# In Situ Measurements of Thermal Properties of Building Fabrics Using Thermography under Non-Steady State Heat Flow Conditions

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}, a difference of at least 15 °C between indoor and outdoor ambient air temperature should be obtained, and the outdoor temperature should have less than 6 °C temperature swing during the 12 h prior to the measurement. In similarity to steady-state heat flow, such requirements are not always possible to obtain on demand.

^{−1}, Ohlsson and Olofsson [25] assumed h

_{Conv}= 4·v + 5.6, Sham et al. [29] assumed h

_{Conv}= 3.9·v + 5.62, Albatici et al. [27] assumed h

_{Conv}= 3.8054·v and Fokaides and Kalogirou [28] assumed a constant value of h

_{Conv}= 7.7 W·m

^{−2}·K

^{−1}. Not knowing the exact value of the convection heat transfer coefficient for each experiment conditions may impose errors in the calculations.

## 2. Methods

_{Cond}), convection heat transfer (Q

_{Conv}), and radiation heat flow (Q

_{Rad}) under steady-state heat flow conditions. These expressions are described in Equations (1)–(3) regarding heat transfer through a wall with ε as the material’s emissivity and σ representing the Stefan–Boltzmann constant. h

_{Cond}and h

_{Conv}representing the conduction and convection heat transfer coefficients, respectively. T

_{Hot}and T

_{Cold}refer to different temperature measurements in each of the equations as follow: the interior and exterior wall surface temperature in Equation (1); the interior wall surface and indoor ambient air temperatures in Equation (2); and the interior wall surface and radiated temperature on the wall surface (also called the reflected temperature) in Equation (3). Equation (4) describes energy balance on a wall element during steady-state conditions.

_{Cond}) is a property of bulk material, while the convection heat transfer coefficient (h

_{Conv}) is a property of an interface between the wall and the ambient air. Both quantities define the thermal transmittance (U

_{Small}and U

_{Large}), which describes the insulation capability of a wall subjected to temperature difference between ambient air on both sides.

_{Cond}= h_

_{Cond}∙(T

_{Hot}− T

_{Cold}),

_{Conv}= h

_{conv}∙(T

_{Hot}− T

_{Cold}),

_{Rad}= ε∙σ∙(T

_{Hot}

^{4}− T

_{Cold}

^{4}),

_{Cond}= Q

_{Conv}+ Q

_{Rad},

#### 2.1. Test Object

^{2}floor area, as illustrated in Figure 1. The cabin was located about 5 m from a three-storey building to its north with no risk of shadowing from the east, south and west directions. The walls were constructed with massive glued laminated spruce timber which are kiln-dried and joined together with dowel mouldings, a technique developed by Glulam [31]. This study analyses the thermal properties of the north, east and west walls, as they were constructed with different thicknesses: 140 mm, 165 mm and 190 mm, respectively.

#### 2.2. Test Equipment

^{2}), a working temperature range between −30 °C to +70 °C, and an expected typical accuracy of ±5%. The HFMs were connected to data loggers of type LI-19 from Leiderdorp Instruments. Three types of humidity and temperature loggers were used: (i) RHTemp1000 MadgeTech for outdoor ambient air measurements with working temperature between −40 °C and 80 °C, temperature resolution of 0.1 °C and temperature calibrated accuracy of ±0.5 °C; (ii) MicroRHTemp MadgeTech for indoor ambient air measurements with working temperature between 0 °C and 60 °C, temperature resolution of 0.1 °C and temperature calibrated accuracy of ±0.5 °C; and (iii) ELOG9004 for wall surface measurements with temperature resolution of 0.5 °C and temperature calibrated accuracy of ±0.5 °C.

#### 2.3. Experiment Settings

_{Small_wall}), the surface temperature of a large wall segment of 1 m × 0.6 m (T

_{Large_wall}), and the reflected temperature (T

_{Reflected}). T

_{Reflected}was measured with a crinkled aluminium foil near the measurement area, as described in [33]. The thermal images were analysed by the FLIR-Tools software from FLIR System Inc.

_{Outdoor}) and five MicroRHTemp registered the indoor temperatures (T

_{Indoor}). The measurement locations of the reflected temperature, HFM sensors and temperature sensors were near the location of the thermal images at the same height as the small wall segment, as illustrated in Figure 2, and did not affect the thermography measurements.

#### 2.4. Measurements

_{Conv}) was determined separately for each wall using both thermography and HFMs during the corresponding measurement period, as listed in Table 1. The convection heat transfer coefficient (h

_{Conv}) was determined by a linear regression of the convection heat flow (Q

_{Conv}) against the difference between the indoor temperature and the interior surface temperature of the small wall segment area Δ (T

_{Indoor}− T

_{Small_wall}). The convection heat flow (Q

_{Conv}) was calculated according to Equation (5). The conduction heat flow through the wall (Q

_{Cond}) was measured simultaneously by three HFMs. The interior surface temperature on the small wall segment (T

_{Small_wall}) was measured by thermography. The emissivity (ε) of the wood was 0.91; it was measured using the thermography of similar wood material covered partly by black tape with known emissivity (0.95) as describe in [34].

_{Conv}= Q

_{Cond}− ε∙σ∙(T

_{Reflection}

^{4}− T

_{Small_wall}

^{4}),

_{Conv}), as described above, the thermal transmittance of the small wall segment (U

_{Small}) could be determined by a linear regression of the conduction heat flow through the small wall segment (Q

_{Cond,Small_wall}) against the difference between the indoor and outdoor temperatures Δ(T

_{Indoor}− T

_{Outdoor}). Q

_{Cond,Small_wall}was calculated according to Equation (6) using the IR camera and indoor temperature sensors. Equations (5) and (6) are used to compare consistency between the results of the HFM and thermography on the small wall segment, separately for each wall. The thermography and the HFMs were both applied on a similar size of wall area and with similar uniformity of wall surface temperature.

_{Cond,Small_wall}= h

_{conv}∙(T

_{Indoor}− T

_{Small_wall}) + ϵ∙σ∙(T

_{Reflected}

^{4}− T

_{Small_wall}

^{4}),

_{Large}) was determined by a linear regression of the conduction heat flow through the large wall segment (Q

_{Cond,Large_wall}) against the difference between the indoor and outdoor temperatures Δ(T

_{Indoor}− T

_{Outdoorl}). Q

_{Cond,Large_wall}was calculated according to Equation (7) using the IR camera and indoor temperature sensors. The results were compared to the thermal transmittance measured for the small wall segment to evaluate the thermal effects of thermal inhomogeneities in the walls.

_{Cond,Large wall}= h

_{conv}∙(T

_{Indoor}− T

_{Large_wall}) + ϵ∙σ∙(T

_{Reflected}

^{4}− T

_{Large_wall}

^{4}),

_{Cond,Small_wall}) (Equation (6)) against the difference between the interior and exterior wall surface temperatures. The conductivity (λ) was calculated by Equation (8) with L as the wall thickness. The conductivity of the different walls was compared as they are all made by the same wood material, and thus expected to have similar values.

#### 2.5. Near Steady-State Conditions

#### 2.6. Number of Measurements

_{Large}) of the north wall was determined with a different number of thermal images ranging from 1 to 80 and with different combinations out of a total of 115 thermal images. The dispersion of the results and the uncertainty in relation to the expectation value of thermal transmittance were calculated for each set of thermal images.

## 3. Results

#### 3.1. Thermal Images

#### 3.2. Convection Heat-Transfer Coefficient

_{Conv}) of the three walls were determined through regression analysis, as illustrated in Figure 4, with forced intercept (X, Y) = (0, 0). The values obtained for the north and east walls differed by less than 1%. The convection heat-transfer coefficient of the west wall was 11% higher in comparison to the values of the north and east walls. The reason was the effect of direct solar radiation on the temperature of the interior and exterior surfaces of the west wall during the third measurement period (Table 1). Hereafter the value of the convection heat-transfer coefficient of the west wall was assumed to be the average of the convection heat-transfer coefficients of the north and east walls since all three walls were subjected to similar indoor and outdoor conditions.

#### 3.3. Thermal Transmittance: Small Wall Segment

#### 3.4. Thermal Transmittance: Large Wall Segment

_{Large}) for all three walls using thermography. The thermal transmittance of the north and west walls were 3% and 5% higher in comparison with the respective thermal transmittance of the small wall segment. The reason is most likely to be thermal inhomogeneities like wood knots and contact areas between the wood beams, as illustrated in Figure 3. The thermal transmittance of the east wall was 20% higher in comparison with the thermal transmittance of the small wall segment. Thermal inhomogeneities may have a similar effect here as well, but the larger part of the difference is most likely a measurement error in the value of the reflection temperature, which was not uniform over the east wall as is seen in Figure 3, and thus was difficult to evaluate.

#### 3.5. Thermal Conductance and Conductivity

^{−1}·K

^{−1}, 0105 W·m

^{−1}·K

^{−1}and 0.108 W·m

^{−1}·K

^{−1}, respectively, as illustrated in Figure 8.

#### 3.6. Number of Measurements

## 4. Discussion

^{−2}·K

^{−1}for the north wall and 2.46 W·m

^{−2}·K

^{−1}for the east wall with ±3% and ±6% uncertainty, respectively. Due to the effect of solar radiation, the value of the convection heat transfer coefficient of the west wall was 12% to 14% higher. The reason was the effect of direct solar radiation on the temperature of the interior surface of the west wall during the third measurement period. These values seem to be in the lower range of values in comparison to values assumed in similar studies [25,27,28,29]. However, values of convection heat transfer coefficients depend strongly on the experiment’s specific conditions and settings. These can vary considerably among studies [30], e.g., wind velocity, surface texture, tilt of surfaces, temperature, and near objects. Therefore, comparisons to literature values should be made with caution.

^{−1}·K

^{−1}) [35]. The conductivities of the large wall segments could not be determined since the temperature of the exterior surface of the large wall segment were not measured. But the values are expected to be higher by 3% to 5% in comparison to the conductivity of the small wall segment due to the inhomogeneities, as was shown in Section 3.1. Thus, the conductivity values of the large wall segment are expected to be 0.106 W·m

^{−2}·K

^{−1}, 0.108 W·m

^{−2}·K

^{−1}and 0.113 W·m

^{−2}·K

^{−1}for the west, north and east walls with 6%, 2% and 3% deviation from the literature value [35], respectively.

## 5. Conclusions

^{2}up to 400 W/m

^{2}, see Appendix A.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Q_{Cond} | Conduction heat flow, W·m^{−2} |

Q_{Conv} | Convection heat flow, W·m^{−2} |

Q_{Rad} | Radiation heat flow, W·m^{−2} |

Q_{Cond,Small_wall} | Conduction heat flow through a small wall segment, W·m^{−2} |

Q_{Cond,Large_wall} | Conduction heat flow through a large wall segment, W·m^{−2} |

h_{Cond} | Conduction heat transfer coefficient, W·m^{−2}·K^{−1} |

h_{Conv} | Convection heat transfer coefficient, W·m^{−2}·K^{−1} |

T_{Outdoor} | Ambient outdoor temperature, K |

T_{Indoor} | Ambient indoor temperatures, K |

T_{Small_wall} | Surface temperature of a small wall segment, K |

T_{Large_wall} | Surface temperature of a large wall segment, K |

T_{Reflected} | Reflected temperature, K |

T_{Ext} | Surface temperature on the exterior side of the wall |

ɛ | Emissivity |

σ | Stefan–Boltzmann constant |

U_{Small} | Thermal transmittance of the small wall segment, W·m^{−2}·K^{−1} |

U_{Large} | Thermal transmittance of the large wall segment, W·m^{−2}·K^{−1} |

C | Thermal conductance, W·m^{−2}·K^{−1} |

λ | Conductivity, W·m^{−1}·K^{−1} |

## Appendix A. Indoor and Outdoor Temperatures

^{2}) and short daytime (6 to 8 h per day). The effect of the solar irradiation is minor, and therefore no cyclic variations in outdoor temperature were observed between day and night during this period.

^{2}and daytime of about 12 h.

**Figure A1.**The indoor and outdoor ambient air temperatures with 15 min sampling interval between measurements.

**Figure A2.**The difference between the indoor and outdoor ambient air temperature with 15 min sampling interval between measurements.

## Appendix B. Reflected and Indoor Temperatures

**Figure A3.**The indoor temperature and the reflected temperature measured on the three walls during the three measurement periods with 15 min sampling interval between measurements.

## Appendix C. Number of Measurements

^{−2}·K

^{−1}), which contributes to the large spreading of observations in that plot, and also the skewed distribution in Figure 9. That stresses the importance of using several thermal images to obtain accurate results. The effect of this single high measurement value can be observed also in the plots with two and three thermal images; however, after including 10 thermal images its effect diminished and the uncertainty reduced to 11%. Including 27 thermal images was found to reduce the uncertainty to 5%, and 63 thermal images to 3% uncertainty.

**Figure A4.**The distribution of the values of the thermal transmittance obtained by regression analysis as described in Section 2.4 in the main article. Each plot represents a different number of thermal images included in the regression analysis.

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**Figure 1.**Schematic drawing of the wooden cabin. The test objects are the west-, north- and east-facing external walls.

**Figure 2.**Experiment settings on a massive wood wall element including the locations of the sensors and the thermal camera. Each thermal image includes measurements of the reflection temperature (small black square) and the surface temperature of the large wall segment (large red square) and the small wall segment (small red square).

**Figure 3.**Representative example of thermal images of the three walls taken 1st of February. The indoor and outdoor temperatures at the time were 21.2 °C and −7.5 °C, respectively. The temperature scale in each image ranges from 15 °C to 19 °C. The darker areas represent colder surface temperatures.

**Figure 4.**The convection heat transfer coefficient of the west wall (left figure), north wall (middle figure) and east wall (right figure) with confidence interval of 95% certainty (red lines). The Y-axis represents the convection heat transfer (Q

_{Conv}) calculated by Equation (5). The X-axis represent the temperature difference between the indoor temperature and the interior wall surface ΔT = (T

_{Indoor}− T

_{Small_wall}). The dashed lines represent 95% certainty for measurements to disperse around the mean (black trend-line).

**Figure 5.**The thermal transmittance of the small wall segment for the north wall determined using heat flux sensors (HFMs) (left figure), thermography (centre figure) and HFMs during near steady-state conditions (right figure) with confidence interval of 95% certainty (red lines). The Y-axis represents the conduction heat flux Q

_{Cond}measured by HFMs (right and left figures) or Q

_{Cond,Small}wall calculated by Equation (6) for thermography (centre figure). The X-axis represents the difference between the indoor and outdoor ambient air temperatures, ΔT = (T

_{Indoor}– T

_{Outdoor}). The dashed lines represent 95% certainty for measurements to disperse around the mean (black trend-line).

**Figure 6.**The thermal transmittance of the large wall segment calculated using thermography for the west wall (left figure), north wall (centre figure) and east wall (right figure) with confidence interval of 95% certainty (red lines). The Y-axis represents the conduction heat transfer (Q

_{Cond,Large_wall}) calculated by Equation (7). The X-axis represents the difference between the indoor and outdoor ambient air temperatures, ΔT = (T

_{Indoor}– T

_{Outdoor}). The dashed lines represent 95% certainty for measurements to disperse around the mean (black trend-line).

**Figure 7.**The thermal conductance of the west wall (left figure), north wall (centre figure), and east wall (right figure) with confidence interval of 95% certainty (red lines). The Y-axis represents the conduction heat transfer (Q

_{Cond,Small_wall}) calculated by Equation (6). The X-axis represents the difference between the interior and exterior wall surface temperatures. The dashed lines represent 95% certainty for measurements to disperse around the mean (black trend-line).

**Figure 8.**Summary of the main results: the thermal transmittance and the conductivity of the west, north and east walls. Uncertainties of the measurements are represented by the error bars.

**Figure 9.**The span of values of thermal transmittance (upper figure) and the uncertainty in values of thermal transmittance (lower figure) vs. the number of measurements (thermal images).

**Table 1.**Measurement periods of the small and large wall segments, as illustrated in Figure 2.

Measured Wall | Convection Heat Transfer Coefficient (h_{Conv}) Measured on a Small Wall Segment Using Thermography and Heat Flux Sensors (HFMs) | Thermal Properties (U_{Large} and C) Measured on a Large Wall Segment, Using Thermography |
---|---|---|

North | Period I: 24 January–15 February | 24 January–22 March |

East | Period II: 17 February–8 March | 24 January–22 March |

West | Period III: 9 March–22 March * | 24 January–22 March ^{1} |

North wall: near steady-state | Period IV: 5 May–11 June | ------ |

^{1}Thermal images taken between 9 and 22 March for the large wall segment were not considered as many of them were found to be affected by direct solar radiation, see Section 3.2. Only a small part of the values of the HFM measurements were affected by direct solar radiation.

**Table 2.**Temperature statistics obtained from the thermal images in Figure 3.

West Wall | North Wall | East Wall | ||||
---|---|---|---|---|---|---|

Small Segment | Large Segment | Small Segment | Large Segment | Small Segment | Large Segment | |

Min. | 17.9 °C | 16.2 °C | 17.2 °C | 15.0 °C | 17.7 °C | 15.7 °C |

Max. | 18.4 °C | 18.8 °C | 17.5 °C | 17.8 °C | 18.1 °C | 18.2 °C |

Average | 18.2 °C | 18.1 °C | 17.4 °C | 17.3 °C | 17.9 °C | 17.5 °C |

Standard deviation | 0.055 | 0.29 | 0.052 | 0.225 | 0.054 | 0.298 |

Uniformity ^{1} | 99.7% | 98.4% | 99.7% | 98.7% | 99.7% | 98.3% |

^{1}The uniformity values are based on temperatures in Celsius and are suited for relative comparisons only. Uniformity = 1 − Standard deviation/Average.

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## Share and Cite

**MDPI and ACS Style**

Danielski, I.; Fröling, M.
In Situ Measurements of Thermal Properties of Building Fabrics Using Thermography under Non-Steady State Heat Flow Conditions. *Infrastructures* **2018**, *3*, 20.
https://doi.org/10.3390/infrastructures3030020

**AMA Style**

Danielski I, Fröling M.
In Situ Measurements of Thermal Properties of Building Fabrics Using Thermography under Non-Steady State Heat Flow Conditions. *Infrastructures*. 2018; 3(3):20.
https://doi.org/10.3390/infrastructures3030020

**Chicago/Turabian Style**

Danielski, Itai, and Morgan Fröling.
2018. "In Situ Measurements of Thermal Properties of Building Fabrics Using Thermography under Non-Steady State Heat Flow Conditions" *Infrastructures* 3, no. 3: 20.
https://doi.org/10.3390/infrastructures3030020