*2.3. Surface Thermal Resistances*

#### 2.3.1. Simplified Method

The assumption of the correct value of surface thermal resistances (*Rsi* and *Rse*) on both sides of the tested building enclosure has a noticeable effect on the calculated values of its total thermal resistance (*Rtot*) and thermal transmittance (*U*). The European standard ISO 6946 [22] in its Table 7 suggests that *Rsi* = 0.13 m2K/W and *Rse* = 0.04 m2K/W for an external partition and for horizontal heat flow.

#### 2.3.2. Calculation—Surface Temperatures and Air Movement Velocities Are Known

In real situations, depending on weather conditions, surface resistances *Rsi* and *Rse* can diverge from the above values. In such cases, a more accurate method can be the one described in Appendix A of the ISO 6946 standard [22], according to which one can use the actual wind speed to obtain the value of the convective heat transfer coefficient, *hc*. In the research, it was assumed that the air movement caused by the fans of heating/cooling units in the climate chambers was an equivalent of wind, and because of that, coefficients *hci* and *hce* for both sides of the tested walls will be calculated in that way. The air movement was measured on, respectively, the internal side and the external side at the tested building enclosure by means of anemometers. Then, surface thermal resistance *Rsi* and *Rse* should be determined for both sides for the horizontal heat flux flow, using the formulas:

$$R\_{\rm si} = \frac{1}{h\_i} = \frac{1}{h\_{ci} + h\_{ri}} \tag{10}$$

$$R\_{\mathfrak{s}\varepsilon} = \frac{1}{h\_{\mathfrak{e}}} = \frac{1}{h\_{\mathfrak{e}\varepsilon} + h\_{\mathfrak{e}\varepsilon}}\tag{11}$$

where:

*hci, hce*—the convective heat transfer coefficient on respectively the internal side and the external side, calculated from the formulas:

$$
\hbar\_{ci} = 4 + 4\nu\_i \tag{12}
$$

$$h\_{\varepsilon\varepsilon} = 4 + 4\upsilon\_{\varepsilon} \tag{13}$$

where:

*νi*, *νe*—wind speed adjacent to the surface of respectively the internal and the external side (m/s),

*hri*, *hre*—the radiative heat transfer coefficient on respectively the internal side and the external side, calculated from the formulas:

$$h\_{ri} = \varepsilon h\_{ri,0} = \varepsilon 4\sigma T\_{mi}^3 \tag{14}$$

$$
\hbar\_{rc} = \varepsilon h\_{rc,0} = \varepsilon 4\sigma T\_{mc}^3 \tag{15}
$$

where:

ε—surface emissivity into a half-space, assumed as equal to 0.9 (–), *hri*,0, *hre*,0—a black body radiation heat transfer coefficient (W/m2K), <sup>σ</sup>—the Stefan–Boltzmann constant equal to 5.67 × <sup>10</sup>−<sup>8</sup> (W/(m2K4)), *Tmi*, *Tme*—mean thermodynamic temperatures of the surfaces (K).

2.3.3. Calculation—Air Temperatures, Surface Temperatures and Heat Flux Density Are Known

In the case when it is possible to carry out additional surface temperature measurements on both sides of the tested building enclosure and to determine the heat flux, the

surface thermal resistances can be experimentally determined in accordance with the formulas:

$$R\_{si} = \frac{(T\_i - T\_{si})}{q} \tag{16}$$

$$R\_{s\varepsilon} = \frac{(T\_{s\varepsilon} - T\_{\varepsilon})}{q} \tag{17}$$

where:

*Tsi*, *Tse*—the temperature of respectively the internal and external surface of the analyzed element (K),

*Ti*, *Te*—the air temperature on respectively the internal side and the external side (K), *q*—the heat flux flowing through the building enclosure (W/m2).

The above methods were used in the analyses carried out by the authors, but this does not exhaust the subject. There are many methods of estimating radiative heat transfer coefficients, *hr*, and convective heat transfer coefficients, *hc*. A comprehensive analysis of this subject can be found in [63].

#### **3. Materials and Methods**

#### *3.1. Tested Elements*

The research was carried out for a part of the building enclosure, namely the external walls. Three different materials were tested: aerated concrete blocks, ceramic bricks and concrete blocks, as these are some of the most commonly used materials in residential buildings in Poland. The homogeneous tested walls were divided into two groups: uninsulated and insulated. Wall A was made of 240 mm × 240 mm × 590 mm class 600H+H aerated concrete blocks laid in Baumit ThermoMörtel 50 insulating mortar. In the case of the insulated version of wall A, 10 cm thick EPS (expanded polystyrene) boards were glued to it on the cooler side and then covered with fiberglass-reinforced mineral render. Wall B was made of 60 mm × 120 mm × 250 mm solid ceramic bricks laid in cement-lime mortar. In the case of the insulated version of wall B, 10 cm thick EPS boards with the same properties as before were glued to it on the cooler side and then covered with fiberglass-reinforced mineral render. Wall C was made of 120 mm × 250 mm × 380 mm solid concrete blocks laid in cement-lime mortar. In the case of the insulated version of wall C, 10 cm thick EPS boards were also used. After building each wall, a time of 4–6 weeks was used to season the construction and to get rid of construction moisture. During that time, the doors of the climate chambers were left open. The basic material specifications of the walls are presented in Table 1. The given thermal conductivity coefficients are declared values and were taken from producer technical specifications, provided by the construction material warehouse or from tabular data from Polish technical standards [71–73]. These values were not experimentally verified (measured) by the authors.

#### *3.2. Test Setup*

Measurements of the thermal resistance of selected external walls were conducted in a sleeve between two connected climate chambers, as shown in Figure 1. The major specifications of the set are as follows:



**Table 1.** Basic specifications of partitions tested in climate chambers.

\* Taken from the technical data sheet for the material, \*\* provided by construction material warehouse, \*\*\* taken from tabular data from Polish technical standards.

**Figure 1.** Test setup: (**a**) view of two climate chambers connected together, (**b**) locations of tested walls in sleeve connecting two climate chambers.

The tested wall would be placed in a sleeve connecting the two climate chambers, in which conditions simulating the behavior of building enclosures in the heating season were maintained, that is:


All homogenous building enclosures were tested from the instant the temperature settings in the chambers were activated (at the instant of activation the air temperature in the chambers was equal to the temperature in the laboratory room, approximately 20–25 ◦C) until the temperatures in the chambers and the heat fluxes stabilized. Then, the measurements were conducted for at least 7 days. All the enclosures were positioned along the axis of the sleeve connecting the two climate chambers. The erected wall was left for the mortar to set. A schematic diagram of the sensor connection on both sides of the tested building enclosures is shown in Figure 2. Then, sensors were placed on both sides, and as part of the measurements, the following were registered:


**Figure 2.** Schematic showing arrangement of sensors and measuring instrumentation on analyzed wall's warm side (**a**) and on its cold side (**b**). Description of visible elements: 1—black sheet of paper (ambient temperature measurement by IR camera), 2—Hukseflux TRSYS01 system heat flux density sensors, 3—Hukseflux TRSYS01 system sensors measuring building enclosure internal surface temperature, 4—Ahlborn thermal anemometer (measuring internal air temperature and humidity), 5—Ahlborn sensors (thermocouples) measuring building enclosure surface temperature, 6—Ahlborn sensor (0.5 m × 0.5 m) measuring heat flux density, 7—FLIR P65 thermal imaging camera, 8—data loggers, 9—Hukseflux TRSYS01 system sensors for measuring building enclosure external surface temperature, 10—Ahlborn thermal anemometer (measuring external air temperature and humidity), 11—Ahlborn sensors (thermocouples) measuring building enclosure surface temperature.

All the Ahlborn sensors were connected to Ahlborn Almemo data loggers (2690-8, 2890-9 or 5690-2M09). In addition to this, a Hukseflux TRSYS01 system, dedicated to measuring the thermal resistance of building enclosures, with an accuracy of ±3% and the operating range of −30–+70 ◦C, which doubled the surface temperature measurements on both sides of the building enclosure and the density of the heat flux penetrating through the latter, was connected. A photo of one of the measurements carried out is shown in Figure 3.

**Figure 3.** Photo of tested building enclosure (in this case, insulated wall A) with visible arrangement of sensors: (**a**) on warm chamber side, (**b**) on cold chamber side.
