Building thermal bridge heat losses quantification by infrared thermography. Steady-state evaluation and uncertainty calculation

This study deals with the measurement of thermal bridges properties in building walls. The methodology is tested on an experimental wall built in laboratory. The setup thermal bridges transmission coefficients ψ and χ are measured in steady-state by infrared thermography. To do so, the thermal bridges impact factor Itb is calculated. In the proposed method, the value of the surface emissivity is not required: only apparent temperatures are used. Experiments proved good reproducibility. Calculations of the uncertainties enabled to identify infrared measurements as the main sources of error.


Introduction
A building's thermal insulation cannot be homogeneous. Elements such as windows, floor/wall junctions, or mechanical systems used to hold insulating materials generate local additional heat losses. These elements are called "Thermal bridges" and may be responsible for 30% of the building energy demand [1]. This study focuses on thermal bridges originating from insulation material fixing on walls: they are called "Integrated Thermal bridges". The present work was made in the context of a PhD thesis on the measurement of thermal-bridge-induced heat losses using active infrared thermography (that is to say by artificially heating the wall). Results presented here are from a preliminary study focused on the steady-state characterization of several thermal bridges included inside an experimental setup. Measured values will be used as reference for validation of the transient methodology currently under development. The originality of the present paper mainly lays in the calculation of the impact factor I tb (ratio of the heat flux on the thermal bridge over the heat flux on a sound area) only based on infrared thermography measurements. The wall emissivity is not required, which reduces the measurement uncertainties.

Experimental setup 2.1. Presentation
In order to test the thermal bridge characterization methodology, a full scale experimental wall was built in laboratory. As shown in Fig 1a,  inserted to create thermal bridges. These materials are commonly used in internal insulation systems: a metal rail, a wood stud and two metal pins. Several thermocouples and heat flux meters are positioned inside the setup. In addition, a flat heating resistance is placed on the rear side. It is used to generate a temperature gradient that allows thermal bridges visualization. Finally, the assembly is inserted inside a polystyrene frame: only the front face is visible and observed with an infrared camera. The latter is from FLIR (reference SC7000). It has a 320×256 pixels matrix cooled sensor, sensitive to the 7.7-9.2 µm band and of sensitivity 20 mK. Figure 1b shows the front face of the setup, in the infrared spectrum. The presented thermal image is a time-average over several hours of steady-state (reached after feeding the heating resistance with 25W for at least 24h). Thermal bridges are visible. From the recorded thermogram, the apparent temperature profiles T app in the vicinity of the thermal bridges are extracted, as shown in

Wall U -value calculation
The wall U -value is given by: with R si = 0.13 m 2 .K.W −1 and R se = 0.04 m 2 .K.W −1 the internal and external superficial resistances (values from [2]) and R wall the wall thermal resistance. In steady-state: with ϕ stat the surface heat flux and ∆T stat the temperature difference between the two sides.

Thermal bridges transmission coefficients calculation
Transmission coefficients ψ and χ respectively refer to linear and punctual thermal bridges [3].
In steady-state, the ψ coefficient is given by: with φ tb the additional heat flux due to the thermal bridge (as illustrated in Fig 3), ∆T ie the internal/external temperature difference and L z the thermal bridge length. U tb is the mean surface transmission coefficient including the thermal bridge while U 1D is its equivalent without thermal bridge. L tb is the width of the thermal bridge impact zone (heat transfers are supposed 1D outside this zone). Asdrubali et al introduced the impact factor [4] : Therefore, linear and punctual transmission coefficients may be expressed a functions of three parameters: With S tb (m 2 ) the impact zone of the punctual thermal bridge. The following assumption is then made: This equation is true if the air temperature is equal to the mean radiant temperature (which is realistic indoor) and if the radiative and convective heat exchange coefficients are uniform on the portion of the wall studied (also realistic given the small surface temperature difference between thermal bridges and sound areas). The surface emissivity must be uniform as well. Hypothesis of Eq 8 is of interest because radiative heat flux measurements with an infrared camera are straightforward and more accurate than total heat flux measurements. Indeed, the radiative heat flux is easily derived from apparent temperatures and does not depend on the surface emissivity : With σ sb the Stefan-Boltzmann constant. Apparent temperatures are those directly measured by the infrared camera (unit emissivity). It is the temperature of a black body that would have an emitted radiative heat flux equal to the heat flux received by the camera. T app env is the so called the "Mean Radiant Temperature". The environment is supposed black with a view factor equal to 1. Hence the impact factor : with P the considered number of pixels. The heat flux ratio is calculated on each pixel of an apparent temperature profile, such as those given in Fig 2.

Uncertainty Calculation
To demonstrate the advantage of the proposed method that uses apparent temperatures, the measurement uncertainties are calculated and compared with those obtained if real temperature are used (standard method). The example of the metal rail is considered here.

Uncertainty of the proposed method (calculations from apparent temperatures)
Measurement uncertainties on ψ (similarly χ) were propagated according to [5]: with u the uncertainty and β 1 , β i , ...β n the quantities from which ψ is derived. ψ is calculated from three quantities: L tb , U 1D , and I tb (see Eq 6). Each one is itself a function of several parameters that are detailed in Tab 1. Nominal values and uncertainties are also given. The measured thermal bridge width L tb is given by: with N p the number of pixels in the thermal image. A ruler of known length L ref is introduced in the view field of the camera and N ref is its corresponding number of pixels on the image.

Uncertainties of the "standard method" (Calculations from T )
Here, the calculation of I tb is made by replacing apparent temperatures in Eq 10 by real temperatures. Basically, the measurement of the real temperature T with an infrared camera is given by: with the object emissivity, T app its apparent temperature and T env the mean radiant temperature. The later is similarly evaluated by disposing an infrared mirror (aluminum sheet) of known reflexivity on the wall. Its temperature is measured with a thermocouple. From Eq 13, the measurement uncertainty on I tb for the "standard method" is evaluated. Similarly to paragraph 4.1, the uncertainty on ψ and χ coefficients is then derived.

Results
Several experiments were made on the setup to test the presented methodology. They were made in two different rooms, two setup orientations and several different heating powers. This allowed to evaluate the method reproducibility. The estimation results are gathered in   more accurate because it has a higher surface temperature contrast. Also, the spread between measurement is smaller than the calculated uncertainties u. The measurement uncertainties in the "standard method" are significantly higher, which shows the interest of the proposed approach. In addition, parameters relative contribution to the measurement uncertainty on ψ are given in Fig 5. It may be observed that most of the measurement uncertainty on ψ comes from the calculation of the impact factor I tb that is to say from the measurement of the apparent temperatures T app tb and T app 1D . Figure 5: Relative uncertainty of each parameter in ψ coefficient calculation. For a quantity Y function of parameters β i , each parameter relative contribution to Y uncertainty is: ∂Y ∂β i u(β i )

Conclusion
Infrared thermography may be used for the quantification of heat losses due to integrated thermal bridges. In steady-state, thermal images allow to work out an impact factor I tb which is a heat flux ratio. The proposed methodology requires no knowledge of the surface emissivity: the I tb factor is directly calculated from apparent temperatures. This more than halves the measurement uncertainties when compared to the standard method. Linear and punctual transmission coefficients ψ and χ are then derived. Measurements performed on a lab-scale experimental wall proved the method reproducibility and accuracy. The measurement spread is between 5 and 15% depending on the thermal bridge. These values might seem high, but are due to the very small magnitude of ψ and χ coefficients for some of the studied thermal bridges: ψ = 0.0045 W.m −1 .K −1 and χ = 0.0011 W.K −1 for the smallest ones. Finally, infrared measurements were identified as the highest source of uncertainty. The present study is not intended to be applied in-situ. The calculated thermal bridge coefficients will be used as reference values for heat losses estimations using transient methods that are currently being developed.