The influence of specific conditions of their further use was taken into account in in-situ measurements The application of the radiation method gives us the ability to study the emissivity of the sensors This is very important in cases when the sensor and envelope elements have different emissivity values The conductive method is important because of the ability to supply the heat flux of low density, starting from W/ m2 This is a crucial moment in the case of in-situ measurements of envelope elements with high thermal resistance, or in the case of a low temperature difference The following characteristics were determined: the conversion co efficient (sensitivity to the heat flux), the dependence of the conversion coefficient on temperature, the response time of the sensor, and the emissivity of the sensor surface As a result of the studies, it was found Fig 11 Module of the multichannel thermal resistance control system and heat flux sensors [31] O Hotra et al Measurement 182 (2021) 109713 Fig 12 Results of metrological experimental studies for the heat flux measurement channels of the developed system Fig 13 Results of metrological experimental studies for the temperature measurement channels of the developed system Fig 14 Window assembly: the glazed sys tem is marked with white; the opaque part of window assembly sash is marked with green; the frame is marked with blue; (a) layout of homogeneous temperature zones on a win dow assembly: F1…F19 are the areas of ho mogeneous zones; R1…R19 are thermal resistances of the corresponding homoge neous zones; (b) sensors layout: TS – tem perature sensors marked with yellow, HFS – heat flux sensors marked with brown (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) O Hotra et al Measurement 182 (2021) 109713 CRediT authorship contribution statement Table The results obtained on a window assembly Homogeneous zones Average temperature of the inner surface, ◦ C: Glazed system Opaque part (sash) Opaque part (frame) Average temperature of the outer surface, ◦ C: Glazed system Opaque part (sash) Opaque part (frame) Average heat flux density, W/m2: Glazed system Opaque part (sash) Opaque part (frame) Thermal resistance, m2⋅◦ C /W: Glazed system Opaque part (sash) Opaque part (frame) Equipment of the certified laboratory Developed monitoring system Difference between results 20.22 20.05 17.97 19.8 20.35 18.35 0.42 0.3 0.38 Oleksandra Hotra: Conceptualization, Validation, Formal analysis, Resources, Writing - review & editing Svitlana Kovtun: Conceptuali zation, Methodology, Validation, Investigation, Writing - review & editing, Supervision Oleg Dekusha: Conceptualization, Validation, Investigation, Writing - review & editing, Visualization, Supervision Declaration of Competing Interest − 14.89 − 12.51 − 15.80 − 15.2 − 12.91 − 15.3 0.31 0.4 0.5 45.85 40.90 57.00 46.6 41.3 56.5 − 0.75 0.4 0.5 0.76 0.80 0.59 0.75 0.81 0.6 0.01 0.01 0.01 The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper References [1] ISO 6946, Building Components and Building Elements – Thermal Resistance and Thermal Transmittance – Calculation Method, ISO, Geneva, Switzerland, 2007 [2] ISO 10211, Thermal Bridges in Building Construction – Heat Flows and Surface Temperatures – Detailed Calculations, ISO, Geneva, Switzerland, 2007 [3] O Hotra, O Dekusha, A device for thermal conductivity measurement based on the method of local heat influence, Przeglad Elektrotechniczny 88 (5A) (2012) 223–226 [4] ISO 8302, Thermal Insulation – Determination of Steady-State Thermal Resistance and Related Properties – Guarded Hot Plate Apparatus, ISO, Geneva, Switzerland, 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the characteristics of the sensors Thus, at radiation heat exchange, the sensor conversion coefficient increases by 14% compared with the conduction heat exchange, which leads to a decrease in the sensitivity of the measuring system and introduces an additional error in the mea surement result Bimetal heat flux sensors (Ni-Const) and bimetal sensor PU 22 series have a relatively small time constant (τ0.63 = s), which together with a small thickness is a determining factor in heat flux measurements in conditions of unsteady heat transfer To verify the obtained results, studies of the metrological charac teristics of the multi-channel thermal resistance monitoring system of building envelopes using the equipment of the Ukrmetrteststandart laboratory, certified according to ISO 17025, were carried out The system included bimetal heat flux sensors (Ni-Const) and temperature sensors The manufacturing technology of bimetal sensors makes it possible to produce them in any shape (round, 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http://dspace.nbuv.gov.ua/handle/123456789/60921 V Babak, O Dekusha, S Kovtun, S Ivanov, Information-measuring system for monitoring thermal resistance, Available online: CEUR Workshop Proc 2387 (2019) 102–110 http://ceur-ws.org/Vol-2387/20190102.pdf ASTM C1363-19, Standard Test Method for Thermal Performance of Building Materials and Envelope Assemblies by Means of a Hot Box Apparatus, ASTM International, West Conshohocken, PA, 2019, www.astm.org ISO 8990:1994 Thermal insulation — Determination of steady-state thermal transmission properties — Calibrated and guarded hot box, ISO, Geneva, Switzerland, 1994 EN 12412 Thermal performance of windows, doors and shutters - Determination of thermal transmittance by hot box method - Part 2: Frames, Committee for standardisation, Brussels, Belgium, 2003 DSTU B V.2.6-17-2000 “Windows and doors Methods of determination of resistance of thermal transmission”, Ukraine, 2000 O Hotra, Cold-junction temperature compensation of thermoelectric transducers, Przeglad Elektrotechniczny 86 (10) (2010) 24–26 EN ISO 10077-2:2017 Thermal performance of windows, doors and shutters — Calculation of thermal transmittance — Part 2: Numerical method for frames, 2017 EN 673, Glass in building – Determination of thermal transmittance (U value) – Calculation method European Standards, 1997 ... consists of deter mining the ratio of the power of the particle of infrared radiation absorbed by the surface to the power of incident radiation from the heat source [25,26] The value of the emissivity... where q is the radiation heat flux from the heat source, σ is the StefanBoltzmann constant, Th is the temperature of the heat source, Tsens is the temperature of the sensor surface, Seqv is the. .. influence of contact thermal resistance between the sensor and the heat sink The results were obtained by comparison of the output signals of the investigated sensors with the signal of the reference