Ground heat transfer: A numerical simulation of a full-scale experiment

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Building and Environment 42 (2007) 1478–1488 www.elsevier.com/locate/buildenv

Ground heat transfer: A numerical simulation of a full-scale experiment S.W. Rees, Z. Zhou, H.R. Thomas Cardiff School of Engineering, Cardiff University, UK Received 24 October 2005; accepted 6 December 2005

Abstract A numerical simulation of ground-heat transfer adjacent to an experimental earth–contact structure is presented. In particular, a twodimensional time-dependent simulation is compared directly to data measured from an experimental site over a one year period. Determination of representative thermal properties for the materials involved is explored in some detail. Indirect methods of estimating thermal conductivity and volumetric heat capacity have been described and employed. The results show good correlation between the simulated and measured thermal response. The work is viewed as a useful contribution to the overall drive to validate earth–contact simulation. However, difficulties in determining realistic initial conditions when attempting to model field conditions still remain a challenge. Further exploration of material property variations throughout the full range of climatic conditions is also needed. r 2006 Elsevier Ltd. All rights reserved. Keywords: Heat transfer; Ground; Energy efficiency; Buildings; Simulation; Field measurement

1. Introduction A considerable amount of progress has been made with regard to the design of energy efficient buildings. The problem is clearly multi-faceted and this fact is borne out by the diverse range of research that has been published in relation to this area [1]. However, within the last few years steady progress has continued to be made. A brief overview of some of these wide-ranging activities that relate to this area of research is presented below. In terms of numerical simulation, a number of contributions have been made. For example, a preliminary assessment of the importance of three-dimensional effects within the context of a test problem where variations in the geometric proportions of the domain has been considered [2]. This work showed that, even for a relatively simple class of problem, 2D simplification can yield a significant inaccuracy. The relative performance of 2D versus 3D simulation of experimental data has been explored with similar conclusion elsewhere [3]. Corresponding author. Cardiff School of Engineering, Queen’s Buildings, P.O. Box 925, Cardiff CF24 3AA, UK. Tel.: +44 29 20875760; fax: +44 29 20874597. E-mail address: [email protected] (S.W. Rees).

0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.12.022

The influence of varying ground-water-table depth on the thermal properties of soils and hence on the related earth–contact heat transfer has also received some attention [4]. It is clear from this work that variation in soil moisture content can play an important role in the determination of thermal properties for analysis. A two-dimensional numerical simulation of a full-scale heat transfer experiment has also appeared in the literature [5]. In this case, the data was supplied from the Japanese Test House facility [6]. The study focussed on the simulation of the ground heat losses associated with the experiment. The influence of including edge insulation was also explored. More recently, a comparison of fully coupled (heat and moisture content) simulations with linear thermal simulations has been published [7]. It was observed that coupling influenced: (i) the amplitude of surface temperature, (ii) the variation of thermal conductivity with moisture content, and (iii) the advection of sensible heat by liquid transfer. However, it was concluded that the current accuracy of standard (design) methods is sufficient not to warrant the integration of coupling effects in these methods. A numerical analysis of outdoor thermal environment around buildings has been considered by other researchers [8]. Here it is argued that simulation of the thermal

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environment around buildings is of great importance for residential microclimate study. Their simulation includes temperature distributions of the outdoor air, building surfaces and ground surfaces. This was achieved by combining a computational fluid dynamics (CFD) calculation of air flow and an energy balance calculation for the surfaces. Development of a two-dimensional analysis of heat losses and temperatures in a slab-on-grade floor, which is able to dynamically model a floor heating system, has also been reported [9]. This model was validated against measurements obtained from a single-family house and was also coupled to a whole-building energy simulation model. The dynamics of the floor heating system was shown to have an important influence on the overall heat loss to the ground. Furthermore, the foundation was shown to have a large impact on the energy consumption of a building with floor heating. A novel local/global (L–G) analysis technique has been developed to solve transient ground-coupled heat transfer problems [10]. The L–G analysis approach combined analytical and numerical techniques to obtain solutions of building foundation heat transfer problems with significant localised thermal bridges. It was suggested that even though simplified analytical solutions generally fail to account for thermal bridging in building foundations, they can be very useful when used as global solutions in the proposed (L–G) analysis technique. The analysis was shown to be an efficient and useful tool to evaluate transient heat transfer for slab-on-grade floor foundations. Further research on the estimation of the temperature distribution at the fill layer underneath a slab-on-ground structure for a heated building has been developed elsewhere [11]. This research was based on a typical slabon-ground arrangement [in Finland] where the footing walls extend above the surrounding soil surface. From field measurements and a series of numerical simulations it was found that three boundary temperatures have an effect on the temperature distribution underneath a slab-on-ground structure: the internal, the external and the subsoil temperature. A relation between the numerically determined static-state weighting factors of these three boundary temperatures and the interrelations of the theoretical thermal transmittance values of the adjoining structural layers was found. Based on these observations a new semianalytical method for the estimation of temperature distribution along the fill layer underneath a structure under periodic conditions was developed. The method used the principle of superposition, where the annual mean boundary temperatures form a basic steady-state temperature distribution and the amplitude of the external and internal temperatures contribute periodic seasonal alterations. From a slightly broader perspective, the wide range of computational models employed in building design and operation processes has also received attention [12]. This research covered traditional architectural scale models

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through to computer-generated virtual buildings. The paper addressed some specific issues including: representational integration, performance-to-design mapping, design space exploration, and self-organising building models. Briefly, considering progress made in regard to design procedures. A new methodology for a thermal energy building audit has been published [13]. An excellent contribution on Eco-house design, drawing on twenty four case-studies from around the world is also now available [14]. This book aims to show how to take the first steps towards the zero-carbon emission buildings of tomorrow. Guidance on environmental impact, passive solar design, photovoltaics, ventilation amongst other issues is provided. Quite recently, a comparative study of design guide calculations and measured heat loss through the ground was developed [15]. This research involved in situ measurements, numerical simulation and consideration of design guide calculations in relation to the behaviour of a range of real buildings. The results indicate that different design methods can lead to significantly different estimations of earth-related heat losses. Environmental assessment of re-building and possible performance improvements on a national scale has appeared elsewhere [16]. Also in relation to design, a useful contribution on performancebased building regulations is available [17]. In a relatively new area of research [18], the application of multi-objective genetic algorithms in building design optimisation has been explored. The above literature is quite strongly related to building energy issues and in particular earth–contact problems. However, there are numerous publications that are associated (at least in part) to the current research. For example, a coupled heat and mass transfer model to predict the energy conservation potential of an earth–air heat exchanger system has been developed [19]. Here, passive thermal performance of buildings was considered along with various design aspects of an earth–air–tunnel. Elsewhere, the performance evaluation and optimisation of geothermal district heating systems has been considered [20]. In this work, a case study is provided based on data collected from the Balcova geothermal district heating system [Izmir, Turkey]. The evaluation of the cooling potential of green roof and solar thermal shading in buildings has received some attention [21]. In addition, the annual periodic performance of a cooling system utilising a ground coupled chiller and a spherical underground thermal energy storage tank has been analysed by others [22]. In fact, much research has been published in relation to ground-source energy systems (including geothermal/ heat pump developments). However, this area is considered beyond the scope of the current review. The current work focuses on the application of numerical techniques employed to analysis of the ground heat transfer aspect of energy efficient design. On this occasion, a simulation of a full-scale experiment is presented that illustrates some of the strengths and weaknesses of numerical techniques. The field data

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presented can of course be employed by others for the purposes of model validation.

(Eq. (5)) and the second facilitates the solution for crushed materials (Eq. (6)) ldry ¼ 0:039n2:2  25%,

2. Theoretical background The following simulation is based on the solution of the two-dimensional, transient, form of the heat conduction equation:     2   2  q T qT qH qT l , (1) þl ¼ rc qx2 qz2 qT qt where H is the enthalpy, T is temperature, t is time, x and z are the Cartesian co-ordinates, l is the thermal conductivity, c is the specific heat capacity and r is the density. Therefore, the term rc represents the volumetric heat capacity. A numerical solution of Eq. (1) has been achieved via the finite element method for spatial discretisation. The finite difference method provides a time-marching scheme. The details of these methods have been well documented elsewhere and will therefore not be repeated here [23]. Two independent thermal properties define the quantity of heat transferred, namely thermal conductivity and heat capacity per unit volume. Clearly the successful application of Eq. (1) depends upon the use of representative material properties. Therefore, some background is given below on the methods employed herein.

ldry ¼

0:135gd þ 64:7  20%, 2700  0:947gd

(5) (6)

where n is the porosity, gd is the dry density (kg/m3). For saturated soils it has been shown that variations in the microstructure of the soil have relatively little influence on the thermal conductivity. The geometric mean equation can therefore be employed to include values of thermal conductivity for the constituents and their respective volume fractions as illustrated below lsat ¼ lð1nÞ lnw , s

(7)

where the thermal conductivity of the solid phase (ls) can be expressed as . ls ¼ lqq lð1qÞ o

(8)

Eq. (2) includes a normalised thermal conductivity value called Kersten number (Ke), which is dimensionless. The relationship between Ke and the degree of saturation of a soil is effectively linear (both parameters range between zero and one). For unsaturated unfrozen soils, Ke can be obtained from Eq. (3) (for coarse soils) or Eq. (4) (for fine soils)

Eq. (8) is based upon the quartz content (q) expressed as a fraction of the total solids content. Johansen recommended that the thermal conductivity of quartz (lq) can be taken as 7.7 W/mK and the other minerals (lo) can be assumed to be approximately 2.0 W/mK. The method also acknowledges the importance of the degree of saturation on thermal conductivity. However, it does not facilitate the consideration of migration of moisture in soils. As a result, for low degrees of saturation the method tends to derive relatively poor predictions for thermal conductivity. Furthermore, the relatively large change in thermal conductivity that can occur due to small alterations of moisture content at low degrees of saturation is also excluded. Useful guidance on these matters can be found in the literature [25]. Returning to Eq. (1), clearly a representative determination of volumetric heat capacity is also needed for time dependent problems. The densities of the individual constituents of a soil dictate the magnitude of this parameter. Hence gaseous materials are less able to store thermal energy than liquid matter. The large thermal inertia of soils may allow thermal energy to be stored for some periods of time resulting in a time lag effect of heat transfer. The thermal mass of the soil can be employed to advantage for both heating and cooling of buildings (see Section 1). De Vries [26] provided the following approach for the determination of volumetric heat capacity (C):

Ke ffi 0:7 log S r þ 1:0,

(3)

C ¼ ws rs cs þ ww rw cw þ wa ra ca ,

Ke ffi log S r þ 1:0.

(4)

3. Material properties It is well established that the bulk thermal properties of soils are quite strongly dependent on the combined properties of the liquid, air and solid components [1]. Since the current research focuses on earth–contact heat flow this aspect of the problem is given some further consideration below. Johansen [24] proposed an approach which relates thermal conductivity (l) to the dry (ldry) and saturated states (lsat) of a soil of the same density l ¼ ðlsat  ldry ÞKe þ ldry .

(2)

The porosity of the soil structure is recognised to be an important parameter when considering thermal conductivity of soils. Since the emphasis is placed on the microstructure of the soil skeleton two expressions were suggested. One caters for the dry condition of natural soils

(9)

where the subscripts s, w and a refer to the solid, water, and air phases, respectively. Therefore, cs, cw and ca are the specific heat capacities of each phase and ws, ww, wa, are the volume fractions of each phase. It is apparent from this equation that the volumetric heat capacity of a soil continues to increase as the water content increases. For many soils, the air phase occupies a relatively small

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Table 1 Thermal properties of soil constituents at 20 1C and 1 atm [25] Material

Density (r) (kg/m3)

Specific heat (c) (J/kg K)

Vol. heat capacity (C) (J/m3 K)  106

Thermal conductivity (l) (W/m K)

Thermal diffusivity (a) (106 m2/s)

Quartz Many soil mineralsa Soil organic mattera Water Air

2650 2650 1300 1000 1.2

733 733 1926 4187 1005

1.94245 1.94245 2.5037 4.187 0.001206

8.4 2.9 0.25 0.6 0.026

4.3 1.5 0.10 0.142 0.021

NB. These values have been converted to SI units from the original reference. a Typical values.

Table 2 Volumetric heat capacity based on geometric mean Depth below grade (mm)

n

Sr

ws

ww

wa

Soil type: Agricultural silt 0.0–457 0.523 0.618 0.477 0.323 0.2 457–762 0.523 0.618 0.477 0.323 0.2 Soil type: Uniform sand 0.0–457 0.514 0.629 457–762 0.526 0.474 762–1066 0.356 0.293 1066–1371 0.335 0.221 1371–1676 0.320 0.192 1676–1981 0.290 0.455 1981–Wall 0.308 0.233 Bottom Soil type: Undisturbed 0.0–457 0.526 457–762 0.538 762–1066 0.373 1066–1371 0.352 1371–1676 0.338 1676–1981 0.308

soil 0.614 0.464 0.280 0.210 0.182 0.428

Table 3 Average thermal properties C(J/m3 k)

Material

Thermal conductivity (W/m K)

Volumetric heat capacity (J/m3 k)

2700 2700

2.43E+06 2.43E+06

Concrete Agricultural silt Uniform sand Undisturbed soil

1.820 0.942 1.178 1.146

1.47  106 2.43  106 1.91  106 1.87  106

rs (kg/m3)

0.486 0.474 0.644 0.665 0.68 0.710 0.692

0.323 0.249 0.104 0.074 0.061 0.132 0.072

0.191 0.277 0.252 0.261 0.259 0.158 0.236

2650 2650 2650 2650 2650 2650 2650

2.43E+06 2.09E+06 1.87E+06 1.78E+06 1.77E+06 2.13E+06 1.84E+06

0.474 0.462 0.627 0.648 0.662 0.692

0.323 0.250 0.104 0.074 0.062 0.132

0.203 0.288 0.269 0.278 0.276 0.176

2720 2720 2720 2720 2720 2720

2.43E+06 2.10E+06 1.86E+06 1.78E+06 1.76E+06 2.13E+06

proportion of the void space and has a small density, it is therefore often excluded from this calculation. However, water vapour present in the voids can increase c and r and may need to be considered. Some typical thermal properties for the constituents of a number of soils are summarised in Table 1. Previous work by Shipp [27] provided a good indication of the likely variation of material properties at the Minnesota experimental site. For this work, volumetric heat capacity has been determined by direct application of the Geometric Mean approach described above. The results of this are shown in Table 2 and were thought to be in line with other published data [25]. The calculations shown in Table 2 employ the following constants: cs ¼ 837 J/kg K, cw ¼ 4184 J/kg K, ca ¼ 1005 J/kg K, rw ¼ 1000 kg/m3, and ra ¼ 1:25 kg/m3. The final material property specification is

summarised in Table 3. These values have been employed in the numerical simulation presented below.

4. The Minnesota experiment Figs. 1–3 show a plan view, a cross-section and the location of transducers, respectively. The experimental unit is basically a concrete box containing an artificial heating facility. The dimensions of the box are approximately 2.5 m high with a square base 5.89 m  5.89 m in plan. The unit comprises four concrete walls, one concrete floor and an adiabatic cover on top. High thermal resistant extruded polystyrene insulation was placed at the connections between the walls and the adiabatic cover to ensure minimum heat losses at the connections. The thickness of the concrete walls and the concrete slab are 304.8 and 101.6 mm, respectively, and there was no reinforcement steel. Fig. 4 provides an outline of the materials involved. Attention is limited here to the simulation of one complete annual cycle, namely the period; 1st March 1990–28th February 1991. The experiment was essentially symmetrical, hence the current work focuses on measured data relating to one side (the West side) of the structure only. No transducers were located in the soil mass remote from the building. Validation of the numerical simulation is therefore limited to comparison of behaviour near the surface of the walls of the structure. For the sake of

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304.8

5892.8

304.8 304.8

NORTH

5892.8

COORDINATE SYSTEM ORIGIN

Y X

304.8 Fig. 1. Plan view of Minnesota experiment.

brevity, the experimental data recorded during this period is shown later in conjunction with the numerical results achieved. A more comprehensive description of the in situ Minnesota experiment can be found elsewhere [27]. 5. Numerical investigation The following numerical simulation focuses on the thermal energy transferred through the walls of the structure to the surrounding soil. The vertical boundaries are both adiabatic where one is an axis of symmetry and the other is remote from the building. A two-dimensional representation of the problem is therefore attempted in the first instance. Fig. 5 shows the measured internal and external temperature variations over one year commencing 1st March 1990. Clearly, the external temperatures fall well below freezing during the winter period. The finite element mesh employed is illustrated in Fig. 6. The mesh consisted of 307 quadrilateral elements thus forming a mesh composed of 1000 nodes. It extended a lateral distance of 12.95 m and a vertical height of 14.626 m (including the top of the wall). Boundary conditions for the simulation were obtained from the measured data

shown in Fig. 5. These two curves were employed as time varying fixed (Dirichlet) boundary conditions along the related ‘internal’ and ‘external’ nodes of the finite element domain. A preliminary analysis of the data indicated that at depth, the soil temperature remained fairly constant at around 8.8 1C. This value was therefore applied as a fixed boundary condition for the lower surface of the domain. Determination of representative initial conditions for this class of problem is always a difficulty. The approach adopted here was to start with an average initial temperature based on the mean of the upper and lower values measured on the first day of the simulated period (1st March 1990). A ‘pre-conditioning’ run of the model was then conducted applying the full annual cycle of the boundary conditions for four cycles until a degree of stability occurred. Thus, having established a realistic set of initial conditions, shown in Fig. 7, a fifth cycle of the boundary conditions was then used to simulate the required period. The results from this final cycle are presented below. As discussed above, the material properties specified in Table 3 have been employed for this simulation.

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304.8 BACKFILL UNIFORM SAND

SURFACE LAYER AGRICULTURAL SILT

304.8 GROUND SURFACE 50.8

152.4

1483

ADIABATIC BOUNDARY

EXTRUDED POLYSTYRENE INSULATION

457.2

248.9 203.2 POURED CONCRETE WALL AND SLAB (NO REINFORCING STEEL)

EXCAVATION LINE

101.6

406.4

50.8

UNDISTURBED SOIL Fig. 2. Section of Minnesota experiment and surrounding soil.

6. Results The experimental results indicate that regions nearer the ground surface experienced the greatest variations in temperature due to the proximity of the external boundary condition. Temperature profiles relating to deeper locations indicate that the ground was less responsive to seasonal temperature variations. In the first instance, no consideration has been given to the possibility that the soil near ground surface may have been frozen for some of the period under consideration. Simulated results have been plotted against measured data to illustrate the transient temperature variation at selected locations. The temperature transducers were set 6.35 mm into the wall face. Fig. 8 shows the predicted (simulated) results in comparison with measured data at 0.254 m above ground level (transducer WL_11). At this depth, the overall match between predicted results and the measured is reasonable. However, closer inspection shows that the correlation between results is best at higher temperatures and clearly deteriorates at lower values. During the period 20

December to 3rd January when the measured temperatures fall to their minimum (in the order of 10 1C) the simulation tends to predict a much lower minimum of approximately 25 1C. Fig. 9 shows a similar trend at 0.102 m above ground level (transducer WL_10). Once again the overall match is reasonable, but there is some disparity during the coldest part of the year. Fig. 10 presents the results achieved at a sensor location 0.661 m below ground level (transducer WL_08). At this location a direct earth–contact heat transfer can be expected. Again a good overall correlation has been achieved. Fig. 11 shows the results achieved at depths of 1.571 m below ground level. It is of interest to note that in spite of the aforementioned attempt to produce realistic initial temperature, some disparity still existed even at the start of the simulation for this region of the domain. Overall the trend achieved appears satisfactory. 7. Conclusions A two-dimensional numerical simulation of a full-scale experiment has been presented. The results show that

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W_L_08

203.9 661.1

W_L_09

356.3

101.6

W_L_10

51.5

W_L_11 254

W_L_03 W_L_02

W_L_01

Fig. 3. Transducers located on west side wall.

Ground Level

Agricultural Silt Uniform Sand

1.886 m Undisturbed Soil

Fig. 4. Material distribution (used for discretisation).

Concrete

1887.8

W_L_06

1805.1

W_L_07 1575.5

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40

Temperature (°C)

30 20 10 0 External Temperature Internal Temperature

-10

-30

1-Mar 15-Mar 29-Mar 12-Apr 26-Apr 10-May 24-May 7-Jun 21-Jun 5-Jul 19-Jul 2-Aug 16-Aug 30-Aug 13-Sep 27-Sep 11-Oct 25-Oct 8-Nov 22-Nov 6-Dec 20-Dec 3-Jan 17-Jan 31-Jan 14-Feb 28-Feb

-20

Time (days) Fig. 5. Daily mean internal and external temperatures.

Temperature °C 20.165 17.323 14.482 11.64 8.7982 5.9565 3.1148 0.27314 -2.5686 -5.41

Fig. 7. Initial conditions.

Fig. 6. Finite element mesh.

careful determination of the thermal properties of soils can play an important role in earth–contact heat transfer. Representation of field problems necessarily requires some

assumptions and approximations. In this case, the simulated period covered a full annual cycle. However, the distribution of temperature within the foundation soils was not known at the start of this work. A simple ‘preconditioning’ of this field was therefore suggested and shown to provide a reasonable set of initial conditions for the purposes of the simulation. A fair correlation has been

0

1-Mar 15-Mar 29-Mar 12-Apr 26-Apr 10-May 24-May 7-Jun 21-Jun 5-Jul 19-Jul 2-Aug 16-Aug 30-Aug 13-Sep 27-Sep 11-Oct 25-Oct 8-Nov 22-Nov 6-Dec 20-Dec 3-Jan 17-Jan 31-Jan 14-Feb 28-Feb

Temperature (°C)

-30 1-Mar 15-Mar 29-Mar 12-Apr 26-Apr 10-May 24-May 7-Jun 21-Jun 5-Jul 19-Jul 2-Aug 16-Aug 30-Aug 13-Sep 27-Sep 11-Oct 25-Oct 8-Nov 22-Nov 6-Dec 20-Dec 3-Jan 17-Jan 31-Jan 14-Feb 28-Feb

Temperature (°C)

1486

-20

-10

-30 1-Mar 15-Mar 29-Mar 12-Apr 26-Apr 10-May 24-May 7-Jun 21-Jun 5-Jul 19-Jul 2-Aug 16-Aug 30-Aug 13-Sep 27-Sep 11-Oct 25-Oct 8-Nov 22-Nov 6-Dec 20-Dec 3-Jan 17-Jan 31-Jan 14-Feb 28-Feb

Temperature (°C)

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40

30

20

10

0

-10

Measured Data

Measured data

Measured Data

Predicted Values

Time (Days)

Fig. 8. Predicted versus measured data (0.254 m above GL).

40

30

20

10

0

Predicted Values

-20

Time (Days)

30 Fig. 9. Predicted versus measured data (0.102 m above GL).

25

20

15

10

5

Predicted Values

Time (days)

Fig. 10. Predicted versus measured data (0.661 m below GL).

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25

Temperature (°C)

20

15

10

Predicted Values

Measured Data

28-Feb

31-Jan

14-Feb

3-Jan

17-Jan

6-Dec

20-Dec

22-Nov

8-Nov

25-Oct

11-Oct

27-Sep

13-Sep

30-Aug

2-Aug

16-Aug

5-Jul

19-Jul

7-Jun

21-Jun

24-May

26-Apr

10-May

12-Apr

29-Mar

1-Mar

0

15-Mar

5

Time (Days)

Fig. 11. Predicted versus measured data (1.571 m below GL).

obtained between numerical and experimental results. However, further work is needed in terms of fully representing the climatic conditions that existed in the field. In particular, the effect of frozen soil and seasonal changes in soil moisture content require further attention.

Acknowledgements The work reported here was partly funded by EPSRC Grant GR/K77471. This support is gratefully acknowledged.

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[24] Johansen O. Thermal conductivity of soils. PhD thesis, Trondheim, Norway, 1975 (CRREL Draft Translation 637, 1977), ADA 044002. [25] Farouki OT. Thermal properties of soils. Trans Tech Publications; 1986. [26] De Vries DA. In: Van Wisk WR, editor. Physics of plant environment. Amsterdam: North-Holland Publishing Company; 1966. p. 211–35. [27] Shipp PH. Basement, crawlspace, and slab-on-grade thermal performance. Proceedings of the ASHRAE/DOE Conference on Thermal Performance of the Exterior Envelopes of Buildings, Las Vegas, NV (6–9 December 1982) 1983. p. 160–79.