# Heat Transfer Through Insulating Glass Units Subjected to Climatic Loads

## Abstract

**:**

## 1. Introduction

_{g}-value). The authors determined the U

_{g}-value for IGUs with variable gap thickness (limited by the surfaces of deflected panes), considering the average gap thickness in the loaded IGU as reliable. The authors stated that this assumption becomes reasonable when plate curvature is small and it is certainly acceptable in the conduction regime, where the convective movement is not significant. This article provides the results of sample calculations for double- and triple-glazed units under winter conditions. It was found that taking into account the plate curvature increases the calculated U

_{g}-value from 4.4% to 5.8%. Calculations were also made to account for changes in weather conditions (typical meteorological year) for Montreal and Toulouse. The results indicate that U

_{g}may vary up to 5% above and 10% below the yearly average.

_{g}-value calculated from real deflections of double and triple-glazed units, measured in summer and winter at several locations in the USA. It was found that a 20 °C temperature difference reduces thermal performance by 4.6% for double-glazed IGUs and by 3.6% for triple-glazed IGUs.

## 2. Methodology for the Calculation of Static Quantities in IGUs

- p
_{0}, T_{0}, v_{0}—initial gap gas parameters: pressure [kPa], temperature [K], volume [m^{3}], obtained in the production process, - p
_{op}, T_{op}, v_{op}—operating parameters—analogously.

^{2}] is assumed. The latter assumption is considered to be sufficiently accurate if the deflection is not greater than the thickness of the glass [14]. The deflection function of a simply supported single pane of the a [m] width and b [m] length, subjected to the q [kN/m

^{2}] load, placed centrally in the x-y coordinate system, can be recorded as [15]:

- d—is the glass pane thickness [m],
- E—is the Young’s modulus of glass [kPa],
- μ—is the Poisson’s ratio [-].

^{3}] resulting from the deflection of one of the limiting glass pane may be determined by integration of Equation (2):

- α
_{v}—is the proportionality factor, [m^{5}/kN].

^{3}].

- p
_{a}—current atmospheric pressure [kPa], - q
_{z,ex}, q_{z,in}—load per area from outer factors, primarily wind [kN/m^{2}], almost always q_{z,in}= 0.

_{op}for each of the gaps, the resultant loading q for each of the component glass panes can be determined:

- for a double-glazed IGU$${q}_{\mathrm{ex}}={c}_{\mathrm{ex}}-{p}_{\mathrm{op}1},\text{}{q}_{\mathrm{in}}={p}_{\mathrm{op}1}-{c}_{\mathrm{in}},$$
- for a triple-glazed IGU$${q}_{\mathrm{ex}}={c}_{\mathrm{ex}}-{p}_{\mathrm{op}1},\text{}{q}_{1\u20132}={p}_{\mathrm{op}1}-{p}_{\mathrm{op}2},\text{}{q}_{\mathrm{in}}={p}_{\mathrm{op}2}-{c}_{\mathrm{in}}$$

_{c}[mm] in the center of the glass pane can be determined by the formula:

_{m}[mm] was determined from the formula:

## 3. Materials and Methods

_{g}[W/(m

^{2}·K)] of IGUs was calculated on the basis of the methodology described in standard [16], and heat losses were expressed by density of heat-flow rate Φ [W/m

^{2}] from the formula:

_{i}, t

_{e}—are the internal and external air temperature [°C].

_{s}[(m

^{2}·K)/W] has the greatest influence on the U-value. For each gap:

- h
_{r}—is the thermal conductance by radiation [W/(m^{2}·K)], - h
_{g}—is the thermal conductance of gas (by conduction and convection) [W/(m^{2}·K)]. - λ
_{g}—is the thermal conductivity of gas [W/(m·K)], - s—is the gas gap thickness [m],
- Nu—is the Nusselt number [-],
- σ—is the Boltzmann constant 5.6693 × 10
^{−8}W/(m^{2}·K^{4}) - T
_{m}—is the average temperature of both surfaces delimiting the gap [K], - ε
_{sur1}, ε_{sur2}—are the emissivity of surfaces delimiting the gap [-].

- the type of gas; the calculation was based on the use of argon,
- location in the structure; the calculations assume a horizontal position, in units situated horizontally or diagonally convection increases.
- increasing the temperature difference on the surfaces of the glass panes limiting the gap affects the increase in convection,
- convection also increases when the average gas temperature in the gap increases.

_{sur1}= 0.837 and ε

_{sur2}= 0.04 were used in the calculations.

_{g}-value. Physical parameters of argon were adopted on the basis of the standard [17].

_{e}[(m

^{2}·K)/W]) and at the internal side of a window (R

_{i}[(m

^{2}·K)/W]). They depend primarily on the positioning of the window in the structure and the velocity of air (a short analysis on this subject is presented in Chapter 5). The calculations assumed R

_{i}= 0.13 (m

^{2}·K)/W (vertical position) and R

_{e}= 0.04 (m

^{2}·K)/W (for wind velocity V = 4 m/s). These are often accepted comparative values, also in the standard [16].

_{g}-value for double- and triple-glazed IGUs, with glass thickness d = 4 mm, assuming t

_{i}= 20 °C and in two variants of the outside air temperature t

_{e}= 0 °C and t

_{e}= −20 °C. The dashed line was used to determine the limits of gap thickness at which Nu = 1.

_{e}the limit thickness decreases. It can also be stated that in the case of triple-glazed IGUs, the difference in temperature in the gap is smaller, and the thickness of the boundary increases.

## 4. IGUs Under Pressure and Temperature Changes—Presentation and Discussion of Test Results

_{0}= 20 °C = 293.15 K, p

_{0}= 100 kPa. In these conditions, the component glass panes are flat.

_{i}= 20 °C, t

_{e}= −20 °C; the gas temperature in each gap was calculated for each case based on the temperature distribution in the particular IGU: for a double-glazed IGU T

_{op1}= −2.37 to −2.25 °C, for triple-glazed IGU T

_{op1}= −10.09 to −9.66 °C, T

_{op2}= 7.60 to 7.97 °C.

_{i}= 20 °C, t

_{e}= 0 °C; gas temperature: for a double-glazed IGU T

_{op1}= 8.80 to 9.01 °C, for triple-glazed IGU T

_{op1}= 4.97 to 5.08 °C, T

_{op2}= 13.66 to 14.10 °C.

_{a}= p

_{0}= 100 kPa. The results of the calculations are presented in Table 2.

_{ex}and q

_{in}(absolute value) illustrates the underpressure in the gaps in relation to atmospheric pressure. The parameter q

_{1-2}is the difference in operating pressure between the gaps in a triple-glazed IGU. From Equations (18) and (19) the extreme deflection (in the center of the pane) w

_{c}and the average deflection w

_{m}(the w

_{m}values are given between parentheses) were calculated for each pane.

_{c}[mm] and the average gap thickness s

_{m}[mm] were calculated.

_{c}and s

_{m}for analyzed IGUs with gaps of the same nominal thickness do not differ much from each other. This is despite the fact that the deflection of component glass panes varies considerably. The effect of gas interactions in tight gaps can be seen here. Rigid panes are less susceptible to deflection, but the external load is less compensated for by the gas pressure in the gap. After changing the thickness of all the panes in a unit, the load changes, but the deflections are similar. Therefore, when one of the glass panes changes to a stiffer one, the absolute load values of component glass panes increase, although their algebraic sum for each IGU is equal to 0. After such conversion, the less rigid panes deflect more because they are exposed to a higher loading—for this reason, a loaded IGU has approximately constant volume of gaps, despite the change in thickness of the component panes.

_{c}in double-glazed units at 3, 4 i 6 mm thick panes and 16 mm thick gap. It was assumed that IGU is loaded only by a change in atmospheric pressure by ∆p = p

_{a}− p

_{o}= 3 kPa. This means that the current atmospheric pressure is p

_{a}= 103 kPa. It can be added here that the results of calculations of static quantities are not very sensitive to the value of p

_{o}, and to a significant extent to ∆p. This means that if we assumed, for example, p

_{o}= 950 kPa i p

_{a}= 980 kPa, the results would be almost identical.

_{c}, w

_{m}, s

_{c}, and s

_{m}values for units loaded with temperature change as in variant 1 and simultaneously operating loading with external atmospheric pressure increase of ∆p = 3 kPa. These are particularly unfavorable operating conditions in the context of reducing the thickness of the gaps. An analogous calculation was carried out for variant 2 (Table 4).

^{2}]:

- U
_{g}, Φ_{g}—describe heat loss without taking into account the curvature of the panes, calculated for the nominal thickness of the gaps, - U
_{c}, Φ_{c}—describe possible local heat loss near the IGU center, i.e., where the distance between the panes is the smallest, calculated for the thickness of the gaps s_{c}, - U
_{m}, Φ_{m}—describe the average heat loss through the IGU, calculated for the thickness of the gaps s_{m}.

_{c}, ∆Φ

_{m}) for units of nominal gap thickness.

_{g}-value change, i.e., when the conditions inside the gap lead to Nu < 1. It is different when the U

_{g}-value changes in the non-linear range (Nu > 1). Heat losses do not increase. Then, the reduction of gap thickness can lead to a slight decrease in the calculated Nu value, which translates into a slight reduction in the calculated heat losses.

_{g}-value, the indices ∆Φ

_{c}and ∆Φ

_{m}almost do not depend on the thickness of the gaps. This is due to the fact, as additional calculations have shown, that the relationship between the thickness of IGU gaps and static quantities (resultant loading of component glass and their deflections) is also linear.

_{m}for these units on their width (at a constant ratio b/a = 2), under different external temperature conditions t

_{e}. Simultaneous pressure increase ∆p = 3 kPa was assumed. Other data was used as in previous examples.

_{m}changes from 3.9% to 5.0%. These values are characteristic of the average temperature during the winter months in many places around the world.

## 5. Notes on IGUs Wind Load

^{2}, which approximately corresponds [20] to a pressure of wind with velocity V of approx. 80 km/h (22.2 m/s).

_{g}-value. Graphic illustration of this effect is shown in Figure 7. The calculations were made for units with gap thickness of 16 mm. It can be noted that in the case of triple-glazed IGUs, the effect of wind velocity is negligible.

## 6. Conclusions

_{g}of insulating glass units is the thickness of gas-filled tight gaps. It is assumed in the calculation procedures that this thickness is not dependent on temporary changes in climatic factors. The thickness is variable under real operating conditions. In winter conditions in particular, IGU component glass panes take a concave form of deflection, which reduces the thickness of the gaps. This effect increases if the atmospheric pressure increases at the same time.

_{e}= 0 °C. These values almost do not depend on the nominal thickness of the gaps, which results from the linear dependence of static quantities in an IGU on this thickness. Under certain conditions, heat losses calculated according to standard procedures may therefore be underestimated.

_{g}-value change (Nu > 1), i.e., when the outside temperature drops significantly or the gaps are thick enough. The thermal performance of glazing does not deteriorate. It is therefore advantageous to design IGUs so that Nu > 1, but it is necessary to take into account local climatic conditions and analyze loads that may also occur during the summer period.

_{m}index totals then from 3.9% to 5.0%.

## Funding

## Conflicts of Interest

## Nomenclature

A | auxiliary parameter [m^{3}] |

a | width (of glass pane) [m] |

B | auxiliary parameter [m^{5}/kN] |

b | length (of glass pane) [m] |

c | auxiliary parameter [kPa] |

D | flexural rigidity (of glass pane) [kNm] |

d | thickness (of glass pane) [m] or [mm] |

E | Young’s modulus [kPa] or [GPa] |

h | thermal conductance [W/(m^{2}·K)] |

i | consecutive natural number |

Nu | Nusselt number |

p | pressure [kPa] |

q | load per area, [kN/m^{2}] |

R | thermal resistance [(m^{2}·K)/W] |

s | thickness (of gas gap) [mm] |

T | temperature (of gas in the gap) [K] |

t | temperature (of air) [K] or [°C] |

U | thermal transmittance [W/(m^{2}·K)] |

V | wind velocity [km/h] |

v | volume (of the gap) [m^{3}] |

w | deflection [mm] |

w(x,y) | function of deflection, [m] |

x-y | coordinate system |

Greek letters | |

α | proportionality factor, [m^{5}/kN] |

α’ | dimensionless coefficient [-] |

β_{i} | auxiliary parameter [-] |

∆p | pressure change [kPa] |

∆T | temperature difference [K] |

∆v | volume change [m^{3}] |

∆Φ | percentage increase in density of heat-flow rate [%] |

ε | surface emissivity [-] |

λ | thermal conductivity [W/(m·K)] |

μ | Poisson’s ratio [-] |

π | number “pi” |

σ | Boltzmann constant [W/(m^{2}·K^{4})] |

Φ | density of heat-flow rate [W/m^{2}] |

Subscripts and markings | |

0 | initial gas parameters |

1, 2 | specific gas-filled gap |

1-2 | glass pane (between gaps) |

c | center (of glass pane) |

a | atmospheric |

e | external |

ex | exterior glass pane |

g | regarding gas or regarding IGU (at U_{g}, Φ_{g} and ∆Φ_{g}) |

i | internal |

in | interior glass pane |

m | mean, average |

op | operating gas parameters |

r | radiative |

s | regarding gas gap |

sur1, sur2 | regarding surfaces |

v | regarding volume |

w | regarding deflection |

z | outside |

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**Figure 1.**Typical deflections of insulating glass units: (

**a**) concave form of deflection, (

**b**) convex form of deflection, (

**c**) deflection characteristic of wind load.

**Figure 2.**Visible distorted reflection of the image of the neighboring building from both insulating glass unit (IGU) component glass panes indicates the concave form of deflection of the unit.

**Figure 3.**Index designations of IGU elements and location of low-emission coatings (dashed line): (

**a**) double-glazed IGU, (

**b**) triple-glazed IGU.

**Figure 5.**Dependence of the deflection of component glass panes w

_{c}on the width of the IGU (atmospheric pressure increase of ∆p = 3 kPa).

b/a | 1.0 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 |

α′_{v} | 0.001703 | 0.002246 | 0.002848 | 0.003499 | 0.004189 | 0.004912 |

α′_{w} | 0.004062 | 0.004869 | 0.005651 | 0.006392 | 0.007085 | 0.007724 |

b/a | 1.6 | 1.7 | 1.8 | 1.9 | 2.0 | 3.0 |

α′_{v} | 0.005659 | 0.006427 | 0.00721 | 0.008004 | 0.008808 | 0.017055 |

α′_{w} | 0.008308 | 0.008838 | 0.009316 | 0.009745 | 0.010129 | 0.012233 |

**Table 2.**Static quantities and gap thicknesses in IGUs—under reduced temperature conditions (Variant 1).

Structure of IGU [mm] | Resultant Loading q [kN/m^{2}] | Deflection w_{c} (w_{m}) [mm] | Resultant Thickness of Gap s [mm] | |||||||
---|---|---|---|---|---|---|---|---|---|---|

ex | 1-2 | in | ex | 1-2 | in | gap 1 | gap 2 | |||

s_{c1} | s_{m1} | s_{c2} | s_{m2} | |||||||

d_{ex}-s_{1}-d_{in} | Double-glazed units | |||||||||

4-16-4 | 0.218 | - | −0.218 | 1.36 (0.59) | - | −1.36 (−0.59) | 13.28 | 14.82 | - | - |

6-16-4 | 0.330 | - | −0.330 | 0.61 (0.27) | - | −2.08 (−0.90) | 13.31 | 14.83 | - | - |

4-12-4 | 0.164 | - | −0.164 | 1.03 (0.45) | - | −1.03 (−0.45) | 9.94 | 11.10 | - | - |

6-12-4 | 0.251 | - | −0.251 | 0.47 (0.20) | - | −1.57 (−0.68) | 9.96 | 11.12 | - | - |

3-12-3 | 0.070 | - | −0.070 | 1.04 (0.45) | - | −1.04 (−0.45) | 9.92 | 11.10 | - | - |

d_{ex}-s_{1}-d_{1-2}-s_{2}-d_{in} | Triple-glazed units | |||||||||

4-16-4-16-4 | 0.463 | −0.117 | −0.346 | 2.90 (1.26) | −0.73 (−0.32) | −2.16 (−0.94) | 12.37 | 14.42 | 14.57 | 15.38 |

6-16-4-16-4 | 0.840 | −0.311 | −0.529 | 1.56 (0.68) | −1.94 (−0.85) | −3.34 (−1.44) | 12.50 | 14.47 | 14.63 | 15.41 |

4-12-4-12-4 | 0.345 | −0.087 | −0.258 | 2.16 (0.99) | −0.54 (−0.24) | −1.61 (−0.70) | 9.30 | 10.77 | 10.93 | 11.54 |

6-12-4-12-4 | 0.631 | −0.233 | −0.398 | 1.17 (0.51) | −1.46 (−0.63) | −2.49 (−1.08) | 9.37 | 10.86 | 10.97 | 11.55 |

6-12-3-12-4 | 0.540 | −0.112 | −0.429 | 1.00 (0.43) | −1.66 (−0.72) | −2.68 (−1.17) | 9.34 | 10.85 | 10.98 | 11.55 |

3-12-3-12-3 | 0.149 | −0.037 | −0.112 | 2.21 (0.96) | −0.55 (−0.24) | −1.66 (−0.72) | 9.24 | 10.80 | 10.89 | 11.52 |

**Table 3.**Static quantities and gap thicknesses in IGUs under reduced temperature conditions (Variant 1) and atmospheric pressure increase by ∆p = 3 kPa.

Structure of IGU [mm] | Resultant Loading q [kN/m^{2}] | Deflection w_{c} (w_{m}) [mm] | Resultant Thickness of Gap s [mm] | |||||||
---|---|---|---|---|---|---|---|---|---|---|

ex | 1-2 | in | ex | 1-2 | in | gap 1 | gap 2 | |||

s_{c1} | s_{m1} | s_{c2} | s_{m2} | |||||||

d_{ex}-s_{1}-d_{in} | Double-glazed units | |||||||||

4-16-4 | 0.295 | - | −0.295 | 1.84 (0.81) | - | −1.84 (−0.81) | 12.32 | 14.38 | - | - |

4-14-4 | 0.259 | - | −0.259 | 1.62 (0.70) | - | −1.62 (−0.70) | 10.76 | 12.60 | - | - |

4-12-4 | 0.233 | - | −0.233 | 1.39 (0.61) | - | −1.39 (−0.61) | 9.22 | 10.78 | - | - |

4-10-4 | 0.187 | - | −0.187 | 1.17 (0.51) | - | −1.17 (−0.51) | 7.66 | 8.98 | - | - |

d_{ex}-s_{1}-d_{1-2}-s_{2}-d_{in} | Triple-glazed units | |||||||||

4-16-4-16-4 | 0.613 | −0.114 | −0.500 | 3.83 (1.67) | −0.71 (−0.31) | −3.13 (−1.36) | 11.46 | 14.02 | 13.58 | 14.95 |

4-14-4-14-4 | 0.540 | −0.100 | −0.440 | 3.38 (1.47) | −0.63 (−0.27) | −2.75 (−1.20) | 9.99 | 12.26 | 11.88 | 13.07 |

4-12-4-12-4 | 0.460 | −0.085 | −0.375 | 2.87 (1.25) | −0.53 (−0.23) | −2.35 (−1.02) | 8.60 | 10.52 | 10.18 | 11.21 |

4-10-4-10-4 | 0.387 | −0.070 | −0.317 | 2.42 (1.05) | −0.44 (−0.19) | −1.98 (−0.86) | 7.14 | 8.76 | 8.46 | 9.33 |

**Table 4.**Static quantities and gap thicknesses in IGUs under conditions for a “mild winter” (Variant 2) and atmospheric pressure increase by ∆p = 3 kPa.

Structure of IGU [mm] | Resultant Loading q [kN/m^{2}] | Deflection w_{c} (w_{m}) [mm] | Resultant Thickness of Gap s [mm] | |||||||
---|---|---|---|---|---|---|---|---|---|---|

ex | 1-2 | in | ex | 1-2 | in | gap 1 | gap 2 | |||

s_{c1} | s_{m1} | s_{c2} | s_{m2} | |||||||

d_{ex}-s_{1}-d_{in} | Double-glazed units | |||||||||

4-16-4 | 0.188 | - | −0.188 | 1.18 (0.51) | - | −1.18 (−0.51) | 13.64 | 14.98 | - | - |

4-14-4 | 0.165 | - | −0.165 | 1.03 (0.45) | - | −1.03 (−0.45) | 11.94 | 13.10 | - | - |

4-12-4 | 0.143 | - | −0.143 | 0.89 (0.40) | - | −0.89 (−0.40) | 10.22 | 11.20 | - | - |

4-10-4 | 0.120 | - | −0.120 | 0.75 (0.33) | - | −0.75 (−0.33) | 8.50 | 9.34 | - | - |

d_{ex}-s_{1}-d_{1-2}-s_{2}-d_{in} | Triple-glazed units | |||||||||

4-16-4-16-4 | 0.384 | −0.058 | −0.326 | 2.41 (1.04) | −0.36 (−0.16) | −2.04 (−0.89) | 13.23 | 14.80 | 14.32 | 15.27 |

4-14-4-14-4 | 0.339 | −0.050 | −0.289 | 2.12 (0.92) | −0.31 (−0.14) | −1.81 (−0.79) | 11.57 | 12.94 | 12.50 | 13.35 |

4-12-4-12-4 | 0.293 | −0.042 | −0.251 | 1.83 (0.80) | −0.26 (−0.11) | −1.56 (−0.68) | 9.91 | 11.09 | 10.70 | 11.43 |

4-10-4-10-4 | 0.246 | −0.035 | −0.212 | 1.54 (0.67) | −0.22 (−0.09) | −1.32 (−0.57) | 8.24 | 9.24 | 8.90 | 9.52 |

**Table 5.**Quantities describing heat losses by IGUs under conditions of reduced temperature (Variant 1) and atmospheric pressure increase by ∆p = 3 kPa.

Gas Gap Thickness [mm] | Thermal Transmittance [W/(m^{2}·K)] | Density of Heat-Flow Rate Φ [W/m^{2}] | ∆Φ_{c} [%] | ∆Φ_{m} [%] | ||||
---|---|---|---|---|---|---|---|---|

U | U_{c} | U_{m} | Φ | Φ_{c} | Φ_{m} | |||

Double-glazed units | ||||||||

16 | 1.330 | 1.299 | 1.317 | 53.20 | 51.96 | 52.68 | −2.3 | −1.0 |

14 | 1.314 | 1.298 | 1.302 | 52.56 | 51.92 | 52.08 | −1.2 | −0.9 |

12 | 1.296 | 1.441 | 1.297 | 51.84 | 57.64 | 51.88 | 11.2 | −0.1 |

10 | 1.364 | 1.630 | 1.467 | 54.56 | 65.20 | 58.68 | 19.5 | 7.6 |

Triple-glazed units | ||||||||

16 | 0.643 | 0.653 | 0.636 | 25.72 | 26.12 | 25.44 | 1.6 | −1.1 |

14 | 0.634 | 0.727 | 0.648 | 25.36 | 29.08 | 25.92 | 14.7 | 2.2 |

12 | 0.675 | 0.817 | 0.730 | 27.00 | 32.68 | 29.20 | 21.0 | 8.1 |

10 | 0.776 | 0.941 | 0.839 | 31.04 | 37.64 | 33.56 | 21.3 | 8.1 |

**Table 6.**Quantities describing heat losses by IGUs under conditions for a “mild winter” (Variant 2) and atmospheric pressure increase by ∆p = 3 kPa.

Gas Gap Thickness [mm] | Thermal
Transmittance [W/(m^{2}·K)] | Density of
Heat-Flow Rate Φ [W/m^{2}] | ∆Φ_{c} [%] | ∆Φ_{m} [%] | ||||
---|---|---|---|---|---|---|---|---|

U | U_{c} | U_{m} | Φ | Φ_{c} | Φ_{m} | |||

Double-glazed units | ||||||||

16 | 1.113 | 1.142 | 1.107 | 22.26 | 22.84 | 22.14 | 2.6 | −0.5 |

14 | 1.122 | 1.250 | 1.174 | 22.44 | 25.00 | 23.48 | 11.4 | 4.6 |

12 | 1.246 | 1.388 | 1.305 | 24.92 | 27.76 | 26.10 | 11.4 | 4.7 |

10 | 1.408 | 1.567 | 1.473 | 28.16 | 31.34 | 29.46 | 11.3 | 4.6 |

Triple-glazed units | ||||||||

16 | 0.563 | 0.631 | 0.590 | 11.26 | 12.62 | 11.80 | 12.1 | 4.8 |

14 | 0.623 | 0.699 | 0.653 | 12.46 | 13.98 | 13.06 | 12.2 | 4.8 |

12 | 0.700 | 0.786 | 0.735 | 14.00 | 15.72 | 14.70 | 12.3 | 5.0 |

10 | 0.804 | 0.903 | 0.844 | 16.08 | 18.06 | 16.88 | 12.3 | 5.0 |

Structure of IGU [mm] | Resultant Loading q [kN/m^{2}] | Deflection w_{c} [mm] | ||||
---|---|---|---|---|---|---|

ex | 1–2 | in | ex | 1–2 | in | |

d_{ex}-s_{1}-d_{in} | Double-glazed units | |||||

4-16-4 | 0.154 | - | 0.146 | 0.96 | - | 0.91 |

8-16-4 | 0.268 | - | 0.032 | 0.21 | - | 0.20 |

4-16-8 | 0.047 | - | 0.253 | 0.29 | - | 0.20 |

d_{ex}-s_{1}-d_{1-2}-s_{2}-d_{in} | Triple-glazed units | |||||

4-16-4-16-4 | 0.109 | 0.098 | 0.092 | 0.68 | 0.61 | 0.58 |

8-14-4-14-4 | 0.247 | 0.028 | 0.026 | 0.19 | 0.17 | 0.16 |

4-12-4-12-8 | 0.053 | 0.039 | 0.208 | 0.33 | 0.24 | 0.16 |

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**MDPI and ACS Style**

Respondek, Z.
Heat Transfer Through Insulating Glass Units Subjected to Climatic Loads. *Materials* **2020**, *13*, 286.
https://doi.org/10.3390/ma13020286

**AMA Style**

Respondek Z.
Heat Transfer Through Insulating Glass Units Subjected to Climatic Loads. *Materials*. 2020; 13(2):286.
https://doi.org/10.3390/ma13020286

**Chicago/Turabian Style**

Respondek, Zbigniew.
2020. "Heat Transfer Through Insulating Glass Units Subjected to Climatic Loads" *Materials* 13, no. 2: 286.
https://doi.org/10.3390/ma13020286