Experimental and Numerical Studies of Heat Transfer Through a Double-Glazed Window with Electric Heating of the Glass Surface

Abstract

This paper presents experimental and theoretical studies of heat transfer through single- and double-glazed windows with electrical heating of the internal surfaces. Heating is achieved by applying a voltage to the low emissivity coating of the inner glass. A thermophysical model has been developed to simulate the heat transfer through these units, allowing us to determine their thermal characteristics. Experimental data are used to validate the numerical model. The resulting heat flux and temperature distributions on the external and internal surfaces of electrically heated double-glazed units are analysed. According to the results of experimental and numerical studies, it was found that the adopted electric heating scheme allows 83–85% of the heat to enter the room and 15–17% is removed to the outside. This makes it possible to increase the radiation component of the heat flow from the window to the room and improve the thermal comfort in the room. In general, this article shows that existing industrial windows with low-emissivity glass surface coating can be upgraded with simple and inexpensive modernisation, without compromising the main function of the window—efficient transmission of visible light—and create an additional (backup) heating device that can work effectively together with the existing heating system in the event of a sudden cold snap at low temperatures (below −20 °C), to prevent condensation of water vapour in the windows, and to prevent condensation on the surface of the window facade wall. Formally, a back-up (emergency) heating system is created in the room, which contributes to the energy sustainability of the building and therefore to energy security in general.

1. Introduction

The building sector, comprising residential, municipal, and commercial structures, is one of the world’s largest energy consumers, accounting for up to 30% of total energy usage [1]. This is mainly due to the inadequate thermal insulation of many existing buildings and structures, which often do not meet contemporary standards. Windows, in particular, are often the weakest link in maintaining thermal comfort, as their thermal resistance is significantly lower than that of exterior walls. A highly effective strategy to reduce heat loss through building envelopes is to replace outdated windows with modern windows equipped with energy-efficient glazing units and profiles.

To improve the thermal insulation of window structures and the overall thermal performance of building spaces, various strategies can be implemented. For example, reducing radiative heat transfer through the glazing unit can be achieved by incorporating low-emission coatings or specialised energy-saving films. Several studies [1,2] have found that replacing traditional glass with double-glazed windows featuring low-emission coatings typically results in energy savings of 30–40% for heating and cooling. Recent studies have demonstrated significant progress in the development of integrated windows capable of achieving electrical performance up to 30–33 W/m² [3]. A review of the market [4] indicates that silver-based film coatings now account for more than 90% of the total.

The authors of [5] conclude that numerous technologies have been introduced to develop roof windows with transparent coatings due to high market demand. However, the commercial viability of such products will only be realised in the future following appropriate scientific validation. Promising avenues include the development of spectrally selective absorbing glasses [6] and glazes incorporating ions and nanoparticles [7] to modulate solar infrared radiation. It is noteworthy that multilayer constructions combined with low-emissivity coatings can modulate the direction of heat flow through windows depending on the season. This highlights the potential for designing next-generation buildings with advanced glazing and innovative window systems. Switchable smart windows, particularly when powered by photovoltaic systems, represent an attractive strategy [8,9].

Smart window technologies can be categorised as electrochromic [10], photochromic [11], and thermochromic [12]. Electrochromic windows have been the subject of intensive research in recent years; however, their application has been hindered by the requirement for external power sources. A potential solution lies in the development of bifunctional façades that integrate electrochromic windows with other functionalities, primarily by enhancing traditional window designs. Numerous studies have been conducted to investigate the impact of various design and operational parameters on window thermal resistance [13,14].

The thermal resistance of a window structure is influenced by factors such as the gap between the panes [15], the thickness of the glass [16], and the type of insulating glass unit and the profile of the window frame [17]. Multichambered insulating glass units, the use of aluminium, plastic, or specialised ‘warm’ spacer frames, filling the interpane space with inert gases (argon, krypton), or creating a vacuum can significantly reduce heat loss [18,19]. In addition, installing a thermal curtain or enabling ventilation of the interpane space with heated air can further improve the thermal performance of the building [20]. Studies [21,22] have explored the application of vacuum glazing to reduce heat loss due to its superior insulation properties. This technology presents a promising advancement over traditional insulated glass units or gas-filled windows. However, the implementation of vacuum glazing is hindered by economic factors, as it is significantly more expensive than standard insulated glass units and triple-glazed windows that meet passive house standards [23,24]. One review [25] concludes that integrating vacuum glazing with low-emissivity coatings can achieve significant improvements in window thermal resistance, although concerns regarding reliability and high costs persist. Consequently, the widespread adoption of such expensive technological solutions, especially in combination, is challenging.

Another promising approach to heating window glass involves the use of window ventilation [26,27]. In [28], the authors discuss the concept of designing ventilated windows. This solution does not require an external energy source to increase the temperature within the interpane space but may be suitable only for facade office windows [29,30]. A contemporary approach to increasing window thermal insulation involves the use of electrically heated glazed units (EHGU). However, from an energy efficiency point of view, the application of electric heating in double-glazed windows may not be optimal due to substantial heat losses to the external environment. To evaluate the impact of EHGUs on the thermal performance of buildings, thermophysical models have been developed and experimental studies conducted [30,31,32,33].

In [31], a thermophysical model is presented for both standard and electrically heated window configurations. This model demonstrates that the use of heated windows can effectively reduce the heating and cooling loads of buildings. The impact of electrically heated translucent structures on indoor thermal comfort parameters, as assessed using measurement devices and a thermal manikin, is detailed in [32]. Experimental investigations into the thermal performance of electrically heated window structures installed in an energy-efficient building during the winter months (January–February) are documented in [30]. Experimental results showed that reducing the operating temperature of the heated glass by 3 °C resulted in a 44% and 41% decrease in energy consumption in February for south- and north-facing windows, respectively. These experimental findings indicate the potential for developing novel smart window strategies and commercialising these technologies. Reference [33] provides a description of the experimental setup, which consists of an electrically heated glazed unit (EHGU) installed within an insulated enclosure. This setup is designed to evaluate the efficiency of heated windows under various EHGU surface temperature conditions, controlled by adjusting the applied current. A temperature gradient is established using gel-based ice packs on one side of the glazing unit, while the other side is heated by passing current through a low-emission coating applied to the inner surface of the inner pane. Electric heating of varying power is employed.

In [34] the modelling results for the heating capacity of electrically heated windows in a specific room are presented, considering the relationship between the relative glazing area and the total exterior envelope area and ambient temperature. Methodology [35] was used to calculate convective heat transfer. Electric heating is regulated to ensure that the maximum heat flux (450 W/m²) and the temperature (60 °C) on the inner pane of the double-glazed unit are not exceeded. The authors of [36] conducted an analysis of the electrical and thermal characteristics of ventilated windows and highlighted the comparative effectiveness of such a combination of technologies, although the primary objective of such a window is electricity generation. The effect of increasing the temperature of the centre pane could not be assessed as it was not possible to vary the glass surface temperature.

Studies have shown that installing heated glazing on the north or east sides of buildings can result in energy savings of up to 13%. Consequently, the integration of double-glazed windows with additional electric heating is becoming an innovative trend in the window industry.

In studies [37] it was concluded that a double-glazed window with heated double glazing reduces heat loss by up to 50% compared to an unheated double-glazed window if the window temperature is kept close to room temperature. If the window temperature is much higher than the room temperature, the loss through the window increases compared to its unheated counterpart. Similar conclusions were reached by the authors of [38]. The authors of [39] analysed the effect of outdoor temperature on the efficiency of a heated window and showed that the efficiency of a conventional heated window with a heat transfer coefficient of 1.1 W/m² K was about 78% at an outdoor temperature of −10 °C. A study [32] investigated the effect of an electrically heated window on indoor thermal comfort parameters and found that thermal comfort was significantly dependent on the heated glass surface. However, this paper does not provide technical data concerning the heated window. Similar results are presented in [40].

The examples of technical solutions presented in this paper are still under development and there is no common standard for presenting the results, so it is difficult to draw a definitive conclusion on the appropriate focus for research into heated windows. Nevertheless, future applications of heated windows should be seen as one aspect of the technology that should be focused on in order to provide a wider range of possibilities. The authors of the few existing reviews, e.g., [41], come to the same conclusion.

The purpose of these experimental and numerical studies is to analyse the distribution of heat flows and temperatures on the outer and inner surfaces of an electrically heated window and to determine the relationship between the amount of heat received due to the electric heating of the window entering the room and the amount of heat transferred to the environment and lost. Based on these results, it is possible to conclude that windows with additional electric heating are feasible and energy efficient.

2. Materials and Methods

This study presents a comprehensive investigation into the distribution of heat flows and temperatures on the outer and inner surfaces of an electrically heated window and seeks to determine the relationship between the amount of heat received due to the electric heating of the window entering the room and the amount of heat transferred to the environment and lost. Our approach combines rigorous experimental studies with theoretical modelling, utilising a proprietary computer package based on the equations of mathematical physics for transfer phenomena. The experiment was carried out in two versions, the first being a single-chamber double-glazed unit, in which the window under study was installed inside a room with a strictly northern orientation (Figure 1) which was not exposed to direct insolation. These are trial measurements, where the heating effect was studied, modes were tested, the parameter range was selected without glass cracking, let alone its destruction, and the measuring equipment, the system for archiving experimental data and their preliminary processing were set up. The second option is a thorough long-term study in a real climate chamber for a triple-glazed window mounted in the wall of the passive and zero-energy experimental building of the IET of the NAS of Ukraine. The main mission of these basic experiments is to establish the temperature characteristics of the structural elements of double-glazed units and window profiles, and, in particular, to measure the levels of heat loss through the window to the environment. To ensure the completeness and adequacy of the experiment, sensors of different types and manufacturers were used.

The fundamental principle of electric heating, particularly for the inner surface (facing the interior of the glazing unit) of the inner glass with a low-emission coating, involves the creation of a conductive layer by depositing or infusing metal ions into a thin near-surface layer of the glass. This coating acts as a thermal barrier, inhibiting the transmission of short-wave infrared radiation into the external environment and thereby reducing heat loss from the room. However, this surface can also serve as a resistive heating element when an electrical voltage is applied across equidistant points, such as the opposing diagonal corners of a rectangular pane. The resulting current flow generates heat. To elucidate the characteristics of heat transfer through electrically heated double-glazed windows, comprehensive experimental and numerical investigations were conducted, and the findings are presented in this paper.

To support measures for improving window constructions, the Institute of Technical Thermophysics of the National Academy of Sciences of Ukraine developed an experimental setup to study factors related to improving the energy efficiency of transparent enclosures [30,35]. In particular, studies were conducted to determine the characteristics of heat transfer through a transparent enclosure (TE) with electric heating (Figure 1). For this purpose, heat flux sensors of two types (semiconductor and thermopile) and digital semiconductor temperature sensors were installed at specific locations on the surface of the test object. The sensors were glued to the glass using thermal paste. The temperature of the indoor air was also recorded at various locations in the room.

The random error of temperature measurements made with platinum (sputtered platinum) resistance thermometers was ±0.1 °C. The thermometers were built into heat flux sensors developed and mass-produced at the IET NAS of Ukraine. Two types of heat flux sensors were used: multi-junction thermocouple systems (5 junctions per square millimetre of area), the characteristics of which are given in

Table 1. The main technical characteristics of a heat flux converter with a built-in platinum resistance thermometer.

No.	Main Technical Characteristics	Value
1	The limit of the permissible main relative error in the measurement of the heat flux density	±4%
2	Temperature measurement range, °C	−30…90
3	The limit of the permissible main absolute error of temperature measurement, °C	±0.1
4	Electrical resistance of the heat flux sensor, ohms	3889
5	Nominal resistance of the resistance thermoconverter at 0 °C, ohms	100
6	The reaction time at the level of 0.63 is no more, s	30
7	Heat resistance, °C	Up to 100
8	Effective thermal conductivity coefficient, W/(m·K)	1.0 ± 0.05
9	Sensor surface blackness degree	0.91 ± 0.05
10	Dimensions, mm	100 × 40 × 2.0
11	Weight, not more than, kg	0.04

, and semiconductor sensors operating on the Peltier effect, which were switched to work in reverse on the Seebeck effect. These sensors are mass-produced in China, and they were calibrated on a special metrology unit of the IET NAS of Ukraine. They are more sensitive and have low inertia, because the contact area of two dissimilar semiconductors was up to 10 square mm, which is significantly larger than the contact area in a microthermocouple. Their size is 40 × 40 × 4 mm.

A portable 48-channel thermal recording unit, equipped with an appropriate number of heat flux and temperature sensors of different types, along with connection and data transmission adapters, was utilised to measure the specified thermal characteristics. The measurement mode involved a single measurement for each sensor (heat flux or temperature) every 10 min. Automated measurements were conducted continuously throughout the experiment, spanning from 23 October to 4 November. To eliminate external thermal disturbances, the room was unoccupied and devoid of heat-generating objects, including the heating radiator, during this period. The only external heat source was diffuse daylight insolation, as the room was strictly north-facing. Specific heat flux sensors were located in the centre of the glass and at four peripheral positions near the window profile, with a similar distribution of temperature sensors.

The application of an alternating (50 Hz) voltage to the layer of metal ions of a low-emissivity coating sprayed on the glass is optimally organised by arranging the contacts of flexible conductors at the ends of the diagonal (one of the two) of the inner surface of the first glass (from the room side) and connecting a source of alternating voltage, for example, an autotransformer from a 220 or 127 volt household electrical outlet. The thermal mode thermostating was performed automatically when using a standard serial electronic voltage supply control unit, which is used for warm electric floors of the room heating system. Further, it will be seen from the experiment that the automatic unit turned on the voltage only 20 times a day from the middle of 24 October to the middle of the day on 25 October. The maximum voltage was chosen according to the criterion of the mechanical stability of the glass when heated. For our particular window with 4 mm M1 quality glass, this was a voltage at which the glass temperature did not exceed 60 °C. This indicator corresponds to the maximum norms of the temperature of the surface of the heating device.

3. Results

3.1. Measurement of Thermal Modes of a Single-Chamber Glazing Unit

To investigate the thermal behaviour of a single chamber glass unit (SCGU) within a laboratory setting, initial experiments were carried out on a 4M1i-10-4iM1 single-glazed unit with glass 4 mm thick and low-emission coatings. One of these coatings was subjected to an alternating voltage. The glass unit was simply placed in the centre of a 6 × 3 m laboratory room, not within a facade wall. A window with the glass unit was installed parallel to the 3 m wide facade wall, with the ‘cold’ glass facing it (Figure 1). The goal of these measurements was to investigate heat transfer to the room from the heated glass and from the ‘cold’ (opposite) glass of the glass unit, which was not subjected to voltage. The maximum temperature at which the glass did not crack or deform was also determined. Measurements were conducted at the beginning of the heating season under Kyiv’s climatic conditions.

Figure 2 presents the undisturbed specific heat flux data collected on 23–24 October 2019 using thermocouple-battery sensors for the neutral (pre-experiment) unheated state of the window.

The measurement complex recorded a discernible change in daily heat flux values only during periods of maximum diffuse insolation, occurring midday on 23 October. This perturbation was primarily detected by the sensors located on the cold glass (q2, q4, q6, q8, q10, see sensor layout in Figure 2), which is closer to the room’s regular window. The sensors in the glass that would subsequently be heated (q with odd indices) were essentially unaffected by insolation. The designations at the top indicate the average day and night temperatures (in degrees Celsius) for each respective day. Positive heat flux values denote outward flow towards the environment, whereas negative values indicate inward flow towards the room.

The series of experiments began on 23 October, with the central room temperature slightly below 18 °C. Despite the influence of diffuse insolation, all sensors recorded a specific heat flux of 1 ± 0.5 W/m² directed towards the environment, representing the undisturbed (background) state of the investigated window. The sensitivity of the thermocouple-battery heat flux sensors was 0.2 W/m², semiconductor heat flux sensors 0.3 W/m², resistive platinum temperature sensors (platinum sputtering) 0.05 °C, and semiconductor temperature sensors 0.1 °C. Consequently, the estimated random error for heat flux measurements was 0.5 W/m² and 0.8 W/m², and for temperature measurements 0.1 °C and 0.2 °C, which was deemed satisfactory for experimental purposes.

Figure 3 illustrates the temporal variation in specific heat fluxes in the central regions of the panes (the outer surface of the heated glass and the outer surface of the ‘cold’ glass) during the heating mode at 20 °C, spanning from 7:00 a.m. on 23 October to 16:00 a.m. on 24 October. These data were obtained using two types of sensors. The thermostat setpoint temperature of 20 °C was only 2.5 °C higher than the central room temperature.

The fluctuations in heat flux through the heated glass were primarily driven by the periodic on/off cycles of the electric heating system (lower and upper points of the red and pink fluctuation lines, respectively). In contrast, the heat flux through the ‘cold’ glass did not exhibit such cyclical behaviour. The heat flux through the heated glass was approximately 2–3.5 times greater than that through the ‘cold’ glass and remained relatively constant at around 7 W/m².

Using a measurement unit equipped with heat flux and temperature sensors, the distributions of heat flux densities and temperatures across the surfaces of the insulating glass unit were obtained at various glass surface temperatures: 20, 25, 30, 35, and 40 °C (Figure 4 and Figure 5), controlled by a thermostat. The thermostat algorithm involved setting a base temperature level (in °C) and allowing for variations within a ±0.5 °C range. The temperature of the glass surface was regulated by adjusting the electrical alternating voltage; to ensure the stability of the glass, the maximum temperature level did not exceed 60 °C.

The changes in temperature characteristics of the surfaces of the electrically heated glazing unit (EHSCGU) in the dynamics of heating temperature increase, which were compared with the set temperature of the thermostat electronic task book, for all heating modes are presented in Figure 4.

The heating modes of 20 °C, 25 °C, and 30 °C closely align with the experimental data. However, for heating modes of 35 °C and 40 °C, the actual heated surface temperatures were slightly lower than the thermostat set points. Furthermore, the 40 °C mode exhibited instability, leading to the termination of heating to prevent possible glass cracking.

The lower temperature readings at measurement points 9 and 10 (t9 and t10, the blue and light blue lines on the graphs) located at the bottom of the window are attributed to the window profile’s position. The upper and side profiles are exposed to room air, while the lower profile is in mechanical and thermal contact with the window support device. This contact facilitates a more intensive heat loss compared to air, resulting in slightly lower temperatures at the bottom of the window.

The temperature increase in the region of the horizontal top profile is mainly due to the free convective upward movement of heated air and the associated additional heating of this area, as evidenced by measurement points 3 and, in particular, 4 (t3 and t10).

Figure 5 shows data on the comparison of heat flux density obtained using only central sensors of thermocouple-battery type (1, 2) and semiconductor heat flux sensors (1k, 2k). The designations of heating modes are similar to Figure 4.

The graphs show that the values of heat flux obtained by different types of sensors approximately coincide within the errors and scatter of values because of the on-off effects of electric heating. As the graphs in Figure 5 show, within the range of heat flux fluctuations, the readings of both types of sensors (Figure 1) practically coincide. This confirms the adequacy of the experimental data. The average values of the specific heat fluxes from the heated glass and from the conditionally ‘cold’ glass into the room at various given heating temperatures are given in

Table 2. Average values of heat fluxes into the room on different sides of the window—heated and ‘cold’.

No.	Heating Mode, °C/Indicator, W/m2	20	25	30	35	40
1	From heated glass	20	60	110	168	≈220
2	From ‘cold’ glass	7	18	32	47	60
	Ratio 1 to 2	2.9	3.3	3.4	3.6	3.7

.

Some interim conclusions based on the current research block. A low-emissivity coating of the glass surface can be used for its resistive heating. An electronic control unit for warm electric floors (walls) can be used as a thermostat regulator for heating. The recommended and reasonable temperature range for M1 glass with a thickness of 4 mm is up to 50 °C. The estimated ratio of heat fluxes from the heated glass surface to the flux from the conditionally ‘cold’ surface into the room is, on average, 3.5. The results obtained from experimental studies on heat transfer through the glass unit can be used to verify (validate) the results of independent thermophysical modelling [13,14].

3.2. Numerical Thermophysical Studies of the Thermal Regime of Electrically Heated Glass Units

The heat transfer process through a real energy-efficient double-glazed unit with electric heating (EHDGU) was numerically simulated. The double-glazed unit had a height of H = 1 m and a width of L = 0.75 m, with the following glass configuration: 4M1i-10-4M1-10-i4M1. This indicates a glass thickness of δc = 4 mm and a gap between the glass surfaces of δ_g = 10 mm. Both chambers were filled with air and low-emission coatings were applied to the inner surface of the inner (indoor) glass and the inner surface of the outer (environmental) glass. Electric heating was applied to the inner surface of the inner glass. A portion of the heat released by the heated surface was transferred to the indoor environment, while the remaining heat was dissipated to the external surroundings.

Numerical modelling of heat transfer through a double-glazed unit (DGU) was performed by solving a system of equations, including the continuity equation, the momentum equation, and the energy equation for the gaseous medium, the equation of state for the gas within the glass unit chambers, the heat conduction equation for the glass, and the heat transfer equation for the electrically conductive coating. This system of equations is as follows:

$${\displaystyle \frac{\partial {\rho }_g}{\partial \tau }}+{\displaystyle \frac{\partial \left({\rho }_{g}u\right)}{\partial x}}+{\displaystyle \frac{\partial \left({\rho }_{g}v\right)}{\partial y}}=0;$$

(1)

$${\displaystyle \frac{\partial \left({\rho }_{g}u\right)}{\partial \tau }}+{\displaystyle \frac{\partial \left({\rho }_g{u}^2\right)}{\partial x}}+{\displaystyle \frac{\partial \left({\rho }_{g}uv\right)}{\partial y}}=-{\displaystyle \frac{\partial P}{\partial x}}+v_g\left({\displaystyle \frac{{\partial }^{2}u}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial y^2}}\right);$$

(2)

$${\displaystyle \frac{\partial \left({\rho }_{g}u\right)}{\partial \tau }}+{\displaystyle \frac{\partial \left({\rho }_{g}uv\right)}{\partial x}}+{\displaystyle \frac{\partial \left({\rho }_{g}u{v}^2\right)}{\partial y}}=-{\displaystyle \frac{\partial P}{\partial y}}+v_g\left({\displaystyle \frac{{\partial }^{2}v}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial y^2}}\right)-{\rho }_{g}g;$$

(3)

$${\displaystyle \frac{\partial \left(C_{p,g}{\rho }_{g}T\right)}{\partial \tau }}+{\displaystyle \frac{\partial \left(C_{p,g}{\rho }_{g}uT\right)}{\partial x}}+{\displaystyle \frac{\partial \left(C_{p,g}{\rho }_{g}vT\right)}{\partial y}}={\lambda }_g\left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}\right);$$

(4)

$$P={\rho }_g{R}_{g}T;$$

(5)

$${\displaystyle \frac{\partial \left(C_{gl}{\rho }_{gl}T\right)}{\partial \tau }}={\lambda }_{gl}\left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}\right);$$

(6)

$${\displaystyle \frac{\partial \left(C_s{\rho }_{s}T\right)}{\partial \tau }}={\lambda }_s\left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}\right)+q_v.$$

(7)

The problem is solved in a two-dimensional formulation for a vertical cross section of the double-glazed unit. The gaseous medium is considered compressible. The right-hand side of Equation (7) includes the density of the volumetric heat source q_v, which is generated in the electrically conductive coating as a result of the passage of electric current. The velocity components u and v are zero on the glass surfaces. The boundary conditions on the outer surfaces of the glass unit are as follows:

y = 0; y = H: ∂T/∂y = 0

(8)

x = 0:T = T_out(τ); x = B: T = T_in(τ);

(9)

Fourth-kind boundary conditions were specified on the inner surfaces of the glass unit chambers, accounting for conductive heat transfer between the glass and the gaseous medium, as well as radiative heat exchange between adjacent glass surfaces within the electrically heated glass unit.

$$x={\delta }_{gl}:-{\lambda }_{gl}{\displaystyle \frac{\partial T}{\partial x}}=-{\lambda }_g{\displaystyle \frac{\partial T}{\partial x}}-q_{r_2},$$

(10)

$$x={\delta }_{gl}+{\delta }_g:-{\lambda }_g{\displaystyle \frac{\partial T}{\partial x}}-q_{r_1}=-{\lambda }_s{\displaystyle \frac{\partial T}{\partial x}},$$

(11)

$$x={\delta }_{gl}+{\delta }_g+{\delta }_s:-{\lambda }_s{\displaystyle \frac{\partial T}{\partial x}}=-{\lambda }_{gl}{\displaystyle \frac{\partial T}{\partial x}}.$$

(12)

The term in the boundary condition (10) represents the density of the radiative heat flux incident on the inner surface of the outer (cold) glass, while the term in condition (11) represents the density of the radiative heat flux leaving the surface of the electrically conductive coating. The system of Equations (1)–(7) with boundary conditions (8)–(12) is solved using the finite difference method. The first-order derivatives in Equations (2)–(4) are approximated using an upwind scheme. The system of difference equations is solved using the matrix sweep method. A detailed formulation of this problem and the solution method are presented in [4]. Unlike the formulation presented in [4], this study assumes an additional thin layer on the inner surface of the inner glass where heat is generated at a specified power. The energy equation for this layer includes an additional term q_v, which accounts for the heat generation rate due to the electric current flowing through the coating. Time-varying temperature values T_out(τ) and T_in(τ), determined experimentally, are specified on the inner and outer surfaces of the glass unit.

3.3. Experimental Study of a Double-Glazed Unit in a Real Climate Chamber

Further experimental studies were conducted in a real-climate test chamber, which was equipped in a full-scale (four-story, total area 306 m²) passive house of the Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine. Figure 6 shows a photo of the window (with the parameters described in the previous section) and the sensor arrangement scheme.

Using highly sensitive heat flux sensors and platinum temperature sensors, the distributions of heat flux density (Figure 7) and temperature (Figure 8) were obtained on the inner and outer surfaces of the glass with an electrically heated glass temperature set at 60 °C (with an external air temperature of −3 °C).

Unlike the measurements in the previous section, an intensive heating mode was applied up to 60 °C, as the window is not in a real winter climate and is therefore cooled by the cold ambient air. Electrically heated glass was switched to the specified mode on 20 February 2021 at 13:00 and then switched to another mode on 21 February 2021 at 15:10. The highest values of heat flux along the height of the electrically heated glass were observed at the top of the glass on the outer surface (approximately 67.5 W/m²) and the inner surface (approximately 350.5 W/m²) at the specified heating mode, while the lowest values (approximately 47.3 W/m² and 288.2 W/m², respectively) were observed at the bottom. The light blue line at the bottom represents the ambient temperature, while the red line represents the chamber temperature, approximately 30–32 °C.

4. Correlation of Experimental Results with Theoretical Models: Analysis of Results

To compare and contrast the experimental data, the temperature was determined using three resistance thermometers embedded in the heat flux sensor located on the inner surface of the glass unit (Figure 9a) and three resistance thermometers embedded in the heat flux sensor located on the outer surface of the glass unit (Figure 9b).

To determine the temperature distribution on the inner and outer surfaces of the glazing unit, quadratic interpolation was applied to three temperature values measured on each surface. On the basis of the computational results, time-dependent heat flux densities on both the inner and outer surfaces of the glazing unit were determined and compared with experimental data. For this analysis, the emissivity of coated glass surfaces was assumed to be ε_i = 0.15, while for uncoated surfaces it was ε_un = 0.86. The electric heating power was Q = 303 W.

Numerical simulations yielded the thermal characteristics of the electrically heated double-glazed unit. The heat generated by the electrically conductive coating primarily enters the climate chamber where the glazing unit is installed, with a smaller portion being dissipated to the external environment.

Figure 10 shows the time dependence of the heat fluxes integrated on the surfaces of the glazing unit, entering the room and leaving to the outside. As can be seen in this figure, within the time interval of 14 h < τ < 30 h, under the conditions considered, these heat fluxes are 250.7 ... 258.1 W (heat flux entering the room, considered positive) and −50.6 ... −46.19 W (heat flux leaving to the outside, considered negative). Thus, 83% ... 85% of the heat generated by electric heating is transferred to the room. Consequently, 15% ... 17% of the heat is dissipated to the external environment.

Figure 11 presents the distribution of the heat flux density on the surfaces of the glazing unit at time τ = 30 h. The 0Z axis is directed vertically upward. As can be seen from Figure 11, the heat flux density is quite uniformly in the middle part of the glazing unit and is approximately 339 ... 342 W/m² on the inner surface and −68 ... −60 W/m² on the outer surface. In the lower part of the glazing unit (z < 0.05 m), the density of heat flux on the inner surface decreases significantly (to 227 W/m²), while on the outer surface it increases (to −25.7 W/m²). In the upper part of the glazing unit (z > 0.95 m), the density of heat flux on the inner surface increases (to 365 W/m²) and on the outer surface it decreases significantly (to −220 W/m²). The points in the graph represent the heat flux densities obtained experimentally using heat flux sensors. Figure 11 shows that the calculated and experimental data are in fairly good agreement.

Figure 12 presents the distributions of temperature and gas velocity across electrically heated glass at a height of z = 0.5 m and a time of τ = 30 h. The 0X axis is directed from the outer surface of the glazing unit towards the inner surface.

As shown in Figure 12, under these conditions, the maximum velocity of natural convective air movement in the outer chamber of the glazing unit is vz = 0.04 m/s and in the inner chamber is v_z = 0.03 m/s. The maximum temperature inside the glazing unit is observed near the inner surface of the inner glass, where heat is generated. For z = 0.5 m, this temperature is 56.6 °C. The temperature on the outer surface of the inner glass is 55.0 °C. The temperature distribution across the thickness of the gas-filled space in the glazing unit indicates that it is nearly linear, suggesting a negligible influence of convection on the overall heat transfer in this type of glazing unit. The time dependences of the heat flux densities at the points on the inner and outer surfaces of the glazing unit where the heat flux sensors are installed are presented in Figure 13. The time interval considered is 14 h < τ < 30 h.

As shown in Figure 13, the numerical simulation results are in generally good agreement with the experimental data. The best agreement is observed for the middle part of the inner surface (Figure 13c) and the upper part of the outer surface (Figure 13f). On the lower and middle parts of the outer surface of the glazing unit (Figure 13b,d), the calculated data exceed the experimental data by an average of 10–15 W/m². For the lower part of the inner surface (Figure 13a), the calculated heat flux densities are higher than the experimental data in the time interval of 14–18 h and lower in the interval of 18–30 h. A comparison of the obtained experimental and numerical data provides satisfactory results and agreement. The slight increase in the heat flux values for the experimental data (Figure 13a,c,e) can be explained by the initial activation and operation of the thermostat embedded in the electrically heated glass to maintain a specified temperature on the inner surface of the glazing unit within a given range.

5. Discussion

Our research findings align with the existing literature on electrically heated windows, particularly the work of J. Kurnitski [42]. Both studies demonstrate the significant energy efficiency and improved indoor comfort offered by this technology. However, our research expands upon previous work by exploring a wider range of window configurations and heating methods, including the utilisation of low-grade heat. While our results are consistent with the general trend of higher efficiency for windows with lower U-values, our study also highlights the potential for further improvements through advanced window designs and coatings. Additionally, we have identified the benefits of electrically heated windows in preventing condensation and enhancing occupant comfort.

The findings of this study are largely consistent with the research conducted by Lee and Hyomun [43].

A notable difference between our study and Lee’s is the specific climatic conditions and building types considered. Our study focused on buildings in the climatic conditions of Ukraine, while Lee’s study looked at residential buildings in South Korea. This suggests that the optimal configuration and control strategies for electrically heated windows may vary depending on regional climate and building characteristics.

To further strengthen our conclusions, future research could focus on long-term performance analysis, cost–benefit assessments, and comparisons across different geographical regions. This would provide a more comprehensive understanding of the potential of electrically heated windows in various building contexts.

6. Conclusions

This study presents a comprehensive investigation of energy-efficient double-glazed windows equipped with electric heating. Through experimental and numerical analysis, we have demonstrated the effectiveness of this innovative technology in enhancing building energy performance and improving indoor comfort. An experimental and numerical study of heat transfer processes through an energy-efficient double-glazed unit with electric heating was conducted to analyse the distribution of heat fluxes and temperatures on its outer and inner surfaces. It was established that 83–85% of the heat generated by electric heating is transferred to the room, and 15–17% to the outside. Our findings reveal that a substantial portion of the heat generated by the electric heating system is transferred to the indoor space, while a smaller portion is dissipated to the exterior. This efficient heat transfer contributes to a significant reduction in heat losses through the window and improves overall building energy efficiency.

Furthermore, the electrically heated windows effectively prevent condensation and frost formation, enhancing occupant comfort and reducing the risk of moisture-related damage. The built-in thermostat allows for precise temperature control, ensuring optimal conditions for various applications.

The main results of the work include:

-

the creation of two experimental stands (laboratory and pilot) for conducting research on energy-efficient window structures;

-

the development, validation and use of a thermophysical model for aerodynamics and heat transfer in energy-efficient windows;

-

based on the thermal model, it is possible to develop a simplified engineering methodology for calculating the design of energy-efficient windows and recommend it to building norms and regulations for new construction or reconstruction (thermal modernisation) of existing buildings and structures;

-

some engineering recommendations for window manufacturers on low-cost minor upgrades of insulating glass units to convert them to energy-efficient status;

-

tasks for specialised production and testing laboratories on window issues for certified testing of energy-efficient windows for wind stress, water permeability, air permeability, and fire and operational safety with the issuance of relevant permitting documents.

The results of our research have practical implications for both building designers and window manufacturers. The developed thermophysical model and engineering methodology can be incorporated into building codes and regulations to promote the adoption of energy-efficient windows in new construction and retrofit projects. Additionally, the proposed minor upgrades for existing insulating glass units offer a cost-effective solution for improving their energy performance.

In conclusion, this study highlights the potential of electrically heated double-glazed windows to play a vital role in achieving sustainable building practises and reducing energy consumption. By addressing the challenges associated with window heat losses and improving indoor comfort, this technology offers a valuable contribution to the transition towards a more energy-efficient and sustainable built environment.