Geothermics 104 (2022) 102442

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Geothermics
journal homepage: www.elsevier.com/locate/geothermics

Transient assessment of an earth air heat exchanger in warm

climatic conditions
Yousef Belloufi a, b, *, Sakina Zerouali c, Amar Rouag d, e, Faris Aissaoui f, b, Rachid Atmani b,
Abdelhafid Brima b, Noureddine Moummi b
a
Université Kasdi Merbah Ouargla, Faculté des Hydrocarbures, des Energies Renouvelables, des Sciences de la Terre et de l’Univers, Département de Forage et Mécanique
des Chantiers Pétroliers, BP 511 Ouargla 30000, Algeria
b
Laboratoire de Génie Mécanique (LGM), Université Mohamed Khider Biskra, BP 145 Biskra 07000, Algeria
c
Université Mostefa Ben Boulaïd Batna 2, Faculté de Technologie, Département de Socle Commun Science et Technique, BP 05078 Fesdis-Batna, Algeria
d
Université Kasdi Merbah Ouargla, Faculté des Hydrocarbures, des Energies Renouvelables, des Sciences de la Terre et de l’Univers, Département des Energies
Renouvelables, BP 511 Ouargla 30000, Algeria
e
Laboratoire de Génie Energétique et Matériaux (LGEM), Université Mohamed Khider Biskra, BP 145 Biskra 07000, Algeria
f
Université de Ghardaïa, Faculté des sciences et de la technologie, Département d’Automatique et Electromécanique, Ghardaïa 47000, Algeria

A R T I C L E I N F O A B S T R A C T

Keywords: The Earth Air Heat Exchanger (EAHE) is a promising passive technique that utilises shallow geothermal energy to
Earth air heat exchanger improve the thermal comfort in buildings. EAHE has the potential to minimize the amount of electrical energy
Transient thermal performance used by traditional air conditioning systems. The aim of this research is to examine the thermal performance of
Continuous operation
the EAHE under continuous operation. A transient numerical model was developed using the implicit finite
Derating factor
Summer cooling
difference method. Afterwards, the thermal performance was evaluated by using the means of derating factor. In
addition, an experimental setup is realised in Biskra University (Algeria) to take measurements during cooling
period. According to numerical calculations, the high thermal performance of EAHE is dependant on high
thermal conductivity of soil and low air velocity. The values of the derating factor in the studied cases ranged
from 0% to 35% that can mislead the design of the EAHE if ignored. The experimental findings revealed that for
3.5 m/s of air velocity, the maximum air temperature drop can reach up 19 ◦ C. It is noticed that the initial 33 m
of the pipe can provide 91% of the whole reduction in air temperature. In extreme real cases, the maximum air
temperature increasing does not exceed 0.85 ◦ C during all 95 h. Consequently, ambient temperature decreases
during night operation and then cools the heated subsoil and assists the soil to recover its cooling capacity.

occupation (less than 1 m2) and therefore making it suitable for usage in
1. Introduction densely build regions (Zhou et al., 2016; Xi et al., 2017). Furthermore,
the vertical EAHE has a higher geothermal energy use efficiency and a
In recent decades, the world has suffered from the very high con­ simpler discharge of air condensate water to avoid the growth of bac­
sumption of electrical energy required for air conditioning. This high teria, which will improve the air supply quality (Liu et al., 2019c; Liu
consumption is clearly appear in the Saharan areas, especially during the et al., 2021). In addition, the vertical EAHE plays a very important role
cooling period. To meet these energy challenges, several cooling tech­ to enhance heat transfer efficiency and therefore improve the EAHE’s
niques using alterative energies can be implemented. EAHEs are part of thermal performance (Bozis et al., 2011; Jalaluddin et al. 2011). On the
geothermal energy that refers heat energy stored in the subsoil, where other hand, amongst the drawbacks of vertical EAHE is that their layout
the energy coming from the subsoil is mainly consumed in form of heat. necessitates a significant amount of drilling depth, which increases the
(Liu et al., 2019a; Liu et al., 2019b) proposed and designed a vertical expense of a geothermal ventilation system. Horizontal EAHE could be
EAHE based on a buried vertical U-tube. The main advantages of the employed if there are open regions (Zhelykh et al., 2016). Śliwa et al.
vertical EAHE compared to the horizontal EAHE lie in its deeper pipe (2018) discussed other disadvantages of the vertical EAHE such as: the
depths (more than 15 m). This allow soil temperatures to stabilize at the need for a drilling rig with elevators, a high lifting capacity and
needed source temperature, as well as the fact that it requires less land implementation of centralizers, which must ensure that the two pipes

* Corresponding author.
E-mail address: yousef_belloufi@yahoo.fr (Y. Belloufi).

https://doi.org/10.1016/j.geothermics.2022.102442
Received 7 February 2022; Received in revised form 1 May 2022; Accepted 4 May 2022
Available online 8 May 2022
0375-6505/© 2022 Elsevier Ltd. All rights reserved.
Y. Belloufi et al. Geothermics 104 (2022) 102442

respectively.
Nomenclature Rouag et al. (2018) developed a new semi analytical method called
‘RBM’ to design EAHE system. The calculation algorithm is based on the
Cp Specific heat [J/Kg. ◦ C] Bessel functions to estimate the soil temperature. The authors have fixed
h Convective heat transfer coefficient [W/m2. ◦ C] the heat flux at the inner pipe diameter for the full time step. The results
m Mass [Kg] showed that the soil radius can reach 55 cm at constant inlet air tem­
R Thermal Resistance [ ◦ C/W] perature condition in the case of 6 h of operation. Mehdid et al. (2018)
Ri Thermal resistance per unit length [ ◦ C /W.m] used the RBM model proposed by Rouag et al. (2018) to predict the air
r1 Pipe inner radius [m] temperature under transient conditions. Moreover, an experimental
r2 Pipe outer radius [m] measurement is used to validate the developed model ‘GRBM’. The
r3 Undisturbed soil radius [m] authors summarized that this model can be used as practical tool to
s Surface [m] design EAHE system. Belloufi et al. (2017) investigated the EAHE’s
t Time [s] transient thermal behaviour in summer cooling in continuous operation
T1 Air temperature at the pipe inlet [ ◦ C] mode. They validated the numerical results with measured air temper­
Ta Flowing air temperature [ ◦ C] atures on site of Biskra University, Algeria. Due to high soil conductivity,
Ti Undisturbed soil temperature [ ◦ C] the continuous operation of 71 h had no discernible influence on the
Tsoil Soil temperature [ ◦ C] outlet air temperature. Menhoudj et al. (2018) investigated the influ­
u Air flow velocity [m/s] ence of pipe material on EAHE’s thermal performance in cooling mode
in Algeria. Results showed that the decrease in air temperature can reach
Greek symbols 6.5 ◦ C for zinc pipe and 6 ◦ C for PVC pipe. Therefore, the authors noted
α Soil thermal diffusivity [m2/s] that the pipe material is not considered in the evaluating of thermal
λsoil Soil thermal conductivity [W/m. ◦ C] performance of EAHE. At this regards, a lot of parameters including pipe
ρ Air density [kg/m3] material are analysed by Rosa et al. (2018). They also noticed that the
EAHE Earth air heat exchanger type of pipe have no effect on the performance of the system due to very
low increase in COP. However, the most important factor is the air ve­
locity. Hamdane et al. (2021) presented a theoretical approach to
calculate the outlet air temperature. The authors used finite difference
are stable inside the borehole. All these factors affect also the mainte­
method to estimate the axial air temperature and the two dimensional
nance cost comparing to horizontal EAHE, which is intended for cooling
soil temperature in steady and transient conditions respectively. They
and ventilation buildings.
concluded that in comparison to prior models, the model is less sensitive
Several researchers have studied horizontal EAHE systems, to eval­
to the operation duration as well as the periodic temperature condition
uate and enhance its thermal behaviour, whether using theoretical
at the EAHE’s inlet.
modelling or by experiments. Mihalakakou (2003) used a dynamic and
Hermes et al. (2020) analysed the thermal behaviour of three
deterministic model to predict the EAHE’s heating potential. He vali­
different EAHEs installations located in Rio Brande, Brazil. They used
dated experimentally the estimated values of soil temperature, the
finite volume computational model in the simulation. From the results,
author concluded that the air temperature at the outlet of EAHE could be
it noticed that 2 m depth is considered an ideal pipe placement depth
efficiently simulated by the neural network and it affected by the soil
and can increase the EAHE thermal potential in cooling and heating
temperature. (Benhammou and Draoui 2015; Cuny et al., 2019; Minaei
periods. In intermittent and continuous operation modes, Mathur et al.
et al., 2021) observed that heat transfer decreases by increasing pipe
(2015b) compared the soil self-recovery ability and thermal saturation.
length and the increase the mass flow rate causes saturation of soil. Lee
To develop the EAHE model, the authors used a three-dimensional
and Strand (2008) presented the heating and cooling potential in
simulation software package, ANSYS 14.5. They concluded that soil
buildings using an EAHE, they concluded that no remarkable benefits in
temperature can recovered more in the continuous mode than inter­
using EAHE more than 70 m of length. According to Ahmed et al. (2016)
mittent if the nighttime ambient air temperature is significantly lower
EAHE length parameter dominates other thermo-physics parameters of
than the soil temperature. Mathur et al. (2015a) examined the EAHE’s
the system (pipe material, air velocity and soil conductivity) that affect
thermal performance in transient conditions. Three intermittent opera­
the EAHE thermal performances. Niu et al. (2015) tested five air ve­
tion modes are considered for three soil thermal conductivity. Three
locities (0.5, 1.0, 2 and 2.5 m/s) in cooling mode, they found that low
dimensional transient numerical model was applied in the CFD analysis.
flow velocity of 0.5 m/s provides more time to evacuate its heat to
It noticed that EAHE with higher soil conductivity can be run continu­
nearer soil to the EAHE and thus a high temperature drop.
ously while EAHE with poor soil conductivity can be used in intermittent
Rodrigues et al. (2015) presented a numerical study to enhance the
mode. Fazlikhani et al. (2017) developed a theoretical steady state
thermal performance of an EAHE by using the Constructal Design
model to assess the effect of various factors on the heating and cooling
Method. It was found that the increasing of buried pipes number and
potential of EAHE in cold (Hamadan) and hot-arid (Yazd) climates
keeping same air mass flow rate could enhance the thermal performance
respectively. In the winter, the potential for rising air temperature in
of EAHE up to 73% and 115% for cooling and heating respectively.
Hamadan and Yazd was found to be in the range of 0.1 - 17 ◦ C and 0.2 -
Kumar et al. (2003) studied numerically EAHE with 80 m of tube length.
11.2 ◦ C respectively. On the other hand in cooling period, the air tem­
They concluded that the used system could create 296 kWh heating
perature decreases of 5.7 to 11.1 ◦ C and 1.3 to 11.4 ◦ C respectively. They
potential and 456 kWh cooling potential and can keep the room tem­
concluded that, geothermal EAHE have the ability to take up the role of
perature at 27.65 ◦ C. Misra et al. (2013b) used CFD analysis and
cooler in arid and hot climate.
derating factor to evaluate EAHE system according to the following
Zajch and Gough (2021) relies on a climate-based approach and 492
parameters: soil thermal conductivity, pipe length, inlet air velocity and
weather files to compare the heating and cooling potential in Canada for
operation duration. The results showed that high air velocity and poor
different seasonal variation scenarios. They investigate EAHE’s seasonal
soil conductivity affect the EAHE’s thermal behaviour. Barakat et al.
sensitivity to changes in air or soil temperatures caused by natural
(2016) presented a numerical study to evaluate the thermal perfor­
changes in soil surface energy partitioning. Yang and Zhang (2015)
mance of EAHE. The system that is assembled to gas turbine is used to
proposed an analytical solution for evaluating the thermal performance
enhance the power performance. The results reveal that there is an in­
of EAHE under periodic fluctuations in both soil and inlet ambient air
crease in both output power and efficiency with values of 4.8% and 9%
temperatures. The authors found that the coupling of EAHE with

2
Y. Belloufi et al. Geothermics 104 (2022) 102442

2. Mathematical models

The following assumptions have been considered to simplify the

thermal calculation (Belloufi 2017; Mehdid et al., 2018):

• Thermo-physical properties of air and soil are constant.

• Along the buried pipe, the convective heat transfer coefficient is
constant.
• Soil moisture is neglected.
• From a distance δ of the buried pipe surface, the soil temperature
remains constant.
• Longitudinal conduction is neglected.

Fig. 1. One-dimensional scheme of the EAHE.

2.1. Modelling the eahe system

The transient one-dimensional soil temperature is governed by the

following Fourier’s equation:

∂2 Tsoil 1 ∂Tsoil
= (1)
∂z2 α ∂t
Considering the following initial and boundary conditions:
Tsoil (z = 0, t) = Ti +Acos[w(t − t0 )]
Tsoil (z→∞, t) =Ti (2)
Tsoil (z, t = 0) =Ti
Where Tsoil is the soil temperature, α is the soil thermal diffusivity, Ti
is the undisturbed soil temperature, A is the soil temperature amplitude
and w = 2π/365 [rad/day] is the angular frequency.
Fig. 2. Discretized domain of the EAHE. The solution of this problem yields the following equation for
calculating soil temperature (Belloufi 2017):
building can maintain a building’s thermal comfort. (Yang et al., 2016; ( √̅̅̅̅̅ ) [ √̅̅̅̅̅̅ ]
w w
Wei and Yang 2019) developed mathematical models for analysing the Tsoil (z, t) = Ti + Aexp − z cos w(t − t0 ) − z (3)
2a 2α
heat transfer in flat rectangular and circular EAHEs under harmonic
fluctuations, and they compared the differences in thermal perfor­ Then, transient one-dimensional energy balance equation has been
mances. It was showed that the outlet air temperature fluctuation of the adopted to calculate outlet air temperature as shown in Fig. 1.
flat rectangular EAHE was lower, and the wall temperature of EAHE pipe The heat transfer between the soil and the air inside the pipe can be
was more stable compared to the circular EAHE. An experimental study expressed as follows:
carried out by (Wei et al., 2020; Wei et al., 2021) of an EAHE integrated
DTa
to a building to provide space cooling and heating. It was shown that the mcpair = q1 − q2 − q3 (4)
Dt
EAHE can be used as a pre-conditioning system to heat air in cold cli­
mates and to cool air in hot regions. On the other hand, the EAHE system From Eq. (4), it can obtain:
has been found to be highly effective in diverse climates. (
∂Ta ∂Ta
)
∂Ta ∂Ta (Tsoil − Ta )
Through the literature review above, it’s clear that duration opera­ mcpair +u = − λair s | + λair s | + (5)
∂t ∂x ∂x l ∂x l+Δl Rtotal
tion and thermo-physical properties have an important influence on the
functioning of EAHE system. Furthermore, not much literature is Where the total thermal resistance is denoted by the symbol Rtotal:
available on the concept of soil thermal saturation and EAHE’s self-
Rtotal = Rsoil + Rpipe + Rcv (6)
recovery, which is an important factor that determines the useful
EAHE’s operation duration. On the other hand, few researches studied Where:
experimentally and theoretically in detailed manner the effect of these Rsoil = 2π. 1
λsoil . Δl ln(r3 (t)/r2 ) is the soil thermal resistance;
parameters on the performance of EAHE to achieve an optimum design 1
Rpipe = 2π. λpipe . Δl ln(r2 /r1 ) is the pipe thermal resistance;
as function of time. 1
Rcv = 2π h r1 Δl is the convective thermal resistance;
At this regards, the main objective of this work is to suggest both
experimental and numerical analyses to predict the EAHE’s thermal h = (Nu k)/(2 r1 ) is the heat transfer coefficient by convection inside
performances during extreme summer conditions. The influence of soil the pipe;
properties, air velocity and continuous functioning were analysed. The Nu = 0.023Re 0.8 Pr 0.3 is the Nusselt number (Al-Ajmi et al., 2006; de
parameter called Derating Factor ’DF’ using the temperature decrease Jesus Freire et al. 2013; Barakat et al., 2016);
under steady and transient conditions is determined. An experimental Re = ρu/μ is the Reynolds number (Al-Ajmi et al., 2006);
√̅̅̅̅̅̅̅̅̅̅̅̅̅
setup was realized at the University of Biskra (Algeria) to examine the r3 (t)= α.t/π is the distance between the external pipe surface and
effect of continuous operation mode on thermal performance in hot and undisturbed soil (Hollmuller 2003).
arid climatic conditions. Besides, the self-recovery capacity of the soil is Eq. (5) reduced by taking into account that longitudinal conduction
investigated to predict the thermal deterioration with time. For this and heat transfer by convection are neglected.
reasons, the experimental measurements were conducted during the ( )
∂Ta ∂Ta (Tsoil − Ta )
summer period from July to September 2013. ρscpair +u = (7)
∂t ∂x Ritotal

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Y. Belloufi et al. Geothermics 104 (2022) 102442

Table 2
Physical and thermal properties used in the proposed model.
Physical and thermal parameters Values
3
Air density (kg/m ) 1.2
Air flow velocity (m/s) 3.5
Internal diameter of the pipe (m) 0.1
Pipe thermal conductivity (W/m. ◦ C) 0.17
Soil thermal conductivity (W/m. ◦ C) 1.25
Specific heat capacity of air (J/Kg. ◦ C) 1000
Undisturbed soil temperature ( ◦ C) 26

Ta (t = 0) = Tsoil (Philippe et al., 2009; Mnasri and Younès 2010;

Diersch et al., 2011).
To solve Eq. (8), both the time and space domains represented in
Fig. 3. Experimental setup of EAHE. Fig. 2 are discretized using implicit finite differences method. In the
discretization, the centred finite differences method is used up to node
N-1 and the left finite differences method is employed to calculate the
final node.
If the index ‘i’ denotes the variable ‘x’ and the index ‘k’ denotes the
variable ‘t’, the implicit finite differences equation will be getting by
writing the second member of Eq. (8) at next time (k + 1) where the
solution is not known, which gives (Nougier 1987):
1 ( ) u ( ) 1 Tsoil
Ti,k+1 − Ti,k = − Ti+1,k+1 − Ti− 1,k+1 − Ti,k+1 + (9)
Δt 2Δx γ γ
Δt = L/u represents the required time for a slice of air to travel the
entire length of the pipe.
After rearrangement, it obtain:
( )
Δt u Δt Δt u Δt
Ti,k + Tsoil = − Ti− 1,k+1 + + 1 Ti,k+1 + Ti+1,k+1 (10)
γ 2Δx γ 2Δx
Fig. 4. Detailed placement of the air temperature sensor in the EAHE.
This discretized equation is designed for a mesh going from the
second node to the node N-1
For the last node N (outlet air temperature), the left finite differences
is applied to Eq. (8) as follows:
1 ( ) u ( ) 1 Tsoil
TN,k+1 − TN,k = − TN,k+1 − TN− 1,k+1 − TN, k+1 + (11)
Δt Δx γ γ
Therefore, the equation giving the air temperature in the final node N
is written as follows:
( )
Δt u Δt u Δt Δt
TN,k + Tsoil = − TN− 1,k+1 + + + 1 TN, k+1 (12)
γ Δx Δx γ
Eqs. (10) and (12) were solved by the developed program and
Thomas method is applied to calculate the transient temperature of the
air along the EAHE.

Fig. 5. Data acquisition unit. 2.2. Derating factor

To calculate the derating factor DF in thermal performance, the

Table 1 temperature difference in steady state between inlet and outlet of the
Characteristic of measuring equipment. pipe is considered as reference for evaluating EAHE’s thermal perfor­
Equipment Range of measuring Precision Resolution mance in transient condition. The derating factor DF is calculated using
the air temperatures decrease obtained in both transient and steady state
Propeller anemometer 0.3 - 35 m/s 3.1 – 35 m/s 0.1 m/s
0.3 – 3 m/s 0.01 m/s conditions (Bansal et al., 2013; Benhammou and Draoui 2015).
Temperature detector ‘RTD’ − 50 to 200 C
◦
10− 5 ◦ C
(Tinlet − Toutlet )transient state
DF = (13)
(Tinlet − Toutlet )steady state
Ritotal is the thermal resistance divided by unit length (Δl).
Where:
∂Ta ∂Ta (Tsoil − Ta )
=− u + (8)
∂t ∂x γ Toutlet in transient state is derived from Eq. (10).
Toutlet in steady state is derived from the solution of Eq. (8) in steady
With γ = ρ π r12
cpair Ritotal
state as follows (Belloufi 2017).
Choosing the following boundary conditions in order to solve Eq. (8).
dTa (Tsoil − Ta )
Ta (x = 0) = T1 ρπ r12 cpair u = (14)
dx Ritotal

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Y. Belloufi et al. Geothermics 104 (2022) 102442

Table 3
Experimental air temperature variation inside the EAHE on days of (23–25 July 2013).
Duration of operation (h : m) Air temperatures inside the EAHE ( ◦ C), u = 2 m/s.
Length of pipe (m)
Inlet 3.63 7.69 11.73 16.04 20.07 24.12 26.37 29.07 33.10 37.01 38.86 40.82 45.10 48.80

09:30 (After 1 h) 39.37 38.00 34.77 32.49 31.30 30.42 29.41 29.18 28.90 28.47 27.97 27.77 27.60 27.23 27.11
13:30 44.15 41.19 36.76 33.62 32.23 31.06 29.84 29.53 29.16 28.67 28.09 27.88 27.70 27.27 27.14
17:30 45.53 42.92 38.07 34.64 33.02 31.64 30.25 29.88 29.43 28.89 28.24 28.01 27.81 27.34 27.21
21:30 39.64 37.97 35.24 33.17 31.96 30.99 29.90 29.63 29.28 28.79 28.20 27.98 27.80 27.34 27.22
01:30 36.53 35.57 33.68 32.18 31.21 30.47 29.57 29.36 29.09 28.66 28.13 27.92 27.75 27.33 27.21
05:30 31.98 32.27 31.56 30.95 30.28 29.83 29.18 29.05 28.87 28.50 28.04 27.85 27.69 27.32 27.19
09:30 36.90 36.30 33.88 32.07 31.08 30.35 29.46 29.26 29.02 28.61 28.11 27.91 27.74 27.35 27.22
13:30 42.78 40.28 36.27 33.46 32.14 31.06 29.92 29.63 29.28 28.80 28.22 28.01 27.82 27.39 27.26
17:30 44.03 41.77 37.52 34.40 32.91 31.66 30.33 29.98 29.56 29.02 28.37 28.13 27.94 27.44 27.31
21:30 39.03 37.45 34.97 33.02 31.90 31.00 29.96 29.70 29.38 28.90 28.31 28.09 27.91 27.44 27.31
01:30 36.27 35.36 33.59 32.19 31.25 30.54 29.66 29.46 29.20 28.77 28.23 28.03 27.85 27.42 27.30
05:30 32.62 32.72 31.93 31.16 30.52 30.05 29.37 29.23 29.05 28.66 28.18 27.99 27.82 27.42 27.29
08:30 (After 48 h) 36.40 35.84 33.71 32.01 31.14 30.45 29.59 29.40 29.16 28.74 28.24 28.03 27.86 27.45 27.32

Table 4
Experimental air temperature variation inside the EAHE on days of (04–07 August 2013).
Duration of operation (h :m) Air temperatures inside the EAHE ( ◦ C), u = 3.5 m/s.
Length of pipe (m)
Inlet 3.63 7.69 11.73 16.04 20.07 24.12 26.37 29.07 33.10 37.01 38.86 40.82 45.10 48.80

09:30 (After 1 h) 34.83 34.75 32.92 31.28 30.71 30.16 29.47 29.37 29.24 28.89 28.46 28.28 28.13 27.81 27.69
13:30 40.63 39.16 36.23 33.77 32.76 31.79 30.67 30.40 30.09 29.58 28.98 28.75 28.56 28.07 27.94
17:30 42.62 41.14 37.75 34.96 33.75 32.60 31.30 30.94 30.55 29.97 29.28 29.02 28.80 28.22 28.08
21:30 37.34 36.52 34.86 33.41 32.57 31.85 30.89 30.65 30.37 29.87 29.26 29.02 28.82 28.27 28.13
01:30 34.25 33.95 33.00 32.16 31.59 31.12 30.42 30.27 30.09 29.67 29.15 28.94 28.76 28.27 28.13
05:30 32.13 32.26 31.79 31.38 30.94 30.64 30.09 30.00 29.89 29.53 29.07 28.87 28.71 28.27 28.13
09:30 36.56 36.33 34.49 32.91 32.20 31.55 30.68 30.48 30.25 29.80 29.25 29.03 28.84 28.34 28.20
13:30 42.56 40.60 37.27 34.57 33.52 32.48 31.28 30.96 30.61 30.06 29.40 29.15 28.95 28.37 28.23
17:30 42.80 41.36 38.11 35.42 34.22 33.08 31.78 31.39 30.98 30.37 29.63 29.36 29.13 28.48 28.33
21:30 37.30 36.61 35.12 33.76 32.96 32.25 31.30 31.05 30.77 30.23 29.59 29.35 29.13 28.52 28.37
01:30 33.60 33.54 32.91 32.31 31.79 31.38 30.71 30.57 30.40 29.97 29.43 29.21 29.03 28.50 28.35
05:30 29.71 30.45 30.71 30.88 30.59 30.46 30.07 30.04 29.97 29.66 29.22 29.03 28.87 28.44 28.28
09:30 38.50 37.97 35.66 33.62 32.92 32.15 31.17 30.92 30.66 30.16 29.55 29.32 29.12 28.55 28.40
13:30 45.03 42.62 38.86 35.84 34.56 33.33 31.97 31.58 31.16 30.53 29.77 29.50 29.27 28.61 28.45
17:30 47.29 44.52 39.85 36.28 34.82 33.41 31.95 31.53 31.06 30.42 29.64 29.37 29.14 28.49 28.34
21:30 37.79 37.03 35.44 34.11 33.14 32.36 31.37 31.12 30.81 30.27 29.60 29.35 29.13 28.53 28.38
01:30 34.92 34.68 33.72 32.86 32.19 31.64 30.88 30.71 30.50 30.04 29.45 29.22 29.03 28.48 28.33
05:30 34.31 34.01 33.14 32.36 31.79 31.34 30.65 30.52 30.34 29.92 29.37 29.15 28.97 28.46 28.31
08:30 (After 72 h) 37.87 37.32 35.43 33.76 33.03 32.30 31.35 31.11 30.85 30.35 29.72 29.48 29.28 28.67 28.52

depth of 3 m, which was previously determined based on local site data,

with a slope of 2% and spacing of 2 m. To drain the condensed water, a
After integrating Eq. (14), it can obtain: sink is built right at the EAHE’s outlet. Fig. 5 shows a data acquisition
( ) unit supplied by National Instrument (NI) coupled to 15 temperature
1 detectors of the RTD type (Resistance Temperature Detector) along the
ln(Ta − Tsoil ) = − x+C (15)
ρ π r12 cpair u Ritotal EAHE. The air flow velocity is managed by an extractor with variable
flow and reliable consumption in electrical energy (120 W) and
Where C is an integration constant, it can obtained by applying a
measured by an propeller anemometer at the EAHE’s outlet. The tem­
constant temperature at the EAHE’s inlet.
peratures of air inside the pipe were measured at different distances
The outlet air temperature can be expressed as follows:
along the EAHE. Air temperature detectors are correctly placed in the
[ ]
1 EAHE as shown in Fig. 4. In continuous operation during the cooling
Ta (x) = Tsoil + (T1 − Ti ) exp − x (16)
ρ π r1 2 cpair u Ritotale period, air temperatures along the pipe were taken every 15 min. Ta­
bles 1 and 2 show the instruments technical characteristics and the
To evaluate the heat accumulation rejected on the soil, it is recom­
EAHE’s main parameters.
mended to calculate the soil temperature at the first layer of undisturbed
soil using Eq. (16) with injecting Ta (x) from experimental measure­
4. Results
ments as following:
[ ]
1 Tables 3, 4 and 5 illustrate the hourly air temperature variation for
Tsoil = Ta (x) − (T1 − Ti ) exp − x (17)
ρ π r1 cpair u Ritotale
2 15 sections inside the EAHE. As well as the impact of EAHE’s continuous
operation on its thermal performances. It is noted that temperatures of
3. Experimental setup the air up to length of 33 m presented in Tables 3, 4 and 5 are unstable
over time due to the effect of changing temperature at the pipe’s inlet. In
This work was carried out in the LGM laboratory, University of addition, the high temperatures induce heat build-up on the pipe’s
Biskra. The EAHE shown in Fig. 3 composed of a PVC pipe divided into nearby soil. The ambient air temperatures drops at night, cooling the
four horizontal parts of 48 m total length and 0.1 m diameter, buried at a heated soil nearby the EAHE and assisting the soil in regaining its ability

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Y. Belloufi et al. Geothermics 104 (2022) 102442

Table 5
Experimental air temperature variation inside the EAHE on days of (18–19 September 2013).
Duration of operation (h :m) Air temperatures inside the EAHE ( ◦ C), u = 4.5 m/s.
Length of pipe (m)
Inlet 3.63 7.69 11.73 16.04 20.07 24.12 26.37 29.07 33.10 37.01 38.86 40.82 45.10 48.80

10:30 (After 1 h) 35.37 34.99 33.60 32.39 31.89 31.47 30.91 30.85 30.77 30.45 30.06 29.88 29.72 29.40 29.27
12:30 38.09 37.52 35.56 33.84 33.16 32.51 31.69 31.51 31.32 30.90 30.41 30.20 30.02 29.58 29.44
16:30 40.80 39.72 37.41 35.31 34.56 33.72 32.66 32.37 32.08 31.53 30.92 30.68 30.47 29.85 29.70
20:30 35.75 35.22 34.30 33.56 33.02 32.60 31.95 31.82 31.67 31.26 30.77 30.56 30.38 29.85 29.71
00:30 33.64 33.42 32.92 32.53 32.18 31.95 31.48 31.42 31.35 31.02 30.62 30.42 30.27 29.82 29.68
04:30 30.72 30.96 31.05 31.25 31.07 31.08 30.84 30.88 30.91 30.68 30.38 30.22 30.08 29.75 29.60
08:30 34.88 34.76 33.59 32.59 32.24 31.91 31.36 31.28 31.20 30.88 30.50 30.31 30.16 29.77 29.62
12:30 41.70 40.44 37.81 35.52 34.75 33.88 32.82 32.52 32.23 31.69 31.08 30.84 30.64 30.00 29.86
16:30 41.27 39.94 37.81 35.87 35.11 34.29 33.21 32.91 32.60 32.02 31.36 31.10 30.89 30.17 29.98
20:30 38.11 37.18 35.83 34.69 34.05 33.50 32.68 32.48 32.27 31.78 31.21 30.96 30.77 30.13 29.98
00:30 35.85 35.35 34.50 33.81 33.32 32.94 32.30 32.16 32.01 31.59 31.09 30.87 30.69 30.11 29.96
04:30 34.78 34.40 33.73 33.21 32.79 32.51 31.96 31.87 31.77 31.40 30.96 30.75 30.58 30.07 29.91
08:30 32.73 33.37 32.81 32.42 32.05 31.88 31.46 31.42 31.38 31.09 30.72 30.53 30.39 29.97 29.83
12:30 39.26 38.60 36.65 34.86 34.23 33.55 32.64 32.41 32.19 31.70 31.14 30.90 30.71 30.12 29.96
16:30 40.35 39.44 37.57 35.83 35.06 34.27 33.26 32.97 32.67 32.10 31.46 31.21 30.99 30.27 30.12
20:30 36.93 36.27 35.22 34.30 33.79 33.33 32.61 32.44 32.26 31.81 31.27 31.03 30.85 30.22 30.07
00:30 33.52 33.46 33.14 32.91 32.57 32.38 31.93 31.87 31.79 31.45 31.02 30.82 30.66 30.14 29.99
04:30 29.92 30.46 30.88 31.48 31.17 31.26 31.09 31.15 31.20 30.99 30.69 30.52 30.39 30.02 29.89
08:30 30.11 30.61 30.79 31.09 30.87 30.95 30.79 30.86 30.93 30.67 30.49 30.34 30.21 29.91 29.77
12:30 35.52 35.49 34.30 33.24 32.78 32.40 31.79 31.69 31.59 31.24 30.82 30.63 30.47 30.02 29.87
16:30 37.17 36.88 35.47 34.13 33.60 33.10 32.35 32.18 32.01 31.58 31.08 30.87 30.69 30.14 29.98
20:30 23.99 26.08 28.08 30.18 29.95 30.38 30.56 30.74 30.89 30.68 30.55 30.41 30.29 29.98 29.85
00:30 26.18 27.11 28.11 29.14 29.22 29.63 29.81 30.00 30.22 30.18 30.08 29.96 29.88 29.74 29.61
04:30 24.79 25.89 27.08 28.33 28.52 29.02 29.31 29.56 29.83 29.82 29.81 29.73 29.65 29.61 29.46
08:30 (After 95 h) 27.46 28.39 28.77 29.21 29.28 29.56 29.63 29.80 29.98 29.92 29.86 29.75 29.66 29.59 29.47

Fig. 6. Validation of the suggested model using experimental measurements of Fig. 7. Validation of the suggested model using self-experimental
Misra et al. (2013a). measurements.

Table 6 Table 7
Main parameters used for comparative validation with Misra et al. Numerical air temperature drop at the pipe’s exit.
(2013a). Pipe’s length Air temperature inside the EAHE ( ◦ C)
Parameter Value (m)
(Tinlet - Toutlet) (Tinlet - Toutlet) in transient conditions
Air flow velocity 5 m/s in
Pipe diameter 0.1 m steady state 1h 3h 6h 12h 24h
Pipe length 60 m
Pipe thermal conductivity 1.16 W/m.k Inlet 0 0 0 0 0 0
Soil thermal conductivity 0.52 W/m.k 5 3.69 4.69 4.18 3.89 3.62 3.38
Undisturbed soil temperature ( ◦ C) 27 10 10.29 10.07 9.1 8.54 8.03 7.56
15 14.80 14.09 12.91 12.22 11.57 10.97
20 17.87 17.09 15.86 15.12 14.42 13.75
to cool. The air temperatures presented in outlet of the EAHE are almost 25 19.98 19.34 18.15 17.41 16.7 16.02
30 21.41 21.02 19.92 19.22 18.53 17.87
constant and no noticeable effect is recorded of heat accumulation on
35 22.39 22.28 21.29 20.65 20.01 19.37
thermal performance in the outlet of EAHE, due to the soil temperature 40 23.06 23.21 22.35 21.77 21.19 20.6
self recovers at night operation. It is stated that first 33 m of the pipe can 45 23.52 23.92 23.17 22.66 22.14 21.6
provide 89% of the total air temperature drop. From Tables 3, 4 and 5,
the greatest increase in air temperature at the EAHE exit has been
noticed to be 0.85 ◦ C. Besides, it can be concluded that EAHE’s thermal

6
Y. Belloufi et al. Geothermics 104 (2022) 102442

Fig. 8. Hourly soil temperature variation in different rays of the soil along the EAHE.

Fig. 9. Transient air temperature drop inside the EAHE for various soil thermal conductivities.

performance is unaffected by the continuous operating mode. from 04 to 07 August 2013 (table 4) are chosen as typical days to
The experimental values of Misra et al. (2013a) were used to validate perform this validation. From the analysis of validation results shown in
the developed transient numerical model (Fig. 6) for cooling cycle in Fig. 7, mean relative errors of 1.86, 0.47 and 2.40% are recorded after 1
Ajmer, India. Table 6 presents the main parameters used in the h, 30 h and 54 h respectively during the functioning of the EAHE in
validation. continuous operation mode. The comparisons between computed values
It can be seen in Fig. 6a good agreement between the simulated re­ and self-experimental data show satisfactory agreement, which vali­
sults and those of the experimental, mean relative errors of 1.98, 2.99 dates the developed numerical study.
and 0.87 are obtained after 1 h, 4 h and 7 h respectively during the To clearly show the impact of different parameters on the EAHE’s
functioning of EAHE. Therefore, the developed model is validated and thermal performance, the derating factor is used assuming a constant
can be used for further analysis. temperature at the pipe’s inlet during the EAHE’s operation. A
Moreover, the comparison to experimental data of other researchers, maximum inlet air temperature can be used to simulate the effect of
the previous section’s model was also validated with self-experimental various parameters on the thermal performance of EAHE. The derating
results that was carried out at the site of Biskra University. The days factor ‘DF’ is determined using the temperature differences obtained

7
Y. Belloufi et al. Geothermics 104 (2022) 102442

Fig. 10. Transient variation in derating factor along the EAHE for various soil thermal conductivities.

Fig. 11. Transient air temperature drop inside the EAHE for various air flow velocities.

from table 7 under transient and steady state conditions. It is clear that 0.20 ◦ C after 9, 37 and 57 h respectively of continuous operation. which
the thermal performance of EAHE is greatly affected in transient oper­ means that the radius of the soil r3 has no effect in the next length of the
ation mode assuming the condition montioned above. From table 7 pipe.
under steady state condition, it is noted that maximum difference in air In Fig. 9 (a and b), three different soil thermal conductivities of 0.5,
temperature is 23.52 ◦ C. 1.25 and 4 /m.k are considered while assessing thermal performances
Fig. 8 presents the hourly soil temperature variation in different and determining the soil’s ideal thermal conductivity. For soil thermal
layers near the pipe along the EAHE during 57 h of continuous opera­ conductivities of 0.5, 1.25 and 4 W/m.k and a duration of 24 h, it was
tion. 4 rays of the soil are taken into account to show the effect of air observed an increase of 1.53, 0.57 and 0.14 ◦ C in air temperatures at the
temperature on the soil surrounding the pipe. It is noted that the soil EAHE’s outlet respectively. Therefore, low thermal conductivity of the
temperature represented in Fig. 8 was calculated using Eq. (17) by soil has a significant effect on EAHE’s thermal performances. The soil’s
introducing the experimental data of air temperature in tables 3, 4 and high thermal conductivity allows heat accumulated to be evacuated
5. For that the soil temperature at the pipe’s inlet (0 m) is supposed to be away from the EAHE.
the same as the inlet air temperature. It is observed that the drops in soil The curves in Fig. 10 (a, b and c) represent the derating factor of the
temperature between 2r1 and 5r1 at 20 m pipe’s length is 0.23, 0.14 and EAHE’s thermal performances. Derating factor is defined as the ratio of

8
Y. Belloufi et al. Geothermics 104 (2022) 102442

Fig. 12. Transient variation in derating factor along the EAHE for various air flow velocities.

deterioration in thermal performance under transient conditions 5. Conclusion

compared to the thermal performance under steady state conditions. It
also demonstrates how the EAHE’s thermal performance degrades as a In this paper, the impact of EAHE’s continuous operation mode on its
result of the continuous operation mode. To determine the derating thermal performances is discussed. Air temperatures along the EAHE
factor, temperature drops obtained under steady state and transient have been numerically determined exploiting a thermal numerical
conditions are used as shown in Eq. (13). approach based mainly on the energy balances principle in both steady
It is observed that the derating factor increases with duration of and transient conditions. Besides, an experimental setup was realized at
operation due to the increase in the outlet air temperature under tran­ the University of Biskra (Algeria) to examine the effect of EAHE’s
sient condition. The increase in the outlet air temperature with time is continuous operation mode on thermal performance in hot and arid
due to the accumulation of heat in the soil surrounding the EAHE, which climatic conditions. For this reason, experimental measurements were
influences on EAHE’s thermal performance and therefore the derating conducted during the summer period from July to September 2013.
factor increases with time. During the experimental measurements, three different air flow veloc­
When derating factor approaches zero in a section of EAHE, it means ities of 2, 3.5 and 4.5 m/s are considered. The air temperatures inside the
that the thermal performance of EAHE in transient condition at that buried pipe were taken at 15 different locations every 15 min during 95
section approaches the thermal performance of EAHE in steady state. h.
Fig. 11 (a and b) illustrates the transient variation of flowing air The study’s findings are analysed, and the following conclusions can
temperature inside the EAHE for various air flow velocities (1, 3.5 and 5 be inferred:
m/s). The EAHE’s thermal performance is analysed in continuous
operation. Air temperature rise as air flow velocity increases, implying - EAHE’s thermal performances is influenced by high air velocity and
that the air does not have enough time to release its heat to the soil. For low soil thermal conductivity.
an operating period of 3 h to 24 h, temperature differences of 1.03, 0.57 - High inlet air temperatures induce heat to accumulate on the soil
and 0.03 ◦ C are observed at the outlet of EAHE for air flow velocities of layers near the EAHE.
5, 3.5 and 1 m/s respectively. - The first 33 m of the EAHE can provide 91% of the overall air tem­
The impact of air flow velocity on EAHE’s thermal performances in peratures reduction. For this reason, there are no major benefits to
terms of derating factor is represented in Fig. 12 (a, b and c). The adopting EAHE above a 33 m length.
derating factor tends towards zero for all operating times at the EAHE’s - During continuous operation of EAHE with air flow velocity of 3.5
outlet for low air velocities, taking as example 1 m/s in Fig. 12(a), m/s, the highest increase in air temperature at the pipe’s outlet can
because of the rapid exchange of heat in the EAHE’s few first meters reach up 0.85 ◦ C and the maximum air temperature drop can reach
between soil and air. From Fig. 12 (a, b and c), it is clear that thermal up 19 ◦ C.
performance is affected by increasing the air flow velocity inside the - The outlet air temperatures are unaffected by the continuous oper­
pipe. Therefore, it is not advisable to severely increase the air flow ve­ ation mode of 95 h due to high soil thermal conductivity.
locity inside the tube.

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Y. Belloufi et al. Geothermics 104 (2022) 102442

- The ambient air temperature drops during night-time, cooling the Liu, Z., Yu, Z., Yang, T., Li, S., Mankibi, M.E., Roccamena, L., Qin, D., Zhang, G., 2019a.
Designing and evaluating a new earth-to-air heat exchanger system in hot summer
heated sub-soil and assisting the soil in regaining its cooling capacity.
and cold winter areas. Energy Procedia 158, 6087–6092. https://doi.org/10.1016/j.
egypro.2019.01.506.
Declaration of Competing Interest Liu, Z., Yu, Z., Yang, T., Roccamena, L., Sun, P., Li, S., Zhang, G., El Mankibi, M., 2019b.
Numerical modeling and parametric study of a vertical earth-to-air heat exchanger
system. Energy 172, 220–231. https://doi.org/10.1016/j.energy.2019.01.098.
The authors declare that they have no known competing financial Liu, Z., Yu, Z.J., Yang, T., El Mankibi, M., Roccamena, L., Sun, Y., Sun, P., Li, S.,
interests or personal relationships that could have appeared to influence Zhang, G., 2019c. Experimental and numerical study of a vertical earth-to-air heat
the work reported in this paper. exchanger system integrated with annular phase change material. Energy Convers.
Manage. 186, 433–449. https://doi.org/10.1016/j.enconman.2019.02.069.
Mathur, A., Srivastava, A., Agrawal, G.D., Mathur, S., Mathur, J., 2015a. CFD analysis of
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Mathur, A., Surana, A.K., Verma, P., Mathur, S., Agrawal, G.D., Mathur, J., 2015b.
This study was supported by the Directorate General of Scientific Investigation of soil thermal saturation and recovery under intermittent and
Research and Technological Development (DGRSDT) of the Algerian continuous operation of EATHE. Energy Build. 109, 291–303. https://doi.org/
Ministry of Higher Education and Scientific Research as a part of PRFU 10.1016/j.enbuild.2015.10.010.
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