Inferring the thermal resistance and effective thermal mass of a wall using frequent temperature and heat flux measurements

Outline

• Highlights
• Abstract
• Keywords
• Nomenclature
• 1. Introduction
• 2. Case Study and Monitoring Campaign
• 3. Theory and Calculation
• 3.1. Conventional Methods
• 3.1.1. Calculating the Thermal Properties Using Assumed Material Properties
• 3.1.2. Direct Computation: The Average Method
• 3.2. Building Simulation Model
• 3.2.1. Thermal Models of the Wall
• 3.2.2. Estimation of the Thermal Parameters Using Bayesian Analysis
• 4. Results and Discussion
• 4.1. R-Value (and U-Value) Estimation and Evolution
• 4.2. Evolution of U-Values and Systematic Errors
• 4.3. Comparison of U-Values Estimates
• 4.4. Dynamic Performance of Models
• 4.5. Wall Structure and Thermal Mass
• 5. Conclusions
• Acknowledgements
• References

Conclusions

A new technique for significantly reducing the monitoring period required to estimate the thermal properties of building elements using in-situ measurements has been presented and compared to the conventional steady-state in-situ method and values calculated using assumed material properties for a case study wall. Simple physical models of the building element, based on electrical analogy, are combined with Bayesian analysis. The technique may be used to estimate thermal properties, including error estimates, and to compare the probability that different models may have produced the observed data. Two simple models of the wall have been compared: a single thermal resistance, no thermal mass model (NTM) and a two thermal resistance, single thermal mass model (STM). Further models of the wall could be tested, but the STM model is the most complex that can be used to find unique solutions for the parameters without the addition of extra monitoring equipment.

The conventional averaging method of estimating U-values from 14 days of in-situ measurements of heat flux, internal and external temperatures gives 1.16 ± 0.06 W m⁻² K⁻¹, the same as the equivalent NTM model and Bayesian estimation of the U-value: 1.16 ± 0.06^sys+stat W m⁻² K⁻¹. The U-value estimated from the STM model (1.15 ± 0.06^sys+stat W m⁻² K⁻¹) is very similar to that from the NTM model; values incorporate estimates of systematic errors. As expected, the averaging method, the NTM and STM models give similar results for all 93 walls measured during the BSRIA trials [21].

The STM model accounts for the impact of thermal mass on estimated U-values after three days, compared to 10 days for the NTM model: a significant reduction to the time required to thermally characterise the wall. However, estimated U-values continued to evolve after the values were first stable to within ±1% over 24 h. The impact of changing heat transfer due to environmental factors, such as changes to the wind or moisture, were investigated by calculating rolling 4 day U-values with the STM model. Uncertainty due to varying environmental conditions was estimated from the standard deviation of these rolling U-values and is the largest contribution to total error; extended monitoring periods may be used to characterise the performance of building elements accounting for changes in environmental factors. The relatively short timescale required to estimate U- and R-values using this technique makes it well suited to investigating their potentially significant dependence on environmental factors such as wind speed [32].

The STM model was able to reproduce the time evolving heat flux entering the wall from the room more accurately than the NTM model. The probability that the NTM and STM models accurately describe this dynamic data was estimated through the Bayesian Occam’s factor, providing very strong evidence supporting the inclusion of thermal mass in the STM model. The effective thermal mass per unit area of the wall was estimated to be 224,000 ± 19,000^sys-stat J m⁻² K⁻¹, compared to that calculated from published values of approximately 412,000 J m⁻² K⁻¹. The estimated effective thermal mass of the wall is just 40 mm from the interior wall surface in this 300 mm thick wall and represents the apparent thermal mass of the wall from the perspective of the interior space.

The method presented here, combining physical models and Bayesian analysis can be used to significantly reduce the monitoring period required to estimate U- and R-values, compared to conventional steady-state methods. The method utilises dynamic changes in temperature, rather than requiring a consistently high temperature difference (as for steady state methods). This feature may be used to analyse in-situ measurements taken in summer, albeit with higher uncertainty in results due to a greater influence of potential systematic errors.

Accurate knowledge of the thermal properties of building elements is essential to inform the decision making processes at all levels, when estimating the energy savings and cost effectiveness of retrofit measures, such as installing insulation. However, a performance gap has been identified in the cost-effectiveness and energy savings of interventions, based on their expected U-values [34] and is illustrated by the walls analysed here which exhibited significantly lower than expected U-values (expected range from 1.6 to 2.4 W m⁻² K⁻¹, vs measured 1.15 ± 0.06^sys+stat W m⁻² K⁻¹ for the STM model). The U- and R-value estimation technique presented may be used to significantly shorten the monitoring period required per building element, enabling more cases to be cost-effectively measured and promoting better informed decision making. The short timescale of this technique is also well suited to investigating the impact of weather on U-values and the estimation of effective thermal mass may inform thermal comfort considerations.