Elsevier

Energy and Buildings

Volume 43, Issues 2–3, February–March 2011, Pages 379-385
Energy and Buildings

Determining the thermal capacitance, conductivity and the convective heat transfer coefficient of a brick wall by annually monitored temperatures and total heat fluxes

https://doi.org/10.1016/j.enbuild.2010.09.030Get rights and content

Abstract

The finite volume scheme and complex Fourier analysis methods are proposed to determine the thermal capacitance (defined as the product of density and specific capacity) and thermal conductivity for a building construction layer using the monitored inner/outer surface temperatures and heat fluxes. The overall heat transfer coefficient for the air gap, and the convective heat transfer coefficient for air gap surfaces and room surfaces are determined by the linear relationship between the surface convective heat flux and the temperature difference. Convective heat flux is obtained by removing the thermal radiation flux from the total surface heat flux. Finally, the predicted surface heat fluxes using the calculated thermal properties and ASHRAE values were compared with the measurements.

Introduction

For any energy simulation (ES) software the basic input parameters required for a material are the thermal conductivity or heat resistance and the thermal capacitance, which is defined as the product of density and heat capacity. Measuring the thermal conductivity of a material as a walling system requires use of laboratory controlled and natural climatic conditions to create differing climates for both wall surfaces. ASTM C518-04 [1] requires steady state conditions across the test specimen allowing the thermal conductivity to be calculated by the measured steady state heat flux and surface temperatures. Compared to the original guarded hot box method ASTM C1363-05 [2] which determines the steady heat flux by the heat input from fan and coil elements, ASTM C518-04 directly measures the steady state heat flux by a heat flux transducer. Steady state conditions across the tested walling system can only be established in laboratory controlled conditions through heating or cooling. However as initial conditions for the tested building walls differ from the target steady state conditions, it will take some time to establish the desired steady state conditions across the testing walls. Gustafsson [3] and Bouguerra et al. [4] measured thermal conductivity and diffusivity by correlating the electric resistance of the transient plane source heating element with the thermal properties of the tested specimen. Although it is only necessary to record the transient temperature variation history for the transient plane source (TPS) method, it is still classified as a laboratory controlled climate as the TPS element requires heating. Ghazi et al. [5] used a heat flow meter apparatus (HFM) to measure three temperatures at lower, middle and upper heights of two specimens and determined the specific heat capacity of the specimen by comparing the thermal simulation using three different values of Cp with the measured response (the temperature at the middle of the two species). Steady state conditions across the tested specimen are required for ASTM C518-04, ASTM C1363-05 and the HFM but not for the transient plane source method.

One of the disadvantages of measuring the thermal properties under a laboratory-controlled climate is that the tested specimen would then be placed within a natural actual climate which differs from the testing conditions. Thermal properties such as and especially the thermal conductivity are dependent on climatic effects including humidity and solar radiation. Accordingly, some researchers began seeking a derivation for the thermal properties based upon in-situ measurements such as surface temperatures and heat fluxes. Carpentier et al. [6] calculated the thermal diffusivity of the soil based on the monitored temperatures at the ground surface and at a location below the surface. Further, they obtained the thermal conductivity of the soil by the relationship between the amplitudes of the surface temperature and heat flux. Peng and Wu [7] introduced three methods to evaluate the total thermal resistance of a building wall based on the internal and external average air temperatures, internal and external surface average temperatures, inner surface average heat flux and average solar radiant illumination. Cucumo et al. [8] evaluated the wall conductance in terms of the internal wall surface heat flux and the internal and external surface temperatures using the finite difference calculation code. They calculated the inner wall surface heat flux under different equivalent wall thermal conductivities and equivalent thermal capacities using the internal and external surface temperatures as inputs, compared their predictions with measurements and selected the equivalent wall thermal conductivity and equivalent thermal capacity based on the best match between the predictions and measurements.

Emmel et al. [9], Hagishima and Tanimoto [10], Jayamaha et al. [11], Liu and Harris [12], Shao et al. [13] measured the convective heat transfer coefficient (CHTC) of the outer building wall surface under different environmental conditions. The CHTC on the outside wall surface depends on the building geometry, wind speed and wind direction. The CHTC of the inner wall surface does not directly depend on the weather conditions, but on the air movement induced by the internal temperature distribution, which could source from forced air circulation using an electric fan, construction wall infiltration or ventilation. Irving et al. [14] and Delaforce et al. [15] obtained the CHTC through the correlation between the surface heat flux and the temperature difference between the wall surface and the indoor air temperature (in the boundary layer of wall surface) measured by the Meyer ladder.

This study is not aimed at improving the measuring techniques as mentioned above, but focused on calculating the thermal capacitance, thermal conductivity and convective heat transfer coefficients during monitoring of the thermal performance of buildings. Accordingly, the thermal properties (thermal capacitance and thermal conductivity) for homogeneous building materials are determined by in-situ (not laboratory-controlled conditions) measurements using the finite volume and complex Fourier analysis methods for the wall construction. The CHTC is obtained by linear fitting for building wall surfaces surround and air gaps. The effect of the thermal radiation on the CHTC for the indoor wall surfaces is also investigated and the predicted room air temperatures using the fitted thermal properties and the ASHRAE table values will be compared with the measurements.

Section snippets

Instrumentation of modules

The experimental data was obtained from fully instrumented 6 m × 6 m test modules located on the University of Newcastle campus which were constructed to measure and compare the thermal performance of various walling systems under natural conditions. The instrumentation recorded the external weather conditions; wind speed and direction, air temperature, relative humidity and, the incident solar radiation on each wall (vertical-plane) and the horizontal plane. For each module, temperature and heat

Calculating thermal capacitance and thermal conductivity by the finite volume method

For any construction material layer, the heat flux and temperature at both layer surfaces can be correlated by the following two equations as illustrated by Luo et al. [16]:1162kLt2ρCp57Te+24Ti9Ltkqe+6Ltkqin57Te+24Ti9Ltkqe+6Ltkqin1=Δt2Te+Ti+Ltkqen+Te+Ti+Ltkqen1,1162kLt2ρCp24Te+57Ti6Ltkqe+9Ltkqin24Te+57Ti6Ltkqe+9Ltkqin1=Δt2TeTiLtkqin+TeTiLtkqin1,in which k is the thermal conductivity of the construction layer, ρ, Cp are the density and specific heat capacity of the

Thermal capacitance and thermal conductivity from the finite volume scheme and complex Fourier analysis

For the finite volume method (FVM), the thermal capacitance and thermal conductivity are calculated by a Microsoft Excel spreadsheet using Eqs. (1), (3). The input variables are the monitored temperatures and heat fluxes on the outer and inner surfaces of a homogeneous construction layer (110 mm brick layer in this study). The resulting output variables are the thermal capacitance and the thermal conductivity. The time interval is 10 min and thickness of the brick layer is 110 mm. Shown in Fig. 3

Conclusions

Using the annually monitored thermal performance data sourced from the experimental measurements taken at the campus of the University of Newcastle, Australia, the in-situ time varying thermal capacitance and thermal conductivity are determined by the finite volume method, with the constant thermal properties calculated by the complex Fourier analysis method. The difference in thermal properties for the northern and eastern outer brick layers is smaller for the complex Fourier analysis method

Acknowledgements

This work has been supported by Think Brick Australia (formally the Clay Brick and Paver Institute) and the Australian Research Council. The support of both organisations is gratefully acknowledged.

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