Monitoring and Analysing Changes in Temperature and Energy in the Ground with Installed Horizontal Ground Heat Exchangers

The objective of this work was to monitor and analyse temperature changes in the ground with installed linear and Slinky-type horizontal ground heat exchangers (HGHEs), used as low-potential heat pump energy sources. Specific heat flows and specific energies extracted from the ground during the heating season were also measured and compared. The verification results showed that the average daily ground temperatures with the two HGHEs are primarily affected by the temperature of the ambient environment. The ground temperatures were higher than ambient temperature during most of the heating season, were only seldom below zero, and were higher by an average 1.97  ̆ 0.77 K in the ground with the linear HGHE than in the ground with the Slinky-type HGHE. Additionally, the specific thermal output extracted from the ground by the HGHE was higher by 8.45  ̆ 16.57 W/m2 with the linear system than with the Slinky system. The specific energies extracted from the ground over the whole heating season were 110.15 kWh/m2 and 57.85 kWh/m2 for the linear and Slinky-type HGHEs, respectively.


Introduction
According to the Intergovernmental Panel on Climate Change report [1], CO 2 emissions should decrease by 40%-70% during the 2010-2050 period and global temperature increase should be limited by 2 ˝C compared to the level existing before the industrial revolution.The use of heat pumps for room heating and water heating may significantly help reach those ambitious targets.Statistical information of the U.S. Energy Information Administration, Residential Energy Consumption Survey (RECS) [2] shows that the share of energy use in residential and commercial buildings in total energy use in the country exceeds 22%.In this, about 65% energy is spent on room heating, residential house cooling, and hot water heating.Previous research [3] suggested that power systems with heat pumps consume 42%-62% less energy than the conventional heating/cooling systems.In contrast to other renewable sources (solar energy, wind energy), heat pumps transform energy directly between the low-potential energy source and the building without any need for additional heat transfer or accumulation.
Natural low-potential energy sources for heat pumps include air, surface water or groundwater, and ground or rock masses.According to the EHPA statistical report [4], the heat pumps predominating before 2006 were the ground-water type, whereas the air-water type started to predominate after that date.Currently, 61.07% of the installed heat pumps are the air-water type, 33.97% are the ground-water type, 2.84% are the water-water type, and 2.12% use other sources.The air-water pump type seems to owe its large-scale use to the lower investment costs and simple design.The energy savings and the operating costs, however, are not that beneficial.
Energies 2016, 9, 555 2 of 13 In a reversed Carnot cooling cycle, the effect, which is expressed by the heating factor for a heat pump, is higher the smaller the temperature difference is between the cycle heat input and output.Assuming a constant condensation temperature, a higher heating factor can be attained via a higher evaporation temperature.The results of practical testing [5][6][7], as well as modelling [8], have shown that the ground temperatures are higher than the ambient temperatures during the major part of the heating season, whereas the reverse is true during the summer season.Hence, the ground is a convenient, stable, low-potential heat pump source for building heating in winter and for their cooling in summer.
The low-potential heat is extracted from/delivered to the rock/ground by means of vertical ground heat exchangers (VGHEs) or horizontal ground heat exchangers (HGHEs).VGHEs require a minimal land plot area, they work at a high efficiency, and are considered to be among the most stable low-potential energy sources; their installation, however, is very costly.HGHEs, existing in three design variants-linear, helical, or spiral [9], require a larger land area but are less costly.They are a compromise between a high efficiency and the investment costs.Petit and Meyer [10] examined the power and financial parameters of heat pumps using the following low-potential sources: air, HGHEs, and VGHEs.Air, as an energy source for heat pumps, emerged as the poorest of them.VGHEs provided the highest power output and HGHEs exhibited the most convenient heating factor and financial parameters.De Swart and Meyer [11] reported that at low ambient temperatures, the ground-water heat pump type provides a heating power and a heating factor 24% and 20%, respectively, higher than the air-water heat pump type.
Our measurements were aimed to: ‚ Analyse temperature changes in the ground with a linear HGHE and a Slinky-type exchanger during the heating season; ‚ Assess the effect of the HGHE configuration on the temperature values and distribution in the ground; ‚ Assess the effect of the HGHE configuration on the specific heat flows and specific energies extracted from the ground.
The following hypotheses were tested: (a) The ground temperatures will be largely above zero during the heating season for both exchanger types.The ground temperatures in the exchanger area will be rarely below zero; (b) The temperatures of the ground with the linear HGHE will be higher than those with the Slinky-type exchanger; (c) The specific heat flows and specific energies extracted from the ground by the HGHE will be higher for the linear HGHE type than for the Slinky type.
The temperature distribution across the ground, the temperature gradients, and the heat flow densities shared between the ground surface and the surrounding environment were investigated by Popiel et al. [12].Heat energy extraction from the ground, specific heat output of a linear HGHE and a Slinky-type HGHE, and the effect of the incident solar radiation on the ground energy balance were studied in detail by Wu et al. [13].Garcia et al. [14] examined the interaction between the ground and an HGHE and found that heat extraction by the HGHE had a pronounced effect not only on the temperature, but also on the moisture, of the ground.The importance of knowledge of the ground temperature and of the climatic data of the ambient environment and their changes throughout the year, with respect to the HGHE configuration design, is stressed in the publication by Hepburn et al. [15], who examined the power and sustainability of HGHEs as low-potential energy sources for heat pumps depending on the ground temperatures and heat parameters.Extensive measurements resulted in a deeper insight into the effects of heat extraction by an HGHE and of the climatic conditions on the ground temperatures.Sanaye and Niroomand [16] engaged themselves in design optimisation and use Energies 2016, 9, 555 3 of 13 of different configurations of linear HGHEs in relation to the ground temperature, extracted energy flows, and use of ground source heat pump (GSHP) systems, while Wu et al. [13] examined the design and operation of Slinky-type HGHEs with respect to similar parameters and conditions.Zarrella and De Carli [17] paid thorough attention to the impact of the interaction between the ground surface and environment on the performance of HGHE and on the effect of the heat pump.They created a model of thermal resistances and capacities respecting the state of the environment, solar radiation intensity, heat transfer via the radiation of the Earth's surface to the sky, and the influence of the spacing of tubes of a spiral heat exchanger.They analysed the model in detail and verified it in operational mode.The simulation results showed good agreement with measurements and also showed an insignificant effect of the spacing of tubes of a spiral heat exchanger.
Requirements for the ground temperature with respect to the temperature of the HGHE's heat-transfer fluid are set by the German VDI standard [18].The effects of the ground moisture on the HGHE heat output and on the COP were investigated by Leong et al. [19].Wu et al. [20] examined the temperatures of the ground with HGHEs used as low-potential energy sources for a conventional heat pump with a compressor and for an absorption type heat pump.The factors that affect the important thermal conductivity coefficient of the ground were analysed by Song et al. [21] and by Banks [22].The effect of rainfall on the ground heat parameters and on the HGHE power was in the focus of Go et al. [23].

Measurement Methods
The linear horizontal ground heat exchanger was manufactured from polyethylene piping PE 100RC 40 mm ˆ3.7 mm (LUNA PLAST a. s., Hořín, Czech Republic), resistant to point loads and to the occurrence of cracks.The heat exchanger piping with the total length of 330 m (41.473 m 2 ) was installed at a depth of 1.8 m in 3 loops at a 1 m span.The length of each loop was 54.62 m.Layouts of the HGHE and the locations of the temperature sensors are shown in Figures 1 and 2.
Energies 2016, 9, 555 3 of 13 HGHE and on the effect of the heat pump.They created a model of thermal resistances and capacities respecting the state of the environment, solar radiation intensity, heat transfer via the radiation of the Earth's surface to the sky, and the influence of the spacing of tubes of a spiral heat exchanger.They analysed the model in detail and verified it in operational mode.The simulation results showed good agreement with measurements and also showed an insignificant effect of the spacing of tubes of a spiral heat exchanger.
Requirements for the ground temperature with respect to the temperature of the HGHE's heat-transfer fluid are set by the German VDI standard [18].The effects of the ground moisture on the HGHE heat output and on the COP were investigated by Leong et al. [19].Wu et al. [20] examined the temperatures of the ground with HGHEs used as low-potential energy sources for a conventional heat pump with a compressor and for an absorption type heat pump.The factors that affect the important thermal conductivity coefficient of the ground were analysed by Song et al. [21] and by Banks [22].The effect of rainfall on the ground heat parameters and on the HGHE power was in the focus of Go et al. [23].

Measurement Methods
The linear horizontal ground heat exchanger was manufactured from polyethylene piping PE 100RC 40 mm × 3.7 mm (LUNA PLAST a. s., Hořín, Czech Republic), resistant to point loads and to the occurrence of cracks.The heat exchanger piping with the total length of 330 m (41.473 m 2 ) was installed at a depth of 1.8 m in 3 loops at a 1 m span.The length of each loop was 54.62 m.Layouts of the HGHE and the locations of the temperature sensors are shown in Figures 1 and 2.   The layouts of the Slinky-type HGHE and the sensor locations are shown in Figures 3 and 4. The heat exchanger was manufactured from polyethylene piping PE 100RC 32 mm × 2.9 mm.It was not placed in a sand bed.The heat exchanger piping 200 m total length (20.107 m 2 ) was installed at a depth of 1.5 m in 53 circular loops at a span of 0.38 m.The layouts of the Slinky-type HGHE and the sensor locations are shown in Figures 3 and 4 The layouts of the Slinky-type HGHE and the sensor locations are shown in Figures 3 and 4. The heat exchanger was manufactured from polyethylene piping PE 100RC 32 mm × 2.9 mm.It was not placed in a sand bed.The heat exchanger piping 200 m total length (20.107 m 2 ) was installed at a depth of 1.5 m in 53 circular loops at a span of 0.38 m.An ethyl alcohol/water 1:2 mixture served as the heat-transfer fluid for the two exchangers.The HGHEs used served as energy sources for IVT PremiumLine EQ E17 (Industriell Värme Teknik, Tnanas, Sweden) heat pumps, rated for 17 kW (0/35 °C) heat output.The heat pumps, along with three additional ones, are used for heating (not for cooling) of an administrative building and of the operational halls of VESKOM s.r.o.(=limited liability company) in Prague-Dolní Měcholupy (Czech Republic).
The ground temperatures were measured with GKF 125 and GKF 200 sensors and recorded every 30 minutes by means of ALMEMO 5990 and ALMEMO 2890-9 data acquisition systems.Ambient air temperatures te were measured 2 m above the ground, 20 m far from the horizontal ground exchangers, by using an ALMEMO FHA646AG sensor.An FLA613GS global radiation sensor was used to measure the incident solar radiation intensity.The total heat flow extracted by the horizontal exchangers was measured with MTW 3 (Itron Inc., Liberty Lake, WA, USA) electronic heat consumption meters.
The ground heat parameters-thermal conductivity coefficient λ (W/m•K), specific heat capacity C (MJ/m 3 •K) and temperature conductivity coefficient a (mm 2 /s)-at a temperature t (°C) and volumetric moisture w (%), measured with an ISOMET 2104 instrument (Applied Precision, Bratislava, Slovakia).Volumetric moisture of the ground was measured with soil moisture sensor SM 200 (Delta-T Devices Ltd, Burwell, Cambridge, UK).
The ground in which the HGHEs were installed was defined as Technosol [24].The ground profile consisted of two layers: an arable land layer (approximately 0.25 m) and a layer of detritus (approximately 2 m) consisting of dark-brown sand-clay soil, coarse-grain gravel, crushed rock, and brick debris.
The measurements were performed from 17 September 2012 and covered one heating season.

Method to Determine the Development of the Average Daily Temperatures
The development of the rock mass' average daily temperatures during the heating season can be described by Equation (1) which is based on the equation of free undamped oscillation of a mass point [6,25]: where: An ethyl alcohol/water 1:2 mixture served as the heat-transfer fluid for the two exchangers.The HGHEs used served as energy sources for IVT PremiumLine EQ E17 (Industriell Värme Teknik, Tnanas, Sweden) heat pumps, rated for 17 kW (0/35 ˝C) heat output.The heat pumps, along with three additional ones, are used for heating (not for cooling) of an administrative building and of the operational halls of VESKOM s.r.o.(=limited liability company) in Prague-Dolní Měcholupy (Czech Republic).
The ground temperatures were measured with GKF 125 and GKF 200 sensors and recorded every 30 minutes by means of ALMEMO 5990 and ALMEMO 2890-9 data acquisition systems.Ambient air temperatures t e were measured 2 m above the ground, 20 m far from the horizontal ground exchangers, by using an ALMEMO FHA646AG sensor.An FLA613GS global radiation sensor was used to measure the incident solar radiation intensity.The total heat flow extracted by the horizontal exchangers was measured with MTW 3 (Itron Inc., Liberty Lake, WA, USA) electronic heat consumption meters.
The ground heat parameters-thermal conductivity coefficient λ (W/m¨K), specific heat capacity C (MJ/m 3 ¨K) and temperature conductivity coefficient a (mm 2 /s)-at a temperature t ( ˝C) and volumetric moisture w (%), measured with an ISOMET 2104 instrument (Applied Precision, Bratislava, Slovakia).Volumetric moisture of the ground was measured with soil moisture sensor SM 200 (Delta-T Devices Ltd, Burwell, Cambridge, UK).
The ground in which the HGHEs were installed was defined as Technosol [24].The ground profile consisted of two layers: an arable land layer (approximately 0.25 m) and a layer of detritus (approximately 2 m) consisting of dark-brown sand-clay soil, coarse-grain gravel, crushed rock, and brick debris.
The measurements were performed from 17 September 2012 and covered one heating season.

Method to Determine the Development of the Average Daily Temperatures
The development of the rock mass' average daily temperatures during the heating season can be described by Equation (1) which is based on the equation of free undamped oscillation of a mass point [6,25]: where: Energies 2016, 9, 555 6 of 13 t GR = ground temperature ( ˝C) t G = mean ground temperature ( ˝C) ∆t A = oscillation amplitude around the temperature t G (K) τ = number of days from the start of measurement (day) ϕ = initial phase of oscillation (rad) Ω = angular velocity (2π/365 rad/day) This equation expresses nonlinear regression of y on x, and so the degree of tightness between the two parameters was characterized by the determination index I 2 yx (Bowerman et al. [26]).Equation ( 1) expresses only the course of the ground temperature in the HGHE area during the heating season.It does not aim to analyse the interaction between the ambient environment and the ground temperature in the HGHE area.However, it also includes the influence of climatic conditions on the ground.

Basic Ground Heat Parameters
The heat parameters were measured in the ground with a Slinky-type HGHE in June 2012, during the exchanger stagnation period.The results are listed in Table 1.

Ground Temperatures During the Heating Season
Table 2 summarizes the average daily temperatures of the ground with the linear HGHE and the parameters in Equation (1) for the heating season.The average daily temperatures during the heating season calculated from Equation (1) are plotted in Figure 5.The left vertical axis shows the temperatures t LR of the ground with linear HGHE.The right vertical axis t e shows the ambient temperature.
Both the data in Table 2 and the plot in Figure 5 demonstrate that the average daily temperature of the ground with the linear HGHE decreases toward the ground surface.The lowest temperatures were not attained in the HGHE; instead, they were observed near the mass surface.The oscillation amplitude ∆t A around the mean ground temperature t G increases toward the ground surface.Both trends confirm an appreciable effect of ambient temperature t e .Some effect of the linear HGHE on the ground temperature is indicated by the difference between the mean ground temperature t G near the HGHE and the mean reference temperature t L11 , measured at a distance of 12.5 m from the HGHE centre, as well as by the difference between the oscillation amplitudes ∆t A in the ground with the HGHE and beyond it.Table 3 and Figure 6 show the average daily ground temperatures during the heating season for the setting with the Slinky-type HGHE and appropriate parameters in Equation ( 1 6 show the average daily ground temperatures during the heating season for the setting with the Slinky-type HGHE and appropriate parameters in Equation (1).The left vertical axis shows the temperature t SR of the ground with Slinky-type HGHE.The right vertical axis shows ambient temperature t e .The decreasing trend of the average daily ground temperature and the increasing trend of oscillation amplitude ∆t A around the mean ground temperature t G in the setting with the Slinky-type HGHE are similar to in the setting with the linear HGHE, although the former HGHE extracts heat from an appreciably smaller volume than the latter.The smaller mass volume is mirrored in the lower mean daily temperatures.
The determination index values I 2 yx exhibit adequate precision of Equation ( 1), describing the ground temperature development during the heating season, for both HGHE types.
The decreasing trend of the average daily ground temperature and the increasing trend of oscillation amplitude ∆t A around the mean ground temperature t G in the setting with the Slinky-type HGHE are similar to those in the setting with the linear HGHE, although the former HGHE extracts heat from an appreciably smaller mass volume than the latter.The smaller mass volume is mirrored in the lower mean daily temperatures.The difference of the average daily ground temperature t L1 -t S1 during the heating season, at a distance of 0.2 m below HGHEs was ∆t 1 = 2.28 ˘1.13 K.The ground temperature differences decrease toward the surface of ground.The difference of the average daily temperatures at a depth of 0.2 m below the surface was ∆t 9 = t L9 ´tS9 = 1.13 ˘0.71 K.
The determination index values I 2 yx exhibit adequate precision of Equation ( 1), describing the ground temperature development during the heating season, for both HGHE types.

Heat Flows and Specific Energies Extracted from the Ground
Figure 7 displays plot of the ground temperatures t L2 , t S2 in the HGHE area, the reference ground temperatures t L11 , t S10 beyond the HGHE area, and ambient temperatures t e during the heating season.Furthermore, the plots in Figures 8 and 9 include the thermal output values q ,S , q ,L and specific energies q d,S q d,L per m 2 of the HGHEs' external heat exchange area, and also the intensity I s.r and energy I d,s.r. of the incident solar radiation during a day per m 2 .Specific thermal outputs q L , q S were determined based on the measured volume flow of heat transfer fluid, specific heat capacity and heat transfer fluid temperature difference at the inlet and outlet of the evaporator heat pump.Specific energies q d,L , q d,S extracted from the ground were determined based on the specific thermal output and heat pump operation time at a certain power output.The results are summarised in Table 4.          Development of the thermal outputs q S and energies q dS during the heating season-Slinky-type HGHE.The plots in Figure 7 and the summary data in Table 2 show that the average daily ground temperatures near the HGHEs were below zero.Minimum ground temperatures in the HGHE area were reached almost on the same days of the heating season.The minimum average daily temperature was t L2 = 2.00 ˝C (190 days) and t S2 = ´0.19˝C (192 days) with linear HGHE and the Slinky-type HGHE, respectively.The temperatures were decreasing on average 1 K per 12.55 days and per 11.36 days with linear HGHE and Slinky-type HGHE, respectively.Due to the increasing ambient temperature at the end of the heating period, the average daily ground temperature in the HGHE area was also increasing.The ground temperatures t L2 , t S2 in the HGHE area at the end of the heating period differed by only 0.64 K and reached approximately 31.5% of the ground temperatures at the beginning of the heating season.
The average daily ground temperatures in the HGHE area were 1.97 ˘0.77K higher for the linear HGHE than for the Slinky-type HGHE, while the total specific energy extracted from the HGHE during the heating season was nearly twice as high for the linear HGHE than for the Slinky-type HGHE.The ground temperatures in the HGHE area during the heating season were 68.8% (linear HGHE) and 53.6% (Slinky-type HGHE) higher than the ambient temperature t e .VGHEs with a single U-tube exchanger (2 mm ˆ40 mm ˆ3.7 mm) and with a double U-tube exchanger (4 mm ˆ32 mm ˆ2.9 mm) were also examined at the same site, at the same ambient temperatures, and at the same heat-transfer fluid concentration.The average rock mass temperatures were lower for either of the VGHEs than for the linear HGHE.The rock mass temperatures in the VGHE area were higher than the ambient temperatures t e only during 59.72% (single U exchanger) and 62.96% (double U exchanger) of the heating season.
The reference daily rock mass temperature t L11 measured 12.5 m from the centre of the linear HGHE heat exchange area was higher by an average 2.22 ˘1.23 K than the temperature t L2 within the linear HGHE area.The temperature t S10 measured 15.6 m from the centre of the Slinky-type HGHE heat exchange area was higher by an average 3.05 ˘1.41 K, compared to temperature t S2 .
The specific energies q d extracted during a day of the heating season were 239.91 ˘198.35Wh/m 2 ¨day in average higher with the linear HGHE than with the Slinky-type HGHE.The specific energies extracted from the ground over the entire heating season were 110.15 kWh/m 2 (linear HGHE) and 57.85 kWh/m 2 (Slinky-type HGHE).Additionally, the average specific thermal outputs q L extracted from the ground by the linear HGHE were higher by 8.45 ˘16.57W/m 2 than q S extracted by the Slinky-type HGHE.
The better results obtained with the linear HGHE are presumably due to the larger mass volume from which the low-potential energy was extracted.
The importance of solar radiation for the ground energy potential can be documented by the total solar radiation energy hitting the ground surface during the heating season, which is I Σd,s.r.= 350 kWh/m 2 .

Figure 1 .
Figure 1.Ground layout of the linear HGHE and locations of the temperature sensors (Unit: mm).Figure 1. Ground layout of the linear HGHE and locations of the temperature sensors (Unit: mm).

Figure 1 .
Figure 1.Ground layout of the linear HGHE and locations of the temperature sensors (Unit: mm).Figure 1. Ground layout of the linear HGHE and locations of the temperature sensors (Unit: mm).

Figure 2 .
Figure 2. Layout of the linear HGHE and locations of the temperature sensors (Unit: mm).

Figure 3 .
Figure 3. Ground layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).

Figure 2 .
Figure 2. Layout of the linear HGHE and locations of the temperature sensors (Unit: mm).

13 Figure 2 .
Figure 2. Layout of the linear HGHE and locations of the temperature sensors (Unit: mm).

Figure 3 .
Figure 3. Ground layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).Figure 3. Ground layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).

Figure 3 .
Figure 3. Ground layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).Figure 3. Ground layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).

Figure 4 .
Figure 4. Layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm).

Figure 4 .
Figure 4. Layout of the Slinky-type HGHE and locations of the temperature sensors (Unit: mm). tLR3

Figure 5 .
Figure 5. Plot of the average daily ground temperatures during the heating season-linear HGHE.

Table 3 .
).The left vertical axis shows the temperature tSR of the ground with Slinky-type HGHE.The right vertical axis shows ambient temperature te.The decreasing trend of the average daily ground temperature and the increasing trend of oscillation amplitude tA around the mean ground temperature G t in the setting with the Slinky-type HGHE are similar to those in the setting with the linear HGHE, although the former HGHE extracts heat from an appreciably smaller volume than the latter.The smaller mass volume is mirrored in the lower mean daily temperatures.The determination index values exhibit adequate precision of Equation (1), describing the ground temperature development during the heating season, for both HGHE types.Temperatures of the ground with the Slinky-type HGHE during the heating season and the appropriate parameters in Equation (1).Temp.(°C) Average (°C) Min.(°C) Max.(°C) tA (K)  (rad) G t (°C)

Figure 5 .
Figure 5. Plot of the average daily ground temperatures during the heating season-linear HGHE.

Figure 6 .
Figure 6.Plot of the average daily ground temperatures during the heating season-Slinky-type HGHE.

Figure 6 .
Figure 6.Plot of the average daily ground temperatures during the heating season-Slinky-type HGHE.

Figure 7 .
Figure 7. Ground temperatures in the HGHE area and ambient temperature during the heating season.

Figure 8 .
Figure 8. Development of the thermal outputs qL, Is.r. and energies qd,L, Id,s.r.during the heating season-linear HGHE.

Figure 9 .
Figure 9. Development of the thermal outputs qS and energies qdS during the heating season-Slinky-type HGHE.

Figure 7 . 13 Figure 7 .
Figure 7. Ground temperatures in the HGHE area and ambient temperature during the heating season.

Figure 8 .
Figure 8. Development of the thermal outputs qL, Is.r. and energies qd,L, Id,s.r.during the heating season-linear HGHE.

Figure 9 .
Figure 9. Development of the thermal outputs qS and energies qdS during the heating season-Slinky-type HGHE.

Figure 8 . 13 Figure 7 .
Figure 8. Development of the thermal outputs q L , I s.r. and energies q d,L , I d,s.r.during the heating season-linear HGHE.

Figure 8 .
Figure 8. Development of the thermal outputs qL, Is.r. and energies qd,L, Id,s.r.during the heating season-linear HGHE.

Figure 9 .
Figure 9. Development of the thermal outputs qS and energies qdS during the heating season-Slinky-type HGHE.Figure 9.Development of the thermal outputs q S and energies q dS during the heating season-Slinky-type HGHE.
Figure 9. Development of the thermal outputs qS and energies qdS during the heating season-Slinky-type HGHE.Figure 9.Development of the thermal outputs q S and energies q dS during the heating season-Slinky-type HGHE.

Table 1 .
Basic thermal parameters of the ground.

Table 2 .
Temperatures of the ground with the linear HGHE during the heating season and the appropriate parameters of Equation (1).

Table 3 and
Figure

Table 3 .
Temperatures of the ground with the Slinky-type HGHE during the heating season and the appropriate parameters in Equation (1).

Table 4 .
Average and extreme values of the ambient temperatures, specific thermal outputs, and energies during the heating season.