**1. Introduction**

Buildings play an important role in achieving sustainable development goals, among others aimed at reducing greenhouse gas emissions, by using renewable energy sources and reducing annual energy consumption. To achieve this goal, one should use known ways of solar energy (passive and active) utilization, low-temperature geothermal energy, highly efficient heating, ventilation and air conditioning (HVAC) equipment and domestic hot water production equipment. However, the key is to achieve the optimal energy performance of the building by significantly limiting heat losses through its thermal envelope, mainly through its exterior walls.

Apart from the behavior of the users, the specific energy consumption in a building strongly depends on the thermophysical properties of its partitions (building envelope elements) [1,2]. The thermal envelope of the building, especially its exterior walls, is an important factor in shaping its annual heat balance and thermal comfort parameters. The basic quantities that characterize the thermal properties of walls are thermal resistance (*R*), total thermal resistance (*Rtot*) and the thermal transmittance (*U*). The accuracy with which these quantities are determined can significantly affect the accuracy of the actual and forecasted energy consumption of buildings [3,4]. In situ measurements of the

**Citation:** Nowak, H.; Nowak, Ł. Non-Destructive Possibilities of Thermal Performance Evaluation of the External Walls. *Materials* **2021**, *14*, 7438. https://doi.org/10.3390/ ma14237438

Academic Editor: Rui Miguel Novais

Received: 29 September 2021 Accepted: 30 November 2021 Published: 4 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

U-value have been performed since the early 1980s [5–7]. The measurements were found to be very useful for determining the actual thermal performance of the exterior walls in existing buildings, especially since the values determined on-site in buildings in the actual conditions would often significantly differ from the calculated ones. In the subsequent years, several experimental and computational studies aimed at determining the total thermal resistance of walls, using the approach for heat flow steady state, including reviews of the measurement methods [8,9], methodology [10–13], the use of in situ methods [2,14–17] and unsteady state conditions [18–21], were carried out.

There are many different theoretical and practical methods of determining the total thermal resistance of the exterior walls. On the one hand, the simplest way to determine the total thermal resistance of building enclosures consists of performing calculations consistent with ISO 6946 [22], where formulas can be found for the calculations depending on the structural system of the building enclosure. On the other hand, in practice, there often occur discrepancies between the tabular and actual thermal properties of the individual layers of a building partition. This applies mainly to the thermal conductivity coefficient of the particular layers and their density (and therefore their heat capacity) [12,23,24]. As a result, it often becomes necessary to carry out additional measurements, e.g., of the thickness of the individual layers or the density of the materials (destructive methods). Calculations in accordance with ISO 6946 are mainly performed when designing exterior building enclosures for new buildings. Whereas when it is necessary to determine the total thermal resistance through in situ measurements in existing buildings, the international ISO 9869-1 standard [25], recommending the use of the heat flow meter method (HFM), is applied. Although this standard has several advantages, two major problems which can be encountered when using it, i.e., the long duration of the measurements due to unstable boundary conditions and the questionable accuracy of the measurements, were indicated in [26,27]. Standard ISO 9869-1 recommends a minimum measurement duration of 72 h (a multiple of the full 24 h) and that the total thermal resistance values from the two last measurement days should not differ by more than 5%. Moreover, using this standard, one can analyze measurement data by the average method and the dynamic method (the latter yields more accurate measurement results). A new addition to the documents related to in-situ measurement of thermal resistance of building partitions is the ISO 9869-2 standard, which introduces the infrared camera method [28]. In issues related to heat transfer through building partitions and the determination of their thermal resistance, a very important issue is to take into account the variability of material moisture and its transfer [29,30]. However, this research problem was not within the scope of this article.

Another method of determining the total thermal resistance of a building enclosure, and thus determining the latter's U-value, is the generally known and well-established infrared thermography method (ITM). For many years, infrared thermographic surveys of buildings have been a precise and quick quality evaluation method [31–33], mainly used to locate defects in the thermal envelope of buildings [34–36] with presentations of basic and research issues and their applications [37,38]. Using this method, thermal bridges can be identified as caused by discontinuities or absence of thermal insulation [39–42], damp patches in building fabric elements [43–45] and places of air infiltration through the envelope [46–48]. Infrared thermography offers great possibilities to qualitatively assess the heat losses of different types of buildings and to analyze them to fully solve the problem of the energy performance of buildings [49]. This method is most often used as passive thermography, that is, as a method to investigate the building fabric as-is, without controlled outside interference and thermal stimulation of its thermodynamic state [35,38,50,51]. It can also be used as active thermography, i.e., with controlled outside temperature interference in the thermal state of the investigated building fabric [52–55] and inverse contrast in NDT materials' research [56,57]. Furthermore, through thermographic measurements, one can also determine the physical quantities characterizing the investigated building enclosure. Taking this into account, thermal imaging studies have been used to quantify external walls, including the U-value of walls [58,59], heat flux density [60–63] and to compare various

measurement and calculation methods [64,65]. As part of the present study, quantitative thermographic measurements were carried out in climatic test chambers using passive ITM to determine the total thermal resistance of the investigated building enclosure elements, and therefore their thermal transmittance.

For many years, building fabric elements also have been investigated in climate chambers, most often in quasi-stationary conditions. Such investigations deal with many problems related to building physics, energy performance of buildings, including all kinds of building fabric and thermal insulation [66–69], and the effect of ventilation on thermal comfort and indoor air quality (IAQ), particularly in office buildings [70]. The advantage of tests conducted in climate chambers over in situ tests in buildings is that they are independent of the weather conditions and therefore can be conducted practically all year round, whereby they are not limited to only the heating season and can be carried out for a set difference in air temperature between the two sides of a building enclosure. Practically, this means that tests conducted in climate chambers are more productive as regards the number of building fabric elements tested per year.

Taking into account the above, the main aim of the present research was to compare the effectiveness of the various methods of testing masonry walls by comparing the total thermal resistance values calculated and measured under quasi-stationary conditions in climate chambers for three types of masonry walls without thermal insulation and for the same walls insulated with expanded polystyrene. The same difference in air temperature between the walls' two sides was maintained for each of the tested walls. Three testing methods were used and evaluated with respect to the accuracy of the measurement results they produced. The methods were as follows: the temperature-based method (TBM), the heat flow meter method (HFM) and the infrared thermography method (ITM), which is also referred to in the literature as the infrared thermography technique (ITT). The purpose of the investigations was also to evaluate the effectiveness of the methods and to highlight the key factors that influence the accuracy and correctness of the measurement.

#### **2. Thermal Resistance Assessment for Building Enclosure Parts**

#### *2.1. Calculation Method*

In the design stage, an assessment of the thermal properties of a building enclosure is usually based on calculations of the unidirectional heat transmission process described in ISO 6946 [22]. Heat transmission through a building enclosure consists of the absorption of heat from the environment with a higher temperature (usually a heated room) by the building enclosure's surface, the flow of the heat through the building enclosure and the transfer of the heat from the building enclosure's other surface to the air with a lower temperature, and is defined by the partition's total thermal resistance—*Rtot* ((m2K)/W), determined from the relation:

$$R\_{tot} = R\_{si} + R + R\_{sc} \tag{1}$$

where:

*Rsi*, *Rse*—surface thermal resistances, on the internal and external side respectively, assumed or calculated according to Section 2.3.1 ((m2K)/W),

*R*—the design thermal resistances of the partition layers ((m2K)/W), determined from the relation:

$$R = \sum\_{i=1}^{n} \frac{d\_i}{\lambda\_i} \tag{2}$$

where:

*di*—the thickness of a given material layer (m),

*λi*—the thermal conductivity coefficient of the given material layer (W/(mK)).

The above method is commonly used in newly designed buildings to evaluate their energy performance and also to confirm that they meet the energy conservation requirements specified by the binding regulations. However, sometimes, there can arise the need to evaluate the thermal performance of building fabric through measurements, i.e.,


### *2.2. In Situ Measuring Methods*

The thermal properties of building fabric elements are usually measured when a quantitative or qualitative evaluation of their thermal performance is needed. Although thermographic surveys are mainly used for quality assessments of building enclosures, they can also be the basis for a quantitative evaluation of their thermal properties, even without simultaneously carrying out additional measurements of other quantities. Even though qualitative thermographic tests are sufficient for the purpose of assessing the condition of the thermal insulation in building enclosures, for many years in the literature on the subject, attempts have been made to quantitatively evaluate building enclosures through thermographic tests. The following three main methods for solving this problem can be distinguished:


#### 2.2.1. Method 1—The Temperature-Based Method (TBM)

The U-value of a building partition can be determined by measuring the appropriate temperatures and calculating its total thermal resistance, expressed by the relation:

$$R\_{tot} = \frac{R\_{si}(T\_i - T\_{t^\*})}{(T\_i - T\_{si})} \tag{3}$$

or the relation:

$$R\_{tot} = \frac{R\_{sc}(T\_i - T\_c)}{(T\_{sc} - T\_c)}\tag{4}$$

where:

*Rsi*, *Rse*—internal surface thermal resistance and external surface thermal resistance ((m2K)/W),

*Ti*, *Te*—air temperature on respectively the internal and external side of the tested building partition (K),

*Tsi*, *Tse*—the temperature of respectively the internal and external surface of the tested building partition (K).

Temperature sensors should be attached to a building enclosure in a way that ensures proper contact with the latter using, e.g., thermal paste or adhesive tape. Furthermore, they should be so located that air temperature measurements are not exposed to disturbing factors (far from heat sources, windows and air diffusers). Temperature measurements should be conducted for such a period of time that a time window of about 72 h with visible building enclosure surface and air temperature stabilization on both sides of the tested building enclosure could be selected from this period.
