An experimental study of coupled heat and moisture transfer in soils at high temperature conditions for a medium coarse soil

International Journal of Heat and Mass Transfer 137 (2019) 372–389

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An experimental study of coupled heat and moisture transfer in soils at high temperature conditions for a medium coarse soil M. Hedayati-Dezfooli ⇑, Wey H. Leong Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada

a r t i c l e

i n f o

Article history: Received 23 March 2018 Received in revised form 22 March 2019 Accepted 22 March 2019

Keywords: Soil column Moisture flux Temperature gradients Moisture gradients Degree of saturation Differentially-heated plates Heat and moisture transfer

a b s t r a c t A study of one-dimensional heat and moisture transfer within a vertical soil column was conducted experimentally. An experimental soil cell made of stainless-steel tube was exposed to differential heating by sandwiching it between two differentially-heated plates for studying heat and moisture transfer in the soil column at different temperature levels and temperature differences. The main objective of the experimental study was to investigate heat and moisture transfer characteristics in a medium coarse soil at temperatures greater than 40 °C up to 90 °C. In this paper, the results are divided into two parts. In the first part, the results of heat transfer in dry soil are presented and discussed. The purpose was to investigate temperature distributions and heat gains/losses at the steady-state conditions along the soil cell at the various temperature levels. In the second part, the results of heat and moisture transfer in wet soil are presented and discussed. In this part, the transient temperatures, moisture contents and thermal properties along the soil column were obtained using the heat pulse technique. A loamy sand with a porosity and an initial water content of 0.40 and 0.26 m3/m3 (or saturation degree of 65%), respectively, was used in the study. The results of the case with the largest temperature difference of 65 °C (or overall temperature gradient of 440 °C/m) and the mean temperature of 55 °C are presented in detail. The highest temperature gradient of 1450 °C/m was recorded at the top of the soil column during the test, driving downward a moisture flux as high as 3 g/s
m2 when the soil was at temperature of 51 °C and saturation degree of 40%. Under these conditions, the thermal vapor diffusion is the main mechanism for the moisture flux. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Soil is considered, in a strict sense, a non-homogeneous and non-isotropic porous material. The term soil, as used by engineers, refers to a complicated material consisting of solid particles of various compositions (mineral and organic) and various shapes and sizes that are randomly arranged with pore spaces between them. These pores contain air and usually water in its various phases as vapor, liquid or ice. The composition of naturally occurring soil varies continuously because of changes in the amount and phase of water at various locations. These changes result mainly from the continuously varying temperature field to which the soil is subject. The daily temperature fluctuations are superimposed on the seasonal cycle, and there is a geothermal heat flux resulting from the flow of heat upwards from the hot interior of the ground. These changing temperature gradients alter the soil composition, particularly with regard to changes in the amount, phase and condition ⇑ Corresponding author. E-mail address: [email protected] (M. Hedayati-Dezfooli). https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.131 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

of water. This leads to variations in the thermal properties of the soil [5]. The study of moisture and heat distribution in soil is useful in various applications, such as: agriculture, earth-contact structure, underground power cable and so on. Thermal gradients induce moisture transfer and so this transport will affect heat flow. Indeed moisture and temperature fields are more or less coupled. The thermal gradients produced by these temperature fields cause soil moisture to be transferred from warmer to cooler areas in both the vapor and the liquid phases. The thermally induced moisture flow may significantly affect the net transfer of the soil water and nutrients by changing the moisture content gradients and the capillary conductivity, in addition to the direct effects of mass transfer. Thermal moisture transport may be thought of as the moisture flux through soil which arises solely due to a temperature gradient. Thermal gradients and the associated moisture transfer cause changes in moisture contents and pressures. These effects need to be taken into consideration in analysis of net moisture flow through the soil. Moisture flows in the form of liquid and vapor where the flow of the vapor phase is mainly considered as a molecular diffusion process. In unsaturated soils, thermally induced flow

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Nomenclature c C D k q qm Sr t T x

specific heat (J/kg
K) volumetric heat capacity (J/m3
K) diffusivity thermal conductivity (W/m
K) heat flux (W/m2) moisture flux (kg/s
m2) degree of saturation, Sr ¼ h=g (m3 of water/m3 of pore space) time (s) temperature (°C) vertical distance from top (m)

Greek symbols a thermal diffusivity (m2/s) g porosity (m3 of pore space/m3 of soil) h volumetric water content (m3/m3) q density (kg/m3) Dt time difference (s) DT temperature difference (°C) Dx distance difference (m)

increases rapidly as the moisture content decreases. Indeed, the decrease in moisture content is accompanied by a decrease in the thermal liquid moisture flow and an increase in the thermal vapor moisture flow [2]. The process of heat and moisture transfer in soil is basically driven by the thermal gradients. This process forms the temperature and moisture content distribution in the soil as a porous medium. The conveyance of the latent heat by vapor migration through the soil and within the boundary of the soil/atmosphere is a main process which controls the coupling between the heat and the moisture transfer. Precise modeling of coupled heat and moisture transfer in a high-temperature ground thermal storage is yet wanting and so requires further studies. To predict heat transfer in soil under the conditions of steady and unsteady heat flow requires knowledge of the basic thermal properties of soil [23]. While the flow of heat by conduction is the predominating mechanism, all possible mechanisms are involved for the flow of heat from warmer to cooler regions. The soil composition, temperature, moisture content and structure affect the heat transfer. Generally convection and radiation have negligible effects [16]. The heat transfer process may be affected by water phase changes in the soil. In unsaturated soils the process of evaporation along with the vapor diffusion results in condensation and subsequently heat transfer. Freezing of water or melting of ice within soils may also result in considerable latent heat effects. In many situations the transfer of moisture and heat occurs simultaneously [4]. Heat conduction occurs in all the soil constituents. In soil the amount of heat transferred by conduction increases as the soil dry bulk density increases and as its degree of saturation (Sr) increases. Heat being conducted through soil will take all available paths. Paths through contacting solids generally provide the major part of conductive heat transfer but thermal contact resistance may exist. There is a thermal contact resistance that gives a sudden discontinuity in the soil temperature at the contacts between solid particles with an interstitial fluid such as a gas or liquid in the gap around contacts [3]. Similar effects may be expected to occur in the pore spaces of the soil. The physics concerning the process of heat and mass transfer in soils has been a subject of importance for researchers in the past decades. The mathematical analysis of the response of soil to atmospheric conditions is problematical since the temperature and moisture variations in the unsaturated soil rely on the parameters in the

Dh

water-content difference (m3/m3)

Subscripts CVu upper control volume CVl lower control volume b bulk bot bottom dry dry soil l liquid LTD linear temperature profile m moisture max maximum net net ss stainless steel 304 t time top top v vapor w water x x coordinate

transport equations, which in turn depend on the temperature and moisture content [9]. The pioneers in modeling coupled heat and mass transfer in porous media are Philip and de Vries [25] and Luikov [14]. Philip and de Vries [25] came up with theoretical expressions for the thermal moisture and isothermal moisture diffusivities which occur in their governing partial differential equations of combined heat and moisture transfer in which they are dependent on soil hydraulic conductivity, temperature gradients, moisture potential and soil volumetric water content. They also presented an equation of heat conduction that incorporated latent heat transfer by water vapor diffusion. Later de Vries [4] generalized these equations by considering moisture and latent heat storage in the vapor phase and sensible heat transfer by liquid migration in the soil. Hence recent mathematical models mainly engage in modifications of Philip, de Vries and Luikov’s approaches [34] which have been studied by Moukalled and Saleh [17]. In 1982, Milly [15] revised Philip and de Vries [25] and de Vries [4] formulation of moisture and heat transport in partially saturated soil accounting for the coupling between the fields of matric potential and temperature, instead of moisture content and temperature, as dependent variables. In the revised model, the effects of heat of wetting on transport processes were considered. They showed that thermodynamic equilibrium assumptions at pore scale are acceptable for most conditions. To account for the effects of hysteresis for nonisothermal conditions, they proposed a generalization of isothermal hysteresis models according to capillary hypothesis. Indeed, the revised model facilitated an important generalization of the theory to accommodate the complications of hysteresis and inhomogeneity. Based on their previous work, i.e. Nassar and Horton [18,20], Nassar and Horton [22] presented a detailed theory to describe the simultaneous heat, water, and solute transfer in unsaturated nonisothermal, salty porous media. Their theory includes three fully-coupled partial differential equations. Heat, water, and solute move in the presence of temperature, matric pressure head, solution osmotic pressure head and solute concentration gradients. Their theory includes a number of transport coefficients for heat, water, and solute. As the second objective, they showed values of the coefficients and evaluated their dependency on temperature, water content and solute concentration. Their study showed that all the coefficients are affected by water content and temperature.

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Some of the coefficients decrease their values as the solute concentration increases. They concluded that thermal vapor transfer is a main mechanism for flow of vapor in unsaturated porous media. In order to test their theory, Nassar and Horton [19] conducted experimental observations of steady-state distributions of temperature, water content, and solute concentration within horizontal closed soil columns (polyvinyl chloride (PVC) tubes of 0.14-mlong and 0.04-m-diameter) containing either moist salinized or moist solute-free soils. However, they only tested on a silt loam soil at a temperature difference of about 10 °C and a mean temperature of about 14 °C. They found that the presence of solute clearly affected the observed soil water redistributions in the soil columns. Basing the experimental results, Nassar and Horton [18] calculated the transport coefficients and magnitudes of water fluxes for the steady-state soil columns. In 1992, Nassar et al. [21] conducted experimental and numerical studies to compare the measured and simulated soil temperature, water content, and solute concentrations in soil columns (0.10-m-long and 0.04-m-diameter) at 60 and 156 h. Stainless-steel and PVC tubes were used to contain a sandy loam soil and a silt loam soil in their experiments at horizontal and vertical positions with temperature differences of about 10 °C and 6 °C and mean temperatures of about 27 °C and 12 °C, respectively. These experimental studies are very limited and at low temperature levels and differences. In addition, there were no uncertainty analyses to indicate the accuracy of the results and also no discussion about the extent of heat loss/gain from/to the soil columns. In the early 1980s, a team of researchers at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, California, USA developed a computer code for geothermal reservoir simulation. It was first released as TOUGH (TOUGH is an acronym for Transport of Unsaturated Groundwater and Heat) in 1987 [26]. In 2004, Pruess [28] discussed about the TOUGH suite of codes which have the capability to model multiphase flows with phase change in porous or fractured media. Pruess summarized history and goals in the development of the TOUGH codes, and presented the governing equations for multiphase, multicomponent fluid flows and heat flow; but special emphasis was given to space discretization using integral finite differences. TOUGH2 was released in 1991 as a general-purpose numerical simulation program for nonisothermal flows of multiphase, multicomponent fluids in porous media [27]. In early 2008, Finsterle et al. [6] discussed fundamental and computational challenges in simulating vadose zone processes and demonstrated some capabilities of the TOUGH suite of codes using illustrative examples. They demonstrated that the TOUGH simulators are well suited to perform advanced vadose zone studies. Later in 2008, as the preface for a special issue of the Vadose Zone Journal, which contained revised and expanded versions of a selected set of papers presented at the TOUGH Symposium 2006,1 Liu et al. [13] underlined that simulation results from any numerical model are advantages only when the model is precisely validated with data collected at suitable scales, and only when the model can apprehend the key physical mechanisms for the flow and transport processes under consideration. So far, the uses of TOUGH family of codes are mainly in vadose zone hydrology, environmental engineering, hydrocarbon and gas hydrate recovery, carbon sequestration, nuclear waste isolation, mining engineering, and geothermal reservoir engineering. Therefore, its use in the simulations of ground source heat pump (GSHP) and ground thermal energy storage (GTES), especially for high-temperature applications up to 90 °C, has yet to be validated and confirmed.

1 https://www.tough.lbl.gov/documentation/tough-proceedings/proceedingstough-symposium-06/.

Ricerca sul Sistema Energetico [30] in Milano, Italy has developed an integrated Geo-Modeling Analysis System (GeoSIAM) modeling suite, containing Tough2RdS simulator which was developed starting from the TOUGH2 code, to characterize a geological reservoir for low, medium and high enthalpy gas or CO2 or geothermal storage, studying its behavior from a fluid dynamics, geomechanical and geochemical point of view. In 2016, Perego et al. [24] used the GeoSIAM to evaluate a borehole thermal energy storage (BTES) with 15 vertical boreholes in Alessandria (Italy). The objective of their study was to implement sustainability assessment of a medium to large scale GSHP system located in heating-dominated region which was characterized by a heterogeneous subsurface. They found that heterogeneous, stratigraphic subsurface with some poor thermal-property layers can cause thermal imbalance issues especially in heating dominated regions. It was concluded that the developed 3D-model of the BTES, considering geological, energetic and engineering parameters of GSHP systems, is proved to be very valuable in assessing sustainability of the systems. Although the use of GeoSIAM and TOUGH in GSHP and GTES is still very limited, they have great potential for future studies of such applications. In order to better utilize the heat from industrial waste heat or the solar energy, it is beneficial to store it in a high-temperature GTES; so the stored heat can be retrieved directly without the need of using a GSHP. This would improve the efficiency of such systems. The Drake Landing Solar Community2 is a community in Okotoks, Alberta, Canada, equipped with a central solar heating system and other energy efficient technology. It is a first-in-the-world example of successful application of seasonal high-temperature GTES system with over 90% of residential space heating needs being met by solar thermal energy which is collected and stored in the ground at high temperatures up to 80 °C over the summer season. In this project, the GTES contains mainly clay which has relatively low moisture diffusivity and so it can retain its moisture content and be able to store the heat. This type of soil cannot be found in most places; therefore to improve the design of such systems, a fundamental study in high-temperature heat and moisture transfer in other types of soils is essential. From the literature only few studies about high-temperature heat and moisture transfer with experimental or field comparisons were found. For example the existing work, e.g. Reuss et al. [29], showed numerical simulations and compared numerical results with experimental data of 60 °C and below. Therefore, the objective of this study is to precisely measure transient variations of temperature, water content and thermal properties along a vertical closed soil column, which contains a medium coarse soil, exposing to a wide range of thermal conditions (10 < T < 90 °C) and present the experimental results, especially at high-temperature conditions, which can be used in the future as a benchmark to validate any numerical simulation model or code of coupled heat and moisture transfer in soils. The results of other soil types and soilcolumn orientations will also be published in the future. If a numerical simulation model or code, e.g. GeoSIAM, functions well on the benchmark problem, it should also function well on simulating high-temperature GTES.

2. Materials and methods In this study, a specially-designed experimental apparatus for studying one-dimensional heat and moisture transfer in a soil column has been considered. The intended study is focused on hightemperature conditions (up to 90 °C), so that the phenomenon of high-temperature coupled heat and moisture transfer in various soils can be studied more precisely. In this paper, a medium coarse 2

https://www.dlsc.ca/about.htm.

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soil (Matilda soil) was studied. Matilda soil is from Ontario, Canada with an identification code of ON-3 which has loamy sand texture (71% sand, 25.4% silt and 3.6% clay) with a mean solid density of 2706 kg/m3 [31,32,33]. In designing of the experimental apparatus, which houses a soil cell for holding a closed soil column to be tested, three stages of evaluation were performed in order to minimize experimental uncertainty, leading to the final design shown in Fig. 1. In the final design, there were two tubes made of stainless steel 304, namely: the inner and outer tubes. The inside diameters of the tubes were 0.0635 m and 0.1390 m, respectively, with a wall thickness of 0.0635 m for both. The heights of the tubes were 0.1479 m and 0.1510 m, respectively. Both ends of the inner tube were covered by thin stainless-steel plates having a thickness of 0.0015 m and diameter of 0.0762 m each. In addition, the thin stainless-steel plates were secured to the top and bottom ends of the inner tube with six flat head stainless-steel screws on each end, each having total length of 0.0047 m. The secured attachment of thin stainless-steel plates to the inner tube with a very thin layer of thermally-conductive paste for good contact helped to prevent moisture loss from the wet soil inside the tube. For the design, the surface of the soil could be properly leveled with the top of the tube using a straight-edge ruler. A thin heat flux meter (HFM), which had a thermal conductivity of 3.33 W/m
K, thickness of 0.0005 m and diameter of 0.0630 m, was ‘‘pre-glued” to the thin stainless-steel plate using a very thin layer of thermallyconductive paste. Then, by pressing the HFM to the leveled surface of the soil, there would not be any air gaps at the interface between the HFM and the soil. Similar secured attachment of a thin stainless-steel plate and HFM at the bottom of the inner tube was set up, before a readily prepared soil sample was poured into the inner tube and compacted layer by layer using a heavy metal rod to achieve soil uniformity with the same compaction. The inner and outer tubes were sandwiched between a hot and cold plates which were made of aluminum alloy 2024. The hot and cold plates contained grooved channels for circulating hot and cold water streams from thermally-controlled baths. Again, a very thin layer

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of thermally-conductive paste was applied at all the contact surfaces for good contact. Four steel bolts and nuts were used to tie together and secure the entire assembly. In the end, the space between the inner and outer tubes was filled with fiberglass insulation and the entire assembly was also completely covered by a layer of fiberglass insulation. To determine the number of required probes in this study, similar thermo-time domain reflectometry (T-TDR) probes used by Ren et al. [35], in terms of design and size, were considered. The details of the T-TDR probe can be also found in Hedayati-Dezfooli and Leong [7]. To have maximum number of temperature readings along the soil column, the probes were inserted horizontally one after another into the soil column with their three needles aligned vertically, after the soil cell was prepared. The distance between the two probes was determined based on TDR interference and heat pulse effects. In this study, according to the results of the experimental evaluation of the interference of TDR probes, the distance between two adjacent TDR probes must be greater than 0.01 m apart so that the effect of interference would become negligible [7]. Since the probes were to produce simultaneous heat pulses, the generated heat pulse of a probe could travel to adjacent probes, affecting temperature readings of the other probes and thus resulting in inaccurate measurements. Therefore, to avoid the effect of the heat pulse of one probe on another, it is critical to estimate how far the heat travels after it was generated by the middle resistance heating needle of the probe. Using a typical value of thermal diffusivity of 6.7  107 m2/s for a wet loamy sand at 50% saturation and a typical measurement period of 120 s, the estimated travel distance of the heat was found to be 0.018 m. Therefore, it was decided to have five probes and allow them to be spaced equally at 0.0296 m between probe centers or 0.0236 m between the middle resistance heating needle and an adjacent thermocouple needle of another probe. In designing of hot and cold plates, the objective was to maintain a uniform desired temperature throughout the entire front surface of the hot or cold plate. The hot or cold plate consists of two separate plates. One plate would have a grooved channel for

Fig. 1. Sketch of cross section of the final design of the vertical soil cell assembly.

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circulating water and the other would serve as a cover for the grooved plate. The dimensions of the plates were selected to be 0.2030  0.2030  0.0127 m for the grooved plate and 0.2030  0.2030  0.0064 m for the cover plate. The best rectangular cross section of the grooved channel was found to be 0.0150 m wide  0.0064 m high with 0.007 m apart, as it spiraled from the center outward with a total length of about 1.14 m. The plates were to be maintained at isothermal conditions by circulating water from two thermally-controlled baths. The design was established based on the criterion that the change of circulating water temperature through the plate must be not greater than 0.1 °C for a water mass flow rate of 0.1 kg/s. In the process of selecting the best material, aluminum alloy 2024 was considered and evaluated based on its thermal capacitance, yield strength and easy to machine. Fig. 2 illustrates a schematic of experimental setup. The data acquisition system was supplied by Campbell Scientific Co., which includes a data acquisition unit (CR1000), a TDR signal generator and receiver (TDR100), a TDR multiplexer (SDMX50) for connecting to the five coaxial cables of T-TDR probes, a power relay controller (SDM-CD16S) for providing pulsed DC power supply to the middle resistance heating needles of the five T-TDR probes, and a thermocouple multiplexer (AM25T) for connecting to a total of 12 T-type thermocouples (ten from the five T-TDR probes and two from the two HFMs). The two thermally-controlled circulator baths were supplied by LAUDA-Brinkmann, LP. (Proline RP1845). The sequential operation of the TDR via the multiplexer has a time delay within a range of 0–14 ms depending on the lengths of coaxial cable and TDR probe, as well as the apparent dielectric constant of the soil due to the presence of soil water. The differential voltage signals from the HFMs were directly measured by the data acquisition unit. The setup has the capability to measure soil moisture content using the heat pulse and/or TDR methods. However, the TDR method is so far limited for the present study because Topp’s equation used in TDR software for relating the dielectric constant of a soil to its volumetric moisture content was developed for T < 40 °C [36]. Thus, the heat pulse method is used in the present study for measuring soil moisture content as temperatures up to 90 °C are involved. 3. Results and discussion 3.1. Heat transfer in dry soil The study of dry soil is beneficial because the capability of the apparatus to have one-dimensional heat transfer can be examined in the most critical condition. The critical condition is expected for dry soil because of its low thermal conductivity; therefore, the highest temperature and heat transfer deviations are expected to occur within the soil. Several tests were carried out to investigate the heat transfer in dry soil. For the series of tests, dry Matilda soil

was evenly packed in the stainless-steel cylindrical tube with an average bulk density qb = 1620 kg/m3 and was vertically sandwiched between the hot plate at the top and cold plate at the bottom. The two heat flux meters (HFMs) were placed separately at both ends of the soil column to measure the heat fluxes entering and exiting the soil, as well as to measure the temperatures of the HFMs at the top and bottom of the soil column. The HFMs contain type-T thermocouples embedded in them. The tests were carried out at various temperature levels while the temperature difference between the top and bottom plates was kept at about 15 °C. The temperature level is defined as the average temperature between the temperatures of the HFMs, and the temperature difference is defined as the temperature difference between the temperatures of the HFMs. In all cases, when plotting the temperature distributions along the soil column in the subsequent figures, the linear line connecting the temperatures of the HFMs was considered to be a reference temperature distribution along the soil column for a one-dimensional heat transfer condition. 3.1.1. Observations and analysis of results Figs. 3–6 illustrate temperature variations along the soil column at four different temperature levels of 37.9, 52.9, 67.8 and 82.6 °C, respectively, at steady-state conditions after 4.5 h. Since all four temperature levels were higher than the ambient temperature of about 23 °C, there was heat loss from the entire soil cell to the ambient air, causing the entire measured soil temperature profiles to be below the reference linear temperature profile with the highest deviations occurred at the top part of the soil column. From the results, it was found that the maximum temperature deviation from the linear temperature profile occur at around 40 mm from the top of the soil column. It can be seen from Figs. 3–6 that the deviation increases as the temperature level increases. From Figs. 3–6, it can be observed that there were higher heat losses in the upper portion of the soil cell due to the higher temperature difference between the upper portion of the soil cell and the ambient air. In fact, since the thermal conductivity of stainless steel is significantly larger than that of the dry soil and the surrounding insulation layer, the heat that enters the soil column from the top near the stainless-steel tube prefers to flow toward the stainless-steel tube wall and bypasses the soil. Later, some of the heat flows back from the stainless-tube wall to the soil in the lower portion of the soil column, reducing the temperature differences between the measured soil temperatures and the temperatures of the LTP. Fig. 7 presents the highest percent deviations from the linear temperature profile (LTP) with respect to the overall temperature difference,DT ¼ T HFM;top  T HFM;bottom , at different temperature levels, as defined by Eq. (1).

% Temperature Dev iation ¼

Fig. 2. Schematic of experimental setup.

ðT LTP;x  T x Þmax  100 DT

ð1Þ

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Fig. 3. Temperature variations along dry soil column from the top to the bottom at the temperature level of 37.9 °C and the temperature difference of 13.4 °C.

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Fig. 6. Temperature variations along dry soil column from the top to the bottom at the temperature level of 82.6 °C and the temperature difference of 13.5 °C.

the temperature gradient of about 90 °C/m. This deviation is an indication of the existence of two-dimensional heat transfer in the soil column, as some of the heat was conducted radially toward the stainless-steel tube wall. This phenomenon is particularly noticeable due to the low thermal conductivity of dry soil (kdry) relative to the thermal conductivity of stainless-steel tube wall (kss), i.e. kdry/kss  0.015. Thus, it can be realized that the heat conduction in the soil would rather bypass the soil and thermally shortcircuited to the wall. Actually, the different amount of heat transfer between the top and the bottom of the soil column is very small. For example, for amount of heat conduction through the soil column at the same temperature level of 82.6 °C (which is in the order of 20 W/m2 or 0.064 W), the difference in heat transfer is only in the order of 0.022 W, i.e. the top heat transfer is 1.34 times larger than the bottom one. Fig. 4. Temperature variations along dry soil column from the top to the bottom at the temperature level of 52.9 °C and the temperature difference of 13.1 °C.

Fig. 5. Temperature variations along dry soil column from the top to the bottom at the temperature level of 67.8 °C and the temperature difference of 13.3 °C.

where T LTP;x is the temperature of the LTP at a distance x from the top of the soil column, and T x is the measured soil temperature at the same distance x. Fig. 7 also illustrates the percent differences of heat fluxes, measured by the heat flux meters, as defined by Eq. (2).

% Difference of Heat Fluxes ¼

qHFM;top  qHFM;bot  100 qHFM;bot

ð2Þ

where qHFM;top and qHFM;bot are the heat fluxes measured by the top and bottom HFMs, respectively. It was found that the highest temperature deviation is 18.6% at the temperature level of 82.6 °C and

3.2. Heat and moisture transfer in wet soil A series of tests were carried out for a wet Matilda soil (with an average porosity g = 0.40, an initial Sr = 0.65 (or h = 0.26 m3
m3), and an average bulk density qb = 1880 kg/m3) to study heat and moisture transfer in the soil. In this section, the focus of result presentation will be based on the most critical case which is the case of 90–10 °C, i.e. the hot and cold plates were set at 90 and 10 °C, respectively, or temperature level of 54.8 °C. This case was selected since the main purpose of this work is to study high-temperature heat and moisture transfer in soil. The plots of boundary temperatures of top and bottom HFMs versus time are also presented in the appendix. The discussion of the results will be presented in two parts. In the first part, a general analysis of the results will be discussed, and in the second part more in-depth analysis will be discussed. The results of the remaining cases, i.e. various temperature levels and temperature differences, are graphically presented in Hedayati-Dezfooli [8]. 3.2.1. General discussion of results Fig. 8 illustrates the results of the highest percent temperature deviations from the linear temperature profile of four cases of temperature levels (38.1 °C, 52.9 °C, 67.6 °C and 82.1 °C) with respect to the overall temperature differences (12.6 °C) and the percent differences of heat fluxes measured by the heat flux meters. It can be seen that the highest difference of heat fluxes would not be exceeding 4.2% and the highest temperature deviation in the worst case is not more than 7.7%. This was expected, as compared with the results of the dry soil (Fig. 7), because the wet soil has much higher thermal conductivity (1.4 vs. 0.26 W/m
K) which resulted in higher heat transfer through the soil. As a consequence, the amount of heat loss with respect to the heat transfer through

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Fig. 7. The results of highest percent temperature deviations from the LTP with respect to overall temperature differences and the percent differences of heat fluxes between the top and bottom HFMs of dry soil at four different temperature levels with a temperature difference of about 13 °C.

Fig. 8. The results of the highest percent temperature deviations from the LTP with respect to overall temperature differences and the percent differences of heat fluxes of wet soil at four different temperature levels with a temperature difference of about 13 °C.

the soil was relatively smaller; therefore, greater uniformity of heat flux in the radial direction would be achieved along the soil column, i.e. achieving nearly one-dimensional heat and moisture transfer and resulting in closer linear temperature profile along the soil column. From Fig. 8 it was observed that the higher discrepancies of the results occur at higher temperature levels while the temperature differences remain relatively constant. Fig. 9 illustrates the results of the highest percent temperature deviations from the linear temperature profile with respect to overall temperature differences and the percent difference of heat fluxes at various temperature levels and temperature differences. For the highest temperature deviation from the LTP with respect to overall temperature difference, it can be seen that the percent temperature deviation increases with the temperature difference from 5.6% to 7.5% at the temperature differences of about 17 °C (50–30 °C) and 65 °C (90–10 °C), respectively. When the temperature levels are about the same, such as from 40 °C to 41.6 °C, the percent temperature deviation increases almost linearly. However, when there is a larger increase in temperature level, such as from 41.6 °C to 46 °C, the percent temperature deviation increases more significant. Therefore, from the results, it can be concluded that generally speaking the percent temperature deviation increases

as temperature level and temperature difference increase. This is because of higher heat loss as the hot-plate temperature increases higher than the ambient-air temperature, in order to increase the temperature level and temperature difference. For the percent difference of heat fluxes, it can be seen that the variations of the percent difference of heat fluxes are actually quite small and within 1.5%. By carefully looking at the results it can be noticed that the percent difference of heat fluxes reduces from 1.5% to 0.2% as temperature difference increases from about 17 °C (50–30 °C) to about 49 °C (70–10 °C). This is the range that the temperature level would not significantly increases (from 40 to 41.6 °C). Later, the percent difference of heat fluxes increases to 1% as temperature difference increases to roughly 57 °C (80–10 °C). However, this time the change in temperature level would be more significant (from 41.6 to 46 °C). There is a counter-effect between temperature level and temperature difference. At higher temperature level than the ambient-air temperature, there is a higher heat loss from the soil cell, resulting in higher percent difference of heat fluxes; on the other hand, at higher temperature difference between the top and bottom of the soil column, there is a higher heat flux through the soil column relative to a smaller increase of heat loss, resulting in lower percent difference of heat fluxes. Therefore, from the

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Fig. 9. The results of the highest percent temperature deviations from the LTP with respect to overall temperature differences and the percent differences of heat fluxes of wet soil at various temperature levels and temperature differences.

results, it can be concluded that generally speaking the percent difference of heat fluxes increases as temperature level increases and the percent difference of heat fluxes decreases as temperature difference increases for the present experimental studies. Suppose that the total volume of the soil cell was divided into five equal control volumes each associated with a T-TDR probe which was positioned in the center of the corresponding control volume. Fig. 10 shows schematic view of the soil cell’s control volumes. Thus, the data (such as, temperature, volumetric water content, and soil properties obtained from each probe were reasonably assumed to represent the average values of the corresponding volume. Fig. 11 illustrates a general trend of temperature variations versus time along the soil column for the case of 90–10 °C. From the results it can be observed that the steady-state condition was obtained after about 120 min into the test. It is interesting to see that although the temperature set-point at the cold plate was set to be 10 °C, the temperature readings of the heat flux meter were highly affected by relatively large heat flux coming from the hot plate toward the bottom of the soil cell. The temperature gradient was increased to 442.4 °C/m at the steady-state condition. Due to large initial temperature difference (about 65 °C) between the hot plate and the top part of the soil column, the temperature rise at the points closer to the hot plate is more rapid than the temperature drop at the points closer to the cold plate, which has only about 11 °C difference between the cold plate and the bottom part of the soil. By carefully looking at the results, it can be noticed that until 30 min past into the test the lower region of the soil column was not yet significantly affected by the heat flux from the upper side. Therefore, under the effect of the cold plate, the temperature at the bottom of soil column remained at about 13.6 °C; not until at some point in time (between 30 and 60 min), the temperature at the bottom soil column began to rise up to about 17.3 °C at 60 min. This indicates that the heat would take between 30 min and an hour to reach the bottom of the soil column for a temperature difference of 65.4 °C. Based on the temperature gradient at the bottom of the soil column at 15 min into the test and the measured

Fig. 10. Schematic view of soil cell’s control volumes.

soil thermal conductivity of 1.4 W/m
K, the heat flux was found to be about 463 W/m2 from the soil to the cold plate. Therefore, the thermal resistance between the heat flux meter and the cold plate was estimated to be 0.0078 m2
K/W. When the heat from the hot plate was finally transferred to the bottom of the soil column between 30 and 60 min into the test, the heat flux increased up to 1468 W/m2 , which resulted in a temperature difference between the heat flux meter and the cold plate of about 11.5 °C due to the

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Fig. 11. Variations of the temperature vs. time along the soil column.

thermal resistance, in order to transfer the high heat flux into the cold plate. Fig. 12 illustrates a general trend of degree of saturation variation versus time along the soil column for the case of 90–10 °C. From the results, it can be observed that the moisture contents in the two upper control volumes (control volumes 1 and 2) dramatically dropped over time; while in the two lowest control volumes (control volumes 4 and 5), their moisture contents correspondingly increased. By comparing the results of moisture variations with the results of temperature variations, it can be understood that the significant increase of the temperature gradients in control volumes 1 and 2 was the key factor which induced the rapid moisture transfer out from the control volumes. Since the temperature gradients in the upper control volumes are high, the thermal vapor diffusion can be a main mechanism for moisture flow [22]). Therefore, as the temperature increases higher than 40 °C, after t = 30 min, water evaporates and moves downward where it condenses. Evaporation decreases the water contents in the upper soil column and condensation increases the water contents in the lower soil column. As the water contents in the lower soil column increase, liquid water actually begins to move upward

back to the dry areas. So, within the soil column, water vapor moves downward from the hotter soil into colder soil, due to temperature gradient, and liquid water moves upward, when a favorable gradient of water content (or matric potential) has been established. Eventually, after about 2 h, control volumes 3–5 are ‘‘fully saturated” (about 3% short from full saturation, probably due to trapped air), and control volumes 1 and 2 became almost dry; and the exchange of moisture between the upper and lower soil column becomes steady with the downward vapor flux balancing the upward liquid flux. However, due to the gravity, there is more moisture in the lower soil column. Fig. 13 illustrates variations of the thermal properties vs. time along the soil column. From the results it can be perceived that all the thermal properties such as volumetric heat capacity (J/m3
K) (Fig. 13(a)), thermal conductivity (W/m
K) (Fig. 13(b)) and thermal diffusivity (m2 =s) (Fig. 13(c)) are mainly affected by the moisture content variations. Volumetric heat capacity and thermal conductivity increase as moisture content increases; however, thermal diffusivity mainly decreases as moisture content increases. Fig. 13 shows that the volumetric heat capacity, thermal conductivity and thermal diffusivity vary, respectively, within the

Fig. 12. Variations of the degree of saturation vs. time along the soil column.

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Fig. 13. Variations of the thermal properties vs. time along the soil column for the case of 90–10 °C: (a) Volumetric heat capacity, (b) Thermal conductivity, and (c) Thermal diffusivity.

following ranges of 1.3  106  3.0  106 J/m3
K, 0.61  1.5 W/m
K 7

7

and 4.7  10  7.5  10 m /s for Sr range of 1.7–97.4% and T range of 14–87 °C. The lowest and highest property values usually correspond to the combinations of low Sr and high T (e.g., 1.7% and 87 °C) and high Sr and low T (e.g., 97% and 20 °C), respectively. Due to the highly nonlinear characteristics of thermal conductivity at low Sr range, there are exceptional values for thermal diffusivity, 2

such as, the highest thermal diffusivity value of 7.5  107 m2 /s happens at low Sr of 22% and high T of 70 °C. The results of the various cases, i.e. various temperature levels and temperature differences, are graphically presented in Hedayati-Dezfooli [8]. 3.2.2. In-depth discussion of the results Fig. 14 illustrates the variations of the water content differences (Dh = ht  ho ) over time for the case of 90–10 °C. The water content differences at every time increment were referenced to the water contents of the control volumes at the initial time, i.e.

ho = 0.26 m3
m3 or Sr = 0.65. From the results, it can be seen that, after about 15 min, the change in water contents of different control volumes starts to appear. It can be observed that control volumes 1 and 2 lose moisture and at the same time control volumes 4 and 5 gain moisture. Up until 25 min into the test, control volume 3 acts as a transit and remain at relatively constant rates of moisture exchange between its preceding and following control volumes. However, after about 30 min it begins to have net gain of moisture from control volume 2, because control volumes 4 and 5 are becoming near full saturation. It should be noted that the process of moisture loss and gain does not necessarily mean the moisture only leaves the control volume or only enters it. In the case of moisture gains, the term gain is referred to the fact that the amount of the moisture entering the control volume is greater than the amount of the moisture leaving the control volume. Similarly in case of moisture loss it is referred to the fact that the amount of the moisture entering into the control volume is less than the amount of the moisture leaving the control volume.

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ðqm Þnet ¼

Fig. 14. Variations of the water content differences (Dh) vs. time for the case of 90– 10 °C. The symbol Dh is the water content difference of control volumes between time t and initial time t o . The positive value is an indication of moisture gain and the negative value is an indication of moisture loss.

Figs. 15–19 illustrates the variations of the net moisture fluxes (kg
s1
m2), temperature (°C), saturation degrees (Sr (%)), temperature gradients (°C/m) and moisture gradients (m3
m3
m1) over time (min) for control volumes 1–5, respectively. The net moisture flux of each control volume is calculated as follows:

ht  htDt q l Dx Dt

ð3Þ

where ht is the volumetric water content at the present time, htDt is the volumetric water content at the previous time step, ql is the density of liquid water, and Dxis the height of the control volume. The volumetric water contents of all control volumes were measured simultaneously with a time interval of 5 min, i.e. Dt = 5 min. The heights of all control volumes are equal to the height of the soil column divided by 5, i.e. Dx = 29.6 mm. It is known from the theory of heat and moisture transfer in soils [25] de Vries [4] that the three driving forces to result in moisture (solute-free) movement are due to moisture gradient, temperature gradient and gravity.

qm ¼ ql ðDhl þ Dhv Þrh  ql ðDTl þ DT v ÞrT  ql K h b k

ð4Þ

where Dhl and Dhv are the moisture diffusivities due to moisture gradient for liquid and vapor transports (m2 =s), DTl and DT v are the moisture diffusivities due to temperature gradient for liquid and vapor transports (m2 =s
K) and K h is hydraulic conductivity (m/s). To reiterate the observation and discussion in the previous Section 3.2.1, it is worth to point out that Nassar and Horton [22]

Fig. 15. The experimental results for control volume 1 of the soil column for the case of 90 °C hot plate and 10 °C cold plate.

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Fig. 16. The experimental results for control volume 2 of the soil column for the case of 90 °C hot plate and 10 °C cold plate.

determined that the DT v can be few orders of magnitude greater than DTl at moisture content near field capacity, especially when the temperature is high. For example, from Nassar and Horton [22], DT v is about three orders of magnitude greater than DTl at Sr ¼ 0:42 and T = 50 °C (1.6  1010 vs. 1.0  1013 m2 =s
K). Hence, the thermal vapor diffusion can be the main mechanism for moisture flow when the temperature and temperature gradient are high and the moisture content is around field capacity (Sr  0:5). After a wet soil sample was prepared in the soil cell, it was left to stand for over 24 h in vertical position before an experiment would begin. Obviously from Fig. 12 it can be observed that the moisture was quite uniform along the soil column; this indicates that the gravity does not play an important role in liquid movement for Matilda soil. Therefore, the main driving forces causing liquid movement are the moisture gradient and temperature gradient; the following equations (Eqs. (5)–(8)) are used to calculate the temperature gradients and moisture gradients which will help to explain the effects of the gradients on the net moisture flux of each control volume. The temperature gradients at the upper and lower boundaries of each control volume are calculated as follows:

 DT  T CVu  T CV ¼ Dx upper Dx

ð5Þ

 DT  T CV  T CVl ¼ Dx lower Dx

ð6Þ

where T CV is the temperature of the present control volume, T CVu and T CVl are the temperatures of the upper and lower control volumes, respectively. The moisture gradients at the upper and lower boundaries of each control volume are calculated as follows:

 Dh hCVu  hCV ¼ Dxupper Dx

ð7Þ

 Dh hCV  hCVl ¼ Dxlower Dx

ð8Þ

where hCV is the volumetric water content of the present control volume, hCVu and hCVl are the volumetric water contents of the upper and lower control volumes, respectively.

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Fig. 17. The experimental results for control volume 3 of the soil column for the case of 90 °C hot plate and 10 °C cold plate.

In the following, the relationships among the results of each control volume are analyzed. The temperature and moisture gradients are shown for both upper and lower boundaries of each control volume. This helps to have a better understanding of how the heat and moisture enter and exit a specific control volume. Fig. 15 represents the results of control volume 1 for the case of 90–10 °C. In this control volume, the highest temperature was achieved to be 75.6 °C, as shown in Fig. 15(b). Since no moisture enters the control volume from its upper boundary, the moisture gradients remained at zero at the upper boundary. By simultaneously looking at Fig. 15(b) and (d), it can be noticed that the increase of temperature results in the increase of temperature gradients. The temperature gradients are greater in the upper boundary compared to the lower boundary. Considering Fig. 15(a), (d) and (e), it can be perceived that the increase of temperature gradients induces the increase of moisture fluxes and that would induce the increase in moisture gradients in the lower boundary of the control volume. As the temperature becomes relatively constant after about 90 min (Fig. 15(b) and (c)), the changes of temperature gradients and net liquid flux would also become constant; however, the moisture gradient continues to decrease with time. This indicates that control volume 1 continues to get drier. The mois-

ture flux leaves control volume 1 at a relatively high rate from 10 to 30 min into the test with a maximum moisture flux of about 0.003 kg
s1
m2 at t = 30 min (Fig. 15(a)), at which time about half of the water content in control volume 1 has migrated to control volume 2 (Fig. 15(c)). At that moment, the temperature gradients at the upper and lower boundaries have reached 1444 and 560 °C/m (Fig. 15(d)), respectively, which strongly drive the moisture toward control volume 2. Although the moisture gradient at the lower boundary opposes the moisture migration at that moment, it fails to stop the moisture migration because the moisture gradient of 1.33 m3
m3
m1 (Fig. 15(e)) is too small. Fig. 16 represents the results of control volume 2 for the case of 90–10 °C. In this control volume, the highest temperature was achieved to be 63.1 °C, as shown in Fig. 16(b). The amount of moisture leaving control volume 1 would enter the upper boundary of control volume 2. Similar to the previous case, control volume 2 would also get drier over time; however, with relatively lower rate. This can be verified by comparing the values of net moisture fluxes in both control volumes. Considering the results of temperature, saturation degree and temperature gradients, shown in Fig. 16(b), (c) and (d), it can be perceived that, as the temperature and temperature gradients increase, saturation degree decreases. In addition,

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385

Fig. 18. The experimental results for control volume 4 of the soil column for the case of 90 °C hot plate and 10 °C cold plate.

the gravity would also play a role in moving the moisture down toward control volume 3, because the viscosity and surface tension of water reduces as the temperature rises. Hence, this phenomenon results in higher moisture gradients at the lower boundary of control volume 2. By comparing the moisture gradient variations at the upper and lower boundaries of control volume 2, it can be seen that the moisture gradient at the lower boundary increases much higher than the moisture gradient at the upper boundary. From Fig. 16(a), it can be observed that the net moisture fluxes are all negative values, indicating net loss of moisture in control volume 2 at a relatively high rate from 20 to 60 min into the test with an average net loss of moisture flux of about 0.0018 kg
s1
m2 (Fig. 16(a)). By 60 min into the test, even with the moisture gain from control volume 1, the saturation degree of control volume 2 has dropped from original 64.1% to 22.3% due to net loss of moisture to control volume 3 (Fig. 16(c)). At the same moment, the temperature gradients at the upper and lower boundaries have reached 564 and 452 °C/m (Fig. 16(d)), respectively, which drive the moisture toward control volume 3. In this case, similar to the previous control volume, it can be understood that although the moisture gradient at the lower boundary opposes the moisture migration at the moment, it yet fails to stop the

moisture migration even though the moisture gradient is relatively high at 8.2 m3
m3
m1 (Fig. 16(e)). The analysis of control volume 3 is important since it acts as a transit between control volumes 2 and 4. Fig. 17 illustrates the results of control volume 3 for the case of 90–10 °C. In this control volume, the highest temperature was achieved to be 51.1 °C. Similar to the previous control volume, the moisture leaving control volume 2 enters into control volume 3. Unlike control volumes 1 and 2, moisture content increases in control volume 3 (Fig. 17(c)), due to the net gain of moisture (Fig. 17(a)); however, the net gain of moisture is at a lower rate in comparison with control volumes 1 and 2. From Fig. 17(e), it can be noticed that after about 75 min, the variations of the moisture gradients become very small. In fact, the moisture gradient at the lower boundary becomes negligibly small, indicating that both control volumes 3 and 4 have achieved similar moisture contents which are close to the saturation point of the soil at saturation degrees of about 95–96% (Figs. 17(c) and 18(c)). From Fig. 17(a), it can be observed that the net gain of moisture flux in control volume 3 is at relatively high rates from 25 to 75 min into the test with a maximum moisture flux of about 0.0016 kg
s1
m2 at t = 75 min. At the same moment, the

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Fig. 19. The experimental results for control volume 5 of the soil column for the case of 90 °C hot plate and 10 °C cold plate.

temperature gradients at the upper and lower boundaries have reached 438 and 391 °C/m (Fig. 17(d)), respectively, which continue to drive small amount of the moisture toward control volume 4. In this case, it can be seen that although the moisture gradient at the upper boundary opposes the moisture migration from control volume 2 to control volume 3 at that moment, it still cannot completely stop the migration of the moisture even though the moisture gradient is high at 10.9 m3
m3
m1 (Fig. 18(e)). Fig. 18 demonstrates the results of control volume 4 for the case of 90– 10 °C. In this control volume, the highest temperature was achieved to be 39.6 °C. Considering Fig. 18(d) and (e), it can be observed that the highest moisture gradient happens at 60 min and the highest temperature gradient happens at 75 min. However, that is not necessarily the case in control volume 5 (Fig. 19(d) and (e)). Indeed the regions with higher moisture contents have less potential in accepting the incoming moisture. Besides the above reason, it should be noted that more moisture might have been evaporated into vapor at high-temperature regions, due to higher saturation vapor pressure and saturated vapor density corresponding to higher temperatures, which cannot be detected with the applied technique in this study.

The moisture flux enters control volume 4 from control volume 3 at a relatively high rate from 20 to 30 min into the test with a maximum moisture flux of about 0.00356 kg
s1
m2 (the sum of net moisture fluxes for control volumes 4 and 5) at t = 30 min (Figs. 18(a) and 19(a)). At the moment, the temperature gradients at the upper and lower boundaries have reached 204 and 139 °C/m (Fig. 18(d)), respectively, which drive the moisture toward control volume 5 at a relatively high rate of 0.002 kg
s1
m2 (Fig. 19(a)) even though the temperature gradients are not very high in comparison to the temperature gradients in other previous control volumes. From Figs. 18(c) and 19(c), it can be observed that control volume 4 become relatively saturated, i.e. ht = 0.385 m3
m3 or Sr = 0.96, from 60 to 75 min into the test. Within this period, the net moisture fluxes in both control volumes 4 and 5 become almost zero (Figs. 18(a) and 19(a)). From Fig. 19(c) it can be seen that during above period control volume 5 remain relatively saturated. Therefore, the moisture potential become very small in control volume 5 after 60 min into the test. This condition prevents the moisture migration from control volume 4 and so, results in rapid reduction in moisture gradients (Fig. 18(e) and 19(e)).

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4. Experimental uncertainties In this study, the analysis was carried out to estimate the uncertainties of the experimentally-determined quantities using rootsum-square (RSS) technique according to the classic work of Kline and McClintock [10]. The analysis was consisted of four main parts: 1- Uncertainty analysis of heat pulse technique, 2- Uncertainty analysis of soil sample preparation, 3- Uncertainty analysis of temperature measurement via T-TDR Probe and 4- Uncertainty analysis of volumetric moisture content.

solving steady, one-dimensional heat conduction equation along a thermocouple wire in a needle from inside soil column to outside ambient air, based on the solution obtained by Leong [12]. From the analysis, it was found that the thermocouple-wire case is more severe than the stainless-steel tube case, even though the copper wire is so much smaller than the stainless-steel tube. However, the uncertainty for thermocouple-wire case is still negligible. The results from thermocouple-wire case for maximum and minimum uncertainties were found to be respectively 6:24  106 °C and 3:1  107 °C and from stainless-steel tube case for maximum and minimum uncertainties were respectively 2:02  1015 °C

4.1. Uncertainty analysis of heat pulse technique Heat pulse technique was established to allow for concurrent measurement of soil thermal properties such as volumetric heat capacity C, thermal diffusivity a, and thermal conductivity k. The method of heat pulse is based on the theory of heat conduction through the soil away from the line heat source for a short time. In this experimental study, potential sources of uncertainty were studied based on the method used by Kluitenberg et al. [11] which is also recommended for various types of soils. The accuracy of the heat pulse method in measuring thermal properties can be evaluated by computing and systematically investigating potential sources of uncertainty. These potential sources of uncertainty include uncertainty estimations of required inputs such as delivered heat pulse, duration of delivered heat pulse, maximum temperature at receiving needle, spacing between the heat-pulse needle and the receiving needle, and the time it takes to reach the maximum temperature at the receiving needle. The uncertainties associated with the heat pulse technique in measuring the thermal properties and volumetric water content were evaluated for the Matilda soil for cases of dry, half saturated and saturated soil each at two different temperatures (20 and 90 °C). The maximum uncertainty was found to be about 7.2% in the measurement of the thermal conductivity of the dry soil sample at 90 °C. The minimum uncertainty was found to be about 2% in the measurement of the volumetric heat capacity of saturated soil at 20 °C. The detail of analysis can be found in Hedayati-Dezfooli [8]. 4.2. Uncertainty analysis of soil sample preparation

and 1:83  1015 °C. Therefore, the effect of heat conduction along T-TDR probe on temperature measurement was neglected; however, there is still systematic or bias uncertainty of ±0.5 °C or 0.4% (whichever is greater) due to T-type thermocouples. 4.4. Uncertainty analysis of volumetric moisture content The volumetric moisture content h of a soil can be calculated using Eq. (9) [1] after the volumetric heat capacity C of the soil is measured using the heat pulse method.

h¼

C  C dry qw c w

ð9Þ

where C dry is the volumetric heat capacity of the soil at dry conditions with the same soil porosity g as the wet soil, qw and cw are the density and specific heat of water. From Hedayati-Dezfooli [8], the relative uncertainty of the volumetric moisture content is given by

dh ¼ h

"

dC C  C dry

2

   2  2 #1=2 dC dry 2 dqw dcw þ  þ  þ  C  C dry qw cw ð10Þ

Water is a well-studied substance on earth. From literature, the density and specific heat of water can be obtained rather accurately within ±1%, i.e.

dqw

qw

¼ dccww ¼ 1%. Therefore, Eq. (10) can be

simplified to the following:

dh ¼ h

"

dC C  C dry

2

#1=2   dC dry 2 þ  þ 0:0002 C  C dry

The uncertainty of soil sample preparation for three degrees of saturation of 0.25, 0.5 and 1.0 were estimated based on 95% confidence level. For each Sr , the overall uncertainty of the soil sample preparation was evaluated by combining the systematic and the precision uncertainties of the mean of ten (n = 10) independently prepared soil samples with the student’s t multiplier of 2.262 for 95% confidence level. It was found that the maximum overall uncertainty in soil sample preparation can be as high as about 3% when Sr is 0.25. The detail of analysis can be found in HedayatiDezfooli [8] and Hedayati-Dezfooli and Leong [7].

ilarly, the average uncertainty of C of wet soil is obtained as dC ¼ 2:5%, ranging from 3:1% atSr = 0.5 to 2:0% at Sr = 1. Eq. C (11) can now be written as follows:

4.3. Uncertainty analysis of temperature measurement via T-TDR probe

dh ¼ h

One main possible source of uncertainty in temperature measurements using the T-TDR probes was heat conduction via TTDR probes since thermal conductivities of stainless steel needles of the probe and thermocouple wires embedded in the probe’s needles are significantly higher than the surrounding soil. Heat conduction through stainless steel needle and thermocouple wires could cause uncertainty in temperature measurement. An analysis was done to estimate the temperature measurement uncertainty as a results of heat conduction along a T-TDR probe. The effect of heat conduction on temperature measurement was evaluated by

Now, based on the data in Figs. 12 and 13, the uncertainties of volumetric moisture contents at Sr = 0.25, Sr = 0.5 andSr = 1.0 can be calculated to be respectively 22.5%, 9.6% and 5.8%. The above uncertainty values are based on theoretical uncertainty analysis (Eq. (10)). In actual situation, the differences between the measured volumetric moisture contents using the heat pulse method and Eq. (9) and prepared soil volumetric moisture contents atSr = 0.25, 0.5 and 1.0 are found to be ± 11.7%, ±4.8% and ± 2.7%, respectively, for Matilda soil (ON-3), which are about half of the theoretical uncertainties.

ð11Þ

In Eqs. (10) and (11), both C of wet soil and C dry are measured by the heat pulse method. Based on the uncertainty analysis in Section 4.1, the average uncertainty of C dry is obtained as dC dry C dry

¼ 3:9%, ranging from 4:2% at 90 °C to 3:6% at 20 °C. Sim-

"

0:025 1  C dry =C

2

 þ

0:039 C=C dry  1

#1=2

2 þ 0:0002

ð12Þ

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5. Conclusion One-dimensional heat and moisture transfer characteristics of a loamy sand (Matilda soil) was experimentally studied within a vertical soil column at high temperatures. The results were presented for both dry and wet soils. For the case of dry soil, temperature distributions and heat gains/losses at the steady-state conditions along the soil cell at the various temperature levels were investigated. The highest temperature deviation from the LTP was found to be 18.6% at the temperature level of 82.6 °C and the temperature gradient of about 90 °C/m which occurs at around 40 mm from the top of the dry soil column. It was observed that there was higher heat loss in the upper portion of the soil cell due to higher temperature difference between the upper portion of the soil cell and the ambient air. For the case of wet soil, it was observed that the highest difference of heat fluxes between the top and bottom HFMs would not exceed 4.2% and the highest temperature deviation from the LTP in the worst case is not more than 7.7%. The amount of heat loss with respect to the heat transfer through the soil was found to be relatively small; therefore, greater uniformity of heat flux in the radial direction would be achieved along the soil column. Also it was observed that the higher discrepancies of the results occur at higher temperature levels while the temperature differences remain relatively similar. From the results, it was noticed that, until 30 min into the test, the lower region of the soil column was not yet significantly affected by the heat flux from the upper side. It was observed that the heat would take about 30 to 60 min to reach the bottom of the soil column for a temperature difference of 65.4 °C. The moisture contents in the two upper control volumes (control volumes 1 and 2) dramatically dropped over time; while in the two lowest control volumes (control volumes 4 and 5), their moisture contents correspondingly increased. By comparing the results of moisture variations with the results of temperature variations, it can be understood that the significant increase of the temperature gradients in control volumes 1 and 2 was the key factor which induced the rapid moisture transfer out from the control volumes with the thermal vapor diffusion as the main mechanism. A maximum moisture flux of about 0.003 kg
s1
m2 flowed from control volume 1 to control volume 2 at 30 min into the test when the average temperature, temperature gradient and degree of saturation in control volume 1 were about 51 °C, 1002 °C/m and 40%, respectively. The apparatus which was designed and constructed in the present study can be used for more future studies of heat and moisture transfer processes for other types of soils and with different degrees of saturation and orientations of the soil cell. Salinized soils may also be studied. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgements Financial support through a Discovery Grant provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Also the support from the Faculty of Engineering and Architectural Science of Ryerson University through a Dean’s Research Fund-Undergraduate Research Experience (DRF-URE) award for Shekinah Shilesh is much appreciated. Appendix A See Figs. A1 and A2.

Fig. A1. Plot of boundary temperatures versus time as measured by top heat flux meter.

Fig. A2. Plot of boundary temperatures versus time as measured by bottom heat flux meter.

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