International Journal of Renewable Energy Development


Int. J. Renew. Energy Dev. 2023, 12 (3), 448-458 
| 448 

https://doi.org/10.14710/ijred.2023.49759  
ISSN: 2252-4940/© 2023.The Author(s). Published by CBIORE 

 Contents list available at IJRED website 
 

International Journal of Renewable Energy Development 
 
Journal homepage: https://ijred.undip.ac.id 

 

 

Design, optimization and economic viability of an industrial low 
temperature hot water production system in Algeria: A case study 

Karim Kacia* , Mustapha Merzouka , Nachida Kasbadji Merzoukb , Mohammed Missoumc , 
Mohammed El Ganaouid , Omar Behare , Rabah Djedjigd  

aLaboratoire de Physique Fondamental et Appliqué Département des Energies Renouvelables, Faculté de Technologie, Université Blida, W. Blida, Algeria. 
bUnité de Développement des Equipements Solaires, UDES, Centre de Développement des Energies Renouvelables, CDER, 42004, W. Tipaza, Algérie. 
cDepartment of Mechanical Engineering, Faculty of Technology, University Center of Morceli, Abdellah, Tipaza, Algeria.  
dUniversity of Lorraine, LERMAB, IUT de Longwy, 186 rue de Lorriane, 54400 Cosnes-et-Romain, France. 
eCCRC, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955, Saudi Arabia. 

Abstract. Solar energy has a great potential in many areas of industrial activity in Algeria. This is because most of Algeria has high levels of sustainable 
solar insulation. Unfortunately, few industries use solar energy for hot water generation, but some industrial processes require hot water at 
temperatures that can be easily obtained from solar thermal panels. This paper presents a case study to investigate the technical and financial 
feasibility of a solar-powered industrial agro-processing system in Algiers. Based on  the solar collectors connection type for which the economic 
feasibility study was carried out, an appropriate design of the system was determined. The latter was actually done by analyzing the levelized cost of 
energy savings. The design of the thermo-solar process is carried out based on F-chart method with a new approach by integrating the incidence 
angle modifier and of using real and experimental data requirements to determine realistic achievable performance of the solar process. The results 
showed that, in comparison to the currently used electrical system, the electrical energy savings achieved by the solar-powered system make it an 
economically viable option with a solar coverage rate of 80%. The investment depreciation balance shows that the use of such a thermal solar energy 
system will be more competitive than fossil fuels system if the price of electricity in the country increases from 0.048 to 0.075 €/kWh. 

Keywords: Process industrial application, solar thermal collector, Thermo-solar system, Techno-economic assessment, water heating. 

@ The author(s). Published by CBIORE. This is an open access article under the CC BY-SA license 
 (http://creativecommons.org/licenses/by-sa/4.0/). 

Received: 12th Nov 2022; Revised: 24th January 2023; Accepted: 6th March 2023; Available online: 21st March 2023   

1. Introduction 

In recent years, interest in solar development has increased in 
Algeria since the publication of the Renewable Energy and 
Energy Efficiency Plan 2016-2030 (The Minister of Energy 
Transition and Renewable Energies., 2022). The industrial 
sector is a promising area for the development of solar thermal 
technology, accounting for more than 25% of total final energy 
consumption (International Energy Agency, 2020). The 
efficiency of converting solar energy into heat (up to 70%) is 
much higher than converting it into electricity (about 15%), 
demonstrating the benefits of integrating solar thermal energy 
into industrial processes. The heating process consumes a lot of 
thermal energy. Globally, 50% of energy consumption is used 
for heating applications (Valderrama et al., 2022). A great 
fraction (about 90%) of this heat comes from fossil fuels, which 
emit large amounts of greenhouse gas emissions and thus 
exacerbate the effects of climate change (Intergovernmental 
Panel on Climate Change IPCC (2022) Mitigation of Climate 
Change; Assessment Report on Climate Change). Statistics 
show that 60% of industrial processes use heat at temperatures 
below 400°C, while more than 30% operate at temperatures 

 
* Corresponding author 
Email: kkaci2022@gmail.com (K. Kaci) 

below 100°C (Zühlsdorfa et al., 2019). Therefore, integrating 
solar energy into industry can help to reduce the effects of 
climate change, especially in low-temperature processes. 
Nowadays, around 456 GWth of solar thermal output has been 
installed globally (National Renewable Energy Laboratory. 
2021). Low temperature thermal industrial processes recorded 
growth of 1.5% in 2016 (Meyers et al 2018). According to a 
recent study, published by SOLIRCO, the industrial sector used 
416 414 m2of installed space, 40% of which was used in the 
agro-food sector (The International Renewable Energy Agency. 
2015) 

In fact, the heat generated by solar thermal systems is less 
used in industry than in domestic applications (Renewable 
Energy Policy Network for the 21st Century. 2016). However, 
several studies related to the use of solar heat for industrial 
processes revealed that solar thermal industrial heating systems 
can achieve higher efficiencies compared to domestic 
applications, especially at lower temperatures (Farjana et al., 
2017 and Sharma., et al 2017).  A study conducted by Schweiger 
et al. (2000) in the framework of the European project POSHIP, 
which focuses on evaluating the potential of industrial solar 
systems in Spain and Portugal, shows that the latter can supply 

Research Article 

https://doi.org/10.14710/ijred.2023.49759
https://doi.org/10.14710/ijred.2023.49759
mailto:kkaci2022@gmail.com
https://orcid.org/0000-0002-8787-2025
https://orcid.org/0000-0003-0362-5674
https://orcid.org/0000-0001-5900-6675
https://orcid.org/0000-0003-4910-6052
https://orcid.org/0000-0003-4910-6052
https://orcid.org/0000-0002-7058-5935
https://orcid.org/0000-0002-8898-6737
http://crossmark.crossref.org/dialog/?doi=10.14710/ijred.2023.49759&domain=pdf


K. Kaci et al  Int. J. Renew. Energy Dev 2023, 12(3), 448-458 
| 449 

 

ISSN: 2252-4940/© 2023. The Author(s). Published by CBIORE 

5804 GWh, or 3.6% of the total energy demand 
(Schweigeretal.,2000). Muller et al. (2004) investigated solar 
heating systems as part of the European project PROMISE, and 
found that Austria has an energy solar potential of 264 PJ, 
representing 30% of total energy consumption. About 32 % is 
used to generate thermal energy below 200 °C. Kalogirou et al. 
(2003) studied the potential of solar industrial process heating 
in Cyprus for different temperature levels. Similar studies have 
also been reported for Australia by Fuller et al., (2011). Kummert 
et al. (2000) carried out an experimental study on installation of 
a thermo-solar process, considering typical daily profiles. 

Several studies have proven that the application of solar 
thermal systems in industry can lead to significant energy 
savings. As a part of an IEA project SHC Task 33 Solar PECES 
task IV, several configurations for thermo-solar processes 
thermal systems have been carried out in several European 
countries (Weiss., 2005). Lima et al., (2015) demonstrated the 
feasibility of integrating a thermal solar process in a hospital in 
Brazil. Surech el et al., (2017) presented a techno-economic 
study on integrated thermal solar processes in the Indian textile 
industry. Anubhav et al., (2016) developed a model of a thermal 
solar process for the automotive industry in 2016. The economic 
analysis shows a payback period of 18 months.  Quijera et al., 
(2011) studied the feasibility of integrating a solar thermal 
system into the dairy industry through mathematical modeling. 
Therefore, the work suggests that the solar thermal potential of 
the industrial processes studied is important and should be 
considered for future energy. Moreover, Akssas et al, (2013) 
conducted a techno- economic analysis of a solar water heater 
for a hospital center in Batna in Algeria, to study the techno-
economic feasibility of solar heating water integration. The 
results showed the possibility of significant energy savings with 
installation (Total annual provided energy = 1427,1MWh and a 
Total annual net reduction of GHG = 905,84 Tons of CO2 
(Pahlavana 2018). 

Review of previously published studies and various 
applications demonstrate the great potential of integrating solar 
heat into industrial processes. To encourage the deployment of 
solar energy, real case studies must be investigated to provide 
accurate information about the performance and the costs of 
solar-powered industrial processes. In this direction, the 
objective of this work is to design, evaluate the energy 
performance and determine the costs of a thermo-solar process 
that would be integrated to a food industrial process in Algeria. 
The design of the thermo-solar process is carried out based on 
F-chart method with a new approach by integrating the 
incidence angle modifier and of using real and experimental 
data requirements to determine realistic achievable 
performance of the solar process. This methodology was 
implemented into Trnsys software to facilitate modeling and 
device management of the entire system. In the following, firstly 
the case study is presented, then the methodology used to 
design the different solar system components is detailed and 
finally the energy and economic performances of the whole 
thermo-solar system are evaluated. 

2. Methodology  

2.1. Presentation of the case study 

The thermo-solar process system considered in this study is an 
agro-food industrial process producing flavors and perfumes 
located in Algiers, Algeria (Longitude: 2.95°E, latitude: 36.7°N 
and elevation: 350 m).  

 

 
Fig. 1. Thermo-solar process into the industrial food process 

 
The system consists of primary and secondary circuits as 

shown in Figure 1. The primary circuit includes a solar 
collector's field and a heat exchanger.  Water is heated up in flat 
plat collectors and it is used as a working fluid to power a 
secondary circuit through water/water heat exchanger.  

The secondary circuit feeds the industrial process and it is 
equipped with a storage tank which serves to store hot water to 
be used when solar energy is not enough available. Another heat 
exchanger is integrated in storage tank to provide high 
modularity to the system. A back-up electric heater is used in 
addition to the solar heating to ensure the continuous supply of 
hot water to the industrial process. For starting or stopping the 
pump, a regulation system was used. The thermo-solar process 
is designed to produce 3 m3/day of hot water at 60°C. The 
hourly daily load profile imposed by the used process  is 
illustrated in Figure 2. The 3 m3 of hot water demand is situated 
between 11 to 12 am and 14 to 15 pm, which coincide with the 
availability of solar radiation.  

2.2. Weather data and validation 

Validation of the weather data model involves comparing 
predicted and measured solar radiation and ambient 
temperature. The measurements are provided by the Algiers 
Meteorological Station (Centre for the Development of 
Renewable Energy of Algeria., 2021), while the forecasts are 
obtained from the TRNSYS software (Meteonormsoftware8., 
2022). Figure (3a) and (3b) highlight the measured solar 
radiation intensity and ambient temperature at the site of 
Algiers in 2020. A Good agreement between predicted and 
measured results was observed. The model demonstrated high 
accuracy in predicting the site's solar radiation and ambient 
temperature, allowing the system's performance to be estimated 
with reasonable accuracy. 

 

6 7 8 9 10 11 12 13 14 15 16 17 18
0

500

1000

1500

2000

2500

3000

 

 

W
at

er
 lo

ad
 (L

ite
r)

Times (hours)  
 

Fig. 2 Hourly daily load profile imposed by the process 



K. Kaci et al  Int. J. Renew. Energy Dev 2023, 12(3), 448-458 
| 450 

 

ISSN: 2252-4940/© 2023. The Author(s). Published by CBIORE 

Janu Febr Marc Apri May June july Augu Sept Octo Nove Dece
0

50

100

150

200

250

 

 
M

on
th

ly
 s

ol
ar

 ir
ra

di
at

io
n 

(k
W

h/
m

2)

Months

 Results meteonorm 
 Results measured 

a)

 
 

Janu Febr Marc Apri May June july Augu Sept Octo Nove Dece
0

5

10

15

20

25

30

 

 

A
m

bi
en

t t
em

pe
ra

tu
re

 (°
C

)

Months

 Results meteonorm
 Results measured

b)

 
 
Fig.3 The radiometric parameters of the site a) Solar radiation data b) 
Ambient temperature 
 

It can also be noted that the location has a high solar 
radiation intensity, reaching 250 kWh/m2 in July, one of the 
highest potentials in the world, with an average ambient 
temperature of 18ºC. 

The temperature of cold water is an interesting parameter 
to determine the performance of the solar system. The monthly 
average ambient air and network water temperature provided 
by the software are shown in Figure 4 for a period of one year. 
The ambient temperature varies between 10 °C and 25 °C and 
average annual cold water temperature is about 18 °C. These 
values are the same of those provided by the Algerian Water 
Company (Ministry of Water Resources and Water Security, 
Algerian Waters, 2021). This means that the data provided by 
the software is accurate. The difference between summer and 
winter is significant. It can be seen that the temperature of cold 
water is 15°C in winter and reaches 25°C in summer, a 
difference of 10°C between these two periods, which affects 
strongly the system performance (Software Meteonorm 8. 
2022). 

Table 1 
Conditions of parameters during testing 

Measurement parameters Test conditions 

Angle of incidence (θ) (°) -55° to +55° 
Total radiation on tilted surface Ig (W/m2) 840 <Ig< 950  
Diffuse radiation Id(W/m2) 130 < Id< 220 
Ambient temperature Ta(°C)   20°C < Ta< 25°C 
Mass flow rate, �̇�𝑚 (kg/s.m2) 0.02 +/- 10% 
Wind velocity (V)-(m/s) 1 < V < 3  

Source: Kaci et al (2012) 

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
8

10

12

14

16

18

20

22

24

26

 

 

T
em

pe
ra

tu
re

 (°
C

)

Months

 Ambient temperature
 The mains water temperature  

 

Fig.4 Variation of the mains water and ambient temperatures during a 
year 

2.3. Determination of the solar collector’s parameters 

Before evaluating the energy performance of the solar water-
heating system under investigation, an experimenal study was 
carried out to determine the real characteristics of the solar 
collector used; namely the instantaneous efficiency and the 
modified incidence angle. According to the European standard, 
the fluctuations of the variables (incidence angle θ, ambient 
temperature Ta, global radiation Ig, mass flow rate �̇�𝑚 and wind 
speed V) are checked within the limit tolerated by the standard 
as given in Table 1. 

The experimental study was carried out during different 
moments of four days, where inlet and outlet collector’s 
temperatures, ambient temperature as well as the global 
radiation are measured. These parameters allow calculating the 
instantaneous efficiency of the solar collector η. Four inlet 
temperatures are considered (Ta, Ta+10, Ta+20, Ta+30). Each 
temperature is recorded for four times, two before noon and two 
in the afternoon, for a total of sixteen points. Table 2 shows the 
parameters measured during the test period.  

The instantaneous efficiency may be given by the  
equation (1) (Kaci et al2012.) 

𝜂𝜂 = 𝜂𝜂0 − 𝑎𝑎1𝑇𝑇
∗       (1) 

Where:  

𝑇𝑇∗ =
(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)

𝐼𝐼𝑔𝑔
 

𝜂𝜂0 =  F𝑅𝑅(τα) is the collector optical efficiency; and a1=( FRUg) 
is the collector overall energy loss coefficient.  
 

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
0,0

0,1

0,2

0,3

0,4

0,5

 

 

Ef
fic

ie
nc

y 
(-)

T*  
Fig. 5 Representation of the instantaneous performance of the collector 



K. Kaci et al  Int. J. Renew. Energy Dev 2023, 12(3), 448-458 
| 451 

 

ISSN: 2252-4940/© 2023. The Author(s). Published by CBIORE 

Table 2 
 Tests carried out to calculate the instantaneous yield  

Time Te Ts Ta Ig T* η 

(Hour) (°C) (°C) (°C) (W/m2) (Km2/W) - 

11:29 a.m 21.45 25.04 18.61 815 0.056 0.36 

11:44 a.m 21.14 27.18 22.25 941 0.02 0.53 
12:54 p.m 20.46 25.72 20.28 950 0.029 0.46 
01:09 pm 20.82 26.31 20.01 954 0.037 0.48 
11:09 a.m 31.86 36.58 23.20 839 0.131 0.46 
11:24 a.m 31.72 36.39 23.79 850 0.12 0.45 
13:44 p.m 32.16 36.69 22.34 935 0.129 0.40 
13:59 p.m 31.67 35.77 24.62 897 0.101 0.38 
11:41 a.m 39.08 43.38 23.24 940 0.191 0.38 
11:56 a.m 39.75 43.92 22.59 951 0.202 0.36 
13:14 p.m 40.22 43.82 20.26 915 0.237 0.32 
13:29 p.m 40.67 44.46 21.72 889 0.234 0.35 
12:01 p.m 49.15 52.82 22.42 878 0.325 0.34 
12:16 p.m 49.32 52.65 21.50 906 0.325 0.30 
13:11 p.m 49.89 52.52 22.01 918 0.318 0.23 
13:26 p.m 49.15 51.65 21.68 918 0.312 0.22 

Source: Kaci et al (2012) 

 
From Equation (1) and obtained measured values (Table 2), the 
characteristic curve of the instantaneous efficiency related to 
the inlet temperature can be plotted. This curve will satisfy the 
equation 2: 

𝜂𝜂 = 0.49 – 5.7 T*         (2) 

The value 0.49 represents the optical efficiency of the collector 
𝜂𝜂0. It is the intersection of the curve with the y-axis.  
The value 5.7 represents the overall thermal losses of the 
collector a1 which is the slope of the line. 

The incidence angle modifier is a correction factor for the 
effective transmissivity-absorptivity product 𝐾𝐾𝜏𝜏𝜏𝜏is defined as 
the ratio of the instantaneous efficiency at any incidence to the 
efficiency at normal incidence. It allows you tocalculate the 
instantaneous return at any incidence of the day (Kaci et al 
2012). 

𝐾𝐾𝜏𝜏𝜏𝜏 =
𝜂𝜂(𝜃𝜃)

𝜂𝜂(𝜃𝜃=0)
        (3) 

With (𝜏𝜏𝜏𝜏)𝜃𝜃: Optical efficiency of the collector at normal 
incidence; (𝜏𝜏𝜏𝜏)𝑛𝑛: Optical efficiency of the collector at 𝜃𝜃 
incidence. 

The incidence angle modifier tests were carried out by 
measuring the previous parameters (Te, Ts, Ta, Ig) at different 
angle of incidence θ (°). Six points are recorded: Two readings 
in the morning at an incidence of -40° < θ < -50°; Two readings 
around noon TSV (θ < 15°) and two in the afternoon 
(40°<θ<50°). Table 3 shows the experimental values for the of 
the modified angle of incidence of the solar collector studied. 
The adjustment of the measurement points of the modified 
angle of incidence Kτα as a function of the angle of incidence θ 
is presented in parabolic form, as shown in Figure 6. 

Table 3 
Experimental values noted for the calculation of K𝜏𝜏𝜏𝜏 (Kaci et al, 2012) 

Points θ (°) T*(Km2/W) η [(1/cosθ)-1]  Kα 

01 -55 0.028 0.391 0.6689  0.836 

02 -50 0.034 0.343 0.555  0.734 
03 0 0.076 0.468 0  1 
04 15 0.049 0.452 0.025  0.966 
05 50 0.110 0.320 0.657  0.685 
06 55 0.063 0.327 0.750  0.699 

0 10 20 30 40 50 60
0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

 

 

K
τα

Angle of Incidence θ (°)
 

Fig. 6 Angle of incidence modified according to the angle of incidence θ 

Table 4 
Main parameters used in the simulation 
Parameter Value Unit 

Weather data Algiers 
(Algeria) 

(-) 

Collector aperture area 2.6 m2 
Collector type Flat plate (-) 
Optical efficiency  0.49 (-) 
Heat loss coefficients - a1 5.7 W/m2K 
The incidence angle modifier𝐾𝐾𝜏𝜏𝜏𝜏 0.87 (-) 
Collector loop-specific mass flow 0.02 kg/s m2 
Tilt angle  36 ° 
Storage 3000 Liters 
Process temperature 60 °C 

Source : Experimental tests (Kaci et al 2012); Laboref company report (2020) 

The results of the evolution Kτα as a function of θ give a 
second-order curve in parabolic shape. It can be noticedthat 
Kτα is more or less constant in the range of angle of incidence 
lower than 40°. With prismed solar glass, the instantaneous 
efficiency of the flat solar collector can be constant up to an 
angle of incidence of 60°. It reaches a maximum for a value 
equal to 1. The values of Kτα are all less than one 1, which is 
true for the flat solar collector, because the latter reaches a 
maximum efficiency for a normal incidence the minimum value 
is 0.74, for this the average value is of 0.87 will be taken 
throughout our study. The latter represents a correction 
coefficient that must be multiplied by the expression of the 
performance of the capture field. Table 4 summarizes the 
technical characteristics of the experienced solar collector and 
a technical report obtained from the company (Laboref., 
2020), (Laboref: Agro-food industry for the production of 
aromas). 

2.4. System design  

The objective this part is to determine the collector field area 
and its optimal configuration (series-parallel arrangements). The 
F-chart method, which is the most used method in the sizing of 
solar heating systems, is used to determine the solar collector 
field size. The F-chart method was developed by Klein and 
Beckman, using results obtained on a large number of 
simulations with TRNSYS. According to this model, the useful 
energy gained by a solar collector can be given by (Bangura et 
al 2022): 

𝑄𝑄𝑢𝑢 = 𝐴𝐴𝐶𝐶�𝐹𝐹𝑅𝑅(𝜏𝜏𝜏𝜏)𝑒𝑒𝐼𝐼𝑔𝑔 − 𝐹𝐹𝑅𝑅𝑈𝑈𝑔𝑔(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)�                                          (4) 



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ISSN: 2252-4940/© 2023. The Author(s). Published by CBIORE 

In our work, this model was improved by introducing the 
measured performance correction factor  𝐾𝐾𝜏𝜏𝜏𝜏 at any incidence 
for flat plate solar collectors. This correction is among the 
originalities of this work (Bangura et al 2022): 

𝑄𝑄𝑢𝑢 = 𝐴𝐴𝐶𝐶�𝐾𝐾𝜏𝜏𝜏𝜏𝐹𝐹𝑅𝑅(𝜏𝜏𝜏𝜏)𝑒𝑒𝐼𝐼𝑔𝑔 − 𝐹𝐹𝑅𝑅𝑈𝑈𝑔𝑔(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)�                                  (5) 

Using the average values of collector’s parameters obtained 
in the previous section (𝐾𝐾𝜏𝜏𝜏𝜏 =0.87, 𝐹𝐹𝑅𝑅(𝜏𝜏𝜏𝜏)𝑒𝑒= 0.49 and 
𝐹𝐹𝑅𝑅𝑈𝑈𝑔𝑔=6.53), equation (5) become:  

𝑄𝑄𝑢𝑢 = 𝐴𝐴𝐶𝐶�0.87. 0.49 𝐼𝐼𝑔𝑔 − 6.53(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)�       (6)   

This method provides an useful mean for estimating the 
fraction of total heating load that will be supplied by solar 
energy for a given solar heating system. The primary 
designvariable is collector area and secondary variables are 
collector type. Then, the solar fraction is defined by the equation 
7 (Zwalnana et al 2021): 

𝑓𝑓 = 𝑄𝑄𝑢𝑢
𝐿𝐿
𝑜𝑜𝑜𝑜𝑓𝑓 = 1 − 𝐴𝐴𝑢𝑢𝐴𝐴

𝐿𝐿
      (7) 

 
With L : Monthly total heating load for  heating  hot water; 𝐴𝐴𝐴𝐴𝐴𝐴 : 
Monthly total heating auxiliary energy  hot water; By replacing 
the expression of the useful energy in equation (7):  

𝑓𝑓 = 1
𝐿𝐿
∫ 𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅 �(𝜏𝜏𝜏𝜏)𝑒𝑒 𝐼𝐼𝑔𝑔 − 𝑈𝑈𝑔𝑔(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)�𝛥𝛥𝛥𝛥 𝑑𝑑𝑑𝑑   (8) 

Where : 

𝑍𝑍 = 𝑇𝑇𝑒𝑒−𝑇𝑇𝑎𝑎
𝑇𝑇𝑟𝑟𝑒𝑒𝑟𝑟−𝑇𝑇𝑎𝑎

  

Therefore, the equation (8) becomes: 

𝑓𝑓 = 𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅
𝐿𝐿

∫  �(𝜏𝜏𝜏𝜏)𝑒𝑒 𝐼𝐼𝑔𝑔 − 𝑈𝑈𝑔𝑔�𝑇𝑇𝑟𝑟𝑒𝑒𝑟𝑟 − 𝑇𝑇𝑎𝑎�𝑍𝑍�𝛥𝛥𝛥𝛥 𝑑𝑑𝑑𝑑           (9) 

 
The method is a correlation of many hundreds simulation 

results of thermal solar system performances. The conditions of 
the simulations were varied over appropriate ranges of 
parameters for practical system designs. The resulting 
correlations give f, the fraction of monthly heating loads (hot 
water) supplied by solar energy as a function of two 
dimensionless parameters. The first is related to the ratio of 
collector losses and the second is related to the ratio of 
absorbed solar radiation.  

This equation can be decomposed into 2 dimensionless 
terms X (Collector Loss) and Y (Collector Gain), which are given 
in equations (10) and (11)(Klein et al 2013 and Okafor et al 2012): 

𝑋𝑋 = 𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅
𝐿𝐿
𝑈𝑈𝑔𝑔�𝑇𝑇𝑟𝑟𝑒𝑒𝑟𝑟 − 𝑇𝑇𝑎𝑎�𝛥𝛥𝑑𝑑                                                             (10) 

 𝑌𝑌 = 𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅
𝐿𝐿

(𝜏𝜏𝜏𝜏) 𝐻𝐻𝛽𝛽𝑁𝑁                        (11)     

For the system configuration studied, the solar fraction f of 
the monthly total load supplied by water heating system, given 
as a function of X and Y in equations 10 and 11, becomes in the 
form (Deepika et al 2016): 

𝑓𝑓 = 1.029𝑌𝑌 − 0.065𝑋𝑋 − 0.245𝑌𝑌2 + 0.0018𝑋𝑋2 + 0.0215𝑌𝑌3 (12) 

The iterative dichotomy method is used to solve equations 
(10), (11) and (12) which allow to obtain the collector’s area for 
any incidence angle modifier.  

 Concerning the optimal configuration of solar system, the 
latter is designed according to the water temperature of the 
storage tank. The thermal collectors of the solar field may be 
connected in series, in parallel, or in combinations. Once the 
collector parameters, the storage size and loss coefficient, the 
magnitude of the load, and the meteorological data are 
specified, the storage tank temperature can be calculated as a 
function of time.  Also, the energy gained from the collector, 
losses from storage, and energy to load can be determined for 
any desired period of time by integration of the appropriate rate 
quantities with the following equation (Kaci et al 2014). 

(𝑀𝑀𝑀𝑀𝑀𝑀)𝑠𝑠
𝑑𝑑𝑇𝑇𝑠𝑠
𝑑𝑑𝛥𝛥

= 𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅 ��(𝐾𝐾𝜏𝜏𝜏𝜏)𝑒𝑒𝐼𝐼𝑔𝑔 − 𝑈𝑈𝑔𝑔(𝑇𝑇𝑖𝑖 − 𝑇𝑇𝑎𝑎)�� − (𝑈𝑈𝐴𝐴)𝑆𝑆(𝑇𝑇𝑆𝑆 −
𝑇𝑇𝑎𝑎)  − 𝜀𝜀2��̇�𝑚𝐶𝐶𝑝𝑝�𝑚𝑚𝑖𝑖𝑛𝑛(𝑇𝑇𝑆𝑆 − 𝑇𝑇𝑟𝑟)    (13) 

Equation (13) can be integrated using simple Euler method, 

where temperature derivative 
𝑑𝑑𝑇𝑇𝑠𝑠
𝑑𝑑𝛥𝛥

 is expressed as 
𝑇𝑇𝑠𝑠+−𝑇𝑇𝑠𝑠
∆𝛥𝛥

. The time 
step should be taken equal to weather data increments in order 
to ensure numerical stability. 
The storage temperature Ts can be given by (Kaci et al 2014): 

𝑇𝑇𝑆𝑆
+ = 𝑇𝑇𝑆𝑆 +

𝑑𝑑𝛥𝛥
(�̇�𝑚𝑐𝑐𝑝𝑝)𝑠𝑠

�𝜀𝜀𝐴𝐴𝐶𝐶𝐹𝐹𝑅𝑅�𝐾𝐾(𝜏𝜏𝜏𝜏)𝐼𝐼𝑔𝑔 − 𝐹𝐹𝑅𝑅𝑈𝑈𝑔𝑔(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑎𝑎)� −
(𝑈𝑈𝐴𝐴)𝑆𝑆(𝑇𝑇𝑆𝑆 − 𝑇𝑇𝑎𝑎) − 𝜀𝜀(�̇�𝑚𝑀𝑀𝑀𝑀)𝑠𝑠(𝑇𝑇𝑒𝑒 − 𝑇𝑇𝑟𝑟)�   (14) 

𝑇𝑇𝑆𝑆
+: The new tank temperature calculated for the end of the 

hour. 
 
2.5. Economical parameters 
 
The Levelized Cost of Energy (LCOE) is the most indicator to 
evaluate the competitiveness of the proposed solar thermal 
process. Indeed, LCOE represents the average revenue per unit 
of energy generated that would be required to recover the costs 
of operating the thermo-solar process during an assumed 
financial life cycle.  

According to the International Energy Agency (IEA), The 
costs of the thermo-solar process can be classified into three 
different sets: investment costs, operation and maintenance 
costs and electricity costs. The factor multiplying the initial 
investment is called capital recovery factor (Crf). It converts a 
present value into a stream of equal annual payments over a 
specified time (in this case 25 years), at a specified discount rate 
(in this case 8%)(Fernández 2013) . 

𝐿𝐿𝐶𝐶𝐿𝐿𝐿𝐿 =
𝐶𝐶𝑟𝑟𝑟𝑟.𝐾𝐾𝑖𝑖𝑖𝑖𝑖𝑖+𝐾𝐾𝑂𝑂,𝑀𝑀+ 𝐾𝐾𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑟𝑟𝑖𝑖𝑒𝑒𝑖𝑖𝑒𝑒𝑒𝑒

𝐸𝐸𝑖𝑖𝑒𝑒𝑒𝑒
    (15) 

 

𝐶𝐶𝑜𝑜𝑓𝑓 = 𝐾𝐾𝑑𝑑(1+𝐾𝐾𝑑𝑑)
𝑖𝑖

(1+𝐾𝐾𝑑𝑑)𝑖𝑖−1
+ 𝐾𝐾𝑖𝑖𝑛𝑛𝑠𝑠𝑢𝑢𝑟𝑟𝑎𝑎𝑛𝑛𝑐𝑐𝑒𝑒    (16) 

 
Where LCOE is the Levelized Cost of Energy, Crf is the capital 
recovery factor, Kinv is the total investment of the plant, KO&M is 
the annual operation and maintenance costs, Kelectricity is the 
annual electricity costs (7 DZD/kWh), Enet is the annual net 
thermal energy, Kd is the real debt interest rate = 8 %, n is the 
depreciation period in years = 25 years, Kinsurance is the annual 
insurance rate = 1 %. 
 

3. Results and discussions 

3.1. Solar field area and optimal configuration  

In this section, the optimal solar collector area and system 
configuration using F-chart method are investigated. The 
thermo-solar system is sized based on the real parameters of the 



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collector measured in the experimental section. In Figure 7, it is 
shown the variation of the surface area of solar collector in 
function of the incidence angle and incidence angle modifier 
during a typical day of the year. Figure 7a shows that the 
collector area varies inversely proportional with the θ and Kτα. 
That means that the closer the collector is to normal incidence 
(Kτα =1 or θ=0) the more the collector’s efficiency increases 
which obviously induces a minimum surface. This result is in 
accordance with that found by Duffie et al (2013). 

In our case, as shown in Figure 7a and Figure 7b, for  θ=-
30° (East) and θ=+30° (West) and where a value of incidence 
angle modifier of 0.87 is considered (Figure 6), an area of 64 m² 
is obtained, which corresponds to a number of 24 collectors (the 
collector used has a unit area of  2.6 m2). In order to determine 
the optimal configuration of the solar field, four cases are 
considered in function of the number of solar collectors in series. 
The cases consider two, three, four collectors in series and in 
the last case all collectors are connected in parallel. The 
variation of the storage tank temperature for the four different 
cases studied is shown in Figure 8. 

It was observed that the higher the number of collectors in 
series, the higher the water outlet temperature. However, only 
the configuration with four collectors in series is able to reach 
the operating temperature of the industrial process (60°C) 
during the period of hot water utilization, as well Nunes et al 
(2014) reported in their work. Therefore, the solar system will 
be composed of 6 blocks of collectors in parallel with 4 
collectors in series in each block, (i.e. 24 collectors). 

 

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
0

10

20

30

40

50

60

70

80

90

 

 

A
re

a 
(m

2 )

θ 

a)

 

0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
0

10

20

30

40

50

60

70

80

90

 

 

A
re

a 
(m

2 )

Kτα

b)

 
Fig. 7 Determination of the collector’s areas: a) a function of Incidence 
Angle; b) a function of incidence Angle Modifier 

6 7 8 9 10 11 12 13 14 15 16 17 18
0

10

20

30

40

50

60

70

 

 

Te
m

pe
ra

tu
re

 (°
C)

Times (hours)

 Parallel collector
 Two series of collectors
 Trie series of collectors
  Four collectors in series Process temperature

 
Fig. 8 storage tank Temperature during a day

6 7 8 9 10 11 12 13 14 15 16 17 18
0,0

0,2

0,4

0,6

0,8

1,0

 

 

E
ff

ic
ie

nc
y 

Times (hours) 

 The blocks of collector in parallel 
 Two blocks of collector in series
 Three blocks of collector in series
 Four blocks of collector in series
 Five blocks of collector in series
 Six blocks of collector in series

 

Fig.9 Variation of the collector’s efficiency in function of the block’s 
configurations   

Effectively, the result shows that the efficiency of the 
configuration of 6 blocks in parallel is better than that of 
configurations with blocks inseries, as shown in Figure 9. 
Indeed, the blocks of collectors connected in seriesinduce 
greater heat losses by convection and radiation and therefore 
result in a lower thermal efficiency. This design is more efficient 
from an economic point of view because the comparison of 
different configurations also indicates that series configurations 
result in additional pressure drop, which also increases the 
pumping power (Duffie et al.2013) 

3.2. Solar fraction of the solar system  

The energy performance the solar system under 
investigation is determined by calculating the solar fraction of 
the solar system. The solar fraction is defined as the ratio of the 
thermal energy produced by the solar collectors and the thermal 
energy needed for hot water production required by the 
industrial process (Ghafour, 2014). In this work, Eq.12 was used 
to calculate the hourly, monthly and yearly solar fraction  

Considering the variations of the mains water temperature 
(shown in Fig.4) and rhythms of industrial production(hourly 
daily hot water need, Fig.2), the monthly energy needs of hot 
water production are represented on Figure 10. This figure 
illustrates also the global monthly solar radiation available in 
this location. We note that, unfortunately, the maximum needs 



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ISSN: 2252-4940/© 2023. The Author(s). Published by CBIORE 

for hot water correspond to the periods when the availability of 
solar energy is minimal. Indeed, solar radiation energy is high in 
summer. It reaches up to (6000 kWh) while in winter it is about 
2500 kWh. Solar energy could be enough to deliver the required 
amount of hot water during summer. During winter, the solar 
coverage rate is inevitably lower than in summeras shown in 
Figure 10. It is therefore necessary to properly size the 
installation to obtain the best energy/economic compromise. 

Figure 11 represents the monthly solar fraction of the solar 
system. It can reach a maximum of 80% in summer, with an 
average annual solar fraction of about 50 %. This is due to the 
best proposed design, the optimal operating parameterschosen 
for the system and the high intensity of solar radiation at the 
site. In the work conducted by Pahlavan et al (2018),where a 
water heating solar system is applied in 37 regions in Algeria, a 
yearly solar fraction of 60% was found, which is very close to 
our results.This mans that such systems are very interesting. 

 
3.3. Parametrical study 

In order to determine the optimum flow rate for the optimum 
solar collector’s configuration found in the previous section, 
water mass flow rate varying between 0.01 kg/m2.s and 0.04 
kg/m2.s are considered, which are the most useful flow rate 
range for solar heating installations (Duffie et al 2013). The aim 
was to determine the optimum flow for this configuration of 
solar collectors. It was observed that this configuration offers 
the best solar fraction when the mass flow rate is 0.02 kg/s m2.  

6 8 10 12 14 16 18
0

40000

80000

120000

160000

200000

 

 

 0,03 kg/sm2
 0,02 kg/sm2
 0,01 kg/sm2

U
se

fu
l E

ne
rg

y 
(J

ou
le

))

Times (hours)
 

Fig. 12 Effect of mass flow rate on the useful energy gain 

6 7 8 9 10 11 12 13 14 15 16 17 18
0

1000

2000

3000

4000

5000

6000
 

W
at

er
 lo

ad
 (L

ite
r)

Times (Hours)

a)

 

6 7 8 9 10 11 12 13 14 15 16 17 18
0

1000

2000

3000

4000

5000

6000
 

W
at

er
 lo

ad
 (L

ite
r)

Times (hours)

b)

 

6 7 8 9 10 11 12 13 14 15 16 17 18
0

1000

2000

3000

4000

5000

6000
 

W
at

er
 lo

ad
 (L

ite
r)

Times (hours)

c)

 

Fig. 13 Storage capacity for three different casesload profile a)  in 
morning b) afternoon c) shared between hand and afternoon 

Jan Feb Mar Apr May Jun jul Aug Sep Oct Nov Dec --
0

1000

2000

3000

4000

5000

6000

E
ne

rg
y 

(k
W

h)

Month

 Solar radiation
  Monthls needs 

Fig.10 Monthly solar radiation and monthly energy needs 
 

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8
 

 

So
la

r f
ra

ct
io

n 

Months  
Fig. 11Variation of solar Energy efficiency during a year 

 



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6 8 10 12 14 16 18 20
0

1x105

2x105

3x105

4x105

5x105  Case 1
 Case 2
 Case 3

In
te

rn
al

 e
ne

rg
y 

ch
ar

ge
 (J

ou
le

)

Times (Hours)  
Fig. 14 Effect of the water load moment on the performance of the 

installation 
 
 
This is the optimum value of mass flow rate for solar water 
heating systems recommended by ISO 9806 and EN 12975-2 
(Kramer et al. 2017) and which is used throughout this work. The 
results find in this study are also in agreement with those of 
Hang et al. (2012) and Ge et al. (2012). As shown in Figure 12, 
for all cases considered the mass flow rate increase gradually 
with heat flux until reaching its maximum in the middle of the 
day and then decrease with the falling of the sun. The collector 
efficiency shows a proportional relationship with the mass flow 
rate (Mandal and Ghosh, 2020; Yassen et al., 2019). 

The influence of the load profile is investigated for different 
cases. A real load profile was used as an input for the model in 
the brewing water loop to consider the manual interference of 
the discharge control. It has been considered three cases to 
highlight the effect of water load on the effectiveness of the 
installation, as shown in Figure 13. The hot water demand 
occurs, in the first, second and third cases, respectively, in 
morning (Fig.13a), afternoon (Fig.13b), and shared between 
morning and afternoon (Fig.13c).   

It can be seen from  Figure 14, which represents the effect 
of the water load moment on the performance of the installation, 
that the efficiency of the case with a water load in the afternoon 
(case 2) is higher than that in the morning (case 1). Indeed, in 
the latter case, the storage tank is less charged with solar energy 
and the storage tank will be recharged with cold water, which 
induces significant heat losses. It has been observed that the 
water load in the morning or in the evening has a significant 
effect on the performance of the installation. Therefore, the best 
system performance is achieved when the water load is 
occurred in the afternoon. 

It can also be observed from Figure 14, which shows the 
effect of the number of waters loads on the performance of the 
installation, that the efficiency of the case with one water load 
(case 1 and 2) is higher than that with two water loads (case 3), 
nearly double. This is because in the latter case the storage tank 
is re-charged with cold water, which also induces significant 
heat losses.  It has been observed that the number of water load 
during the day has strongly effect of the performance of the 
installation. This means that processes that operate during 
many days in the week are not always preferable unless the total 
load is higher. It can be concluded that the load profile is 
expected to be the most important influence factors for the 
system performance of a solar process. Indeed, the work of 
Schmitt et al (2012) also shows that the load profile is the most 
important influencing factor for the system performance of a 
solar process heat system; 

4. Economical study 

After the design phase, the system is investigated in 
economical point of view. For this reason, various costs of the 
project components are estimated. Table 5 illustrates the costs 
of each component of the thermo-solar process.  
As illustrated in Table 6, three cases have been considered:  

Case 1: Solar system without support (subvention) from the 
Algerian government program of renewable energy; 
Case 2: Solar system with support. The Algerian government 
program of renewable energy offers 45% of the total costs of 
solar collectors (APRUE 2022). 
Case 3: Conventional system. The heating system is powered 
by the electrical energy from the grid. 

The net annual energy produced is calculated taking into 
account the technical report from the company, that is to say 
process temperature of 60 °C and the average daily hot water of 
3000 liters. The solar processes (Cases 1 and 2) are supposed to 
ensure 50 % of the energy needs (result found in Figure 6 
average annual solar fraction of about 50 %),which results in 
annual electricity demand of 25 080 kWh. Table 6 shows the 
actual LCOE in the Algerian market for an electricity price of 
7DZD/kWh, which is equivalent to 0.05 €/kWh. 

Table 5 
Costs of each part of the industrial process 

Component Unit cost (€) Number Total cost (€) 
Investment costs 

Collectors  505,52 24 12 132,48 
Piping 25,28 200 5 056 
Gate valve 27.33 30 819,9 
Safety valve 13.66 12 163.92 
Monometer  21.86 5 109.3 
Purge 10.25 30 307.5 
Check valve  13.66 10 136.6 
Tank  1024.7 2 2049.4 
Pumps 314.57 5 1572.85 
Vase expansion  51.23 1 51.23 
Heat Exchanger  512.35 2 1024.7 
Temperature 
Regulator  

81.98 2 163.96 

Operation and maintenance costs 
Collectors  6.83 24 163.92 
Tanks 153.7 2 307.4 
Piping 170.78 1 170.78 

Source :  Missoum et al (2021) 

 
 
 
 
Table 6 
Total costs of the water heating processes 

Case Kinvest 
(€) 

KO&M 
(€) 

Enet 
(kWh) 

Electricity 
needs 

(KWh) 

LCOE 
(DZD/ 
kWh) 

LCOE 
(Euro/k

Wh) 
Case 1 23587.84 742.1 50160 25080 12.650 0.108 

Case 2 12973.31 742.1 50160 25080 9.071 0.067 

Case 3 3415.67 3204.94 50160 50160 8.246 0.061 
1DZD = 0.0069  € (Source : External Bank of Algeria,. 2023) 

 



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8 12 16 20 24 28 32 36 40
5

10

15

20

25

30

35

40

45

 

 
LC

O
E 

(D
ZD

/k
W

h)

Electricity price (DZD/kWh)

 Case 1
 Case 2
 Case 3

 
Fig. 15 Variation of LCOE as a function of electricity price. 

The latter value is so much lower than international markets. 
For instance, the electricity price in Germany is about six times 
more expensive than in Algeria (0.30 €/kWh).  Under the 
current scenario, the LCOE of the solar thermal process is 
0.1€/kWh, but its price with support is 0.067 €/kWh, slightly 
higher than the one based on electric heating (fossil fuels-based 
processes) is 0.061€/kWh, a very encouraging result. 

Figure 15 shows the variation of the LCOE of the three 
processes (Cases 1, 2, 3) as a function of electricity prices. A 
range from 0.048€ to 0.27€/kWh is intentionally considered. 
The former value is the actual price in the Algerian market while 
the latter is the price in the German market. As showing in 
Figure 15, the solar process with support is becoming 
competitive to the fossil-based heating process at the electricity 
price of 0.061€/kWh; a price corresponds to US and Canada 
markets. For the case of a solar process without support from 
the Government, the electricity price should rise to about 
0.12€/kWh to ensure competitiveness. This price corresponds 
to the French electricity market.   

5. Comparison of results 

To verify and justify the results we obtained, they were analyzed 
and compared with the results of two different process heating 
systems, as shown in Table 7, with the same collector 
technology (flat plate collector), flow rate and set-point water 
heating temperature Tc (60 °C). Therefore, the solar fractions of 
the obtained systems are relatively similar. To verify and justify 
the obtained results, they were analyzed and compared with the 
results of two different process heating systems, as shown in 
Table 7, with the same collector technology (flat plate collector), 
flow rate and set-point water heating temperature Tc (60 °C). 
Therefore, the solar fractions of the obtained systems are 
relatively similar. 

Bahria et al., (2016) investigated the performance of a solar 
heating system in different climates of Algeria. The solar 
fraction for domestic hot water of 80% has been found. 
Kalogirous et al.(2003) studied a solar industrial process heat in 
Chypre. The solar fraction of system was 75%. In other work, 
the authors Kalogirous et al.(2019), have found for the same 
system, a LCOE of 0.2 Euro/kwh. Moreover, for the work 
presented by Strum et al. (2015) on the case study of a medium 
sized Beijing based factory, the result also gave the fraction of 
14% and the LCOE of 0.14, which also confirms the accuracy of 
our result. However, the resulting energy costs (LCOE) obtained 
for solar heat are 0.1 € /kWh. These results are applicable to all 
countries with similar weather and economic conditions to 
these regions. The small difference in the LCOE lies mainly in 
the price of conventional energy in Algeria is subsidized which 
makes its price a bit low compared to other cases 

Table 7 
Comparison of results to others studies 
Case Solar  

potential 
(kWh/m2) 

Collectors 
type 

Flow 
rate 
(Kg/sm2) 

Tc 
(°C) 

Solar 
fraction 
 

LCOE 
(€/kWh) 

This study 1651 (FPC) 0.02 60 50 % 0.1 

Bahria et al 
2016 

1800 (FPC) 0.02 60 82% - 

Kalogirou 
2003, 2019) 

1727 (FPC) 0.015 60 75% 0.2 

Sturm et al. 
(2015) 

1400 (FPC) 0.02 60 14% 0.1 

 

6. Conclusion  

This study presents the results of the design, size and energy 
efficiency of a solar thermal system for the food industry in 
Algeria. The method used to size the system is based on the F-
chart method of the HWB model, improved by introducing a 
new power correction factor at each flat-plate incidence angle, 
which was one of the original features of this work. This value 
has been experimentally tested and calculated according to the 
EN 12975-2 standard, using real data of energy demand and 
water consumption curves to determine the actual solar process 
performance. The results obtained after simulating the model 
used resulted in a collection arrangement taking into account 
the requirements, process temperature and the available area of 
64 m² (i.e. 24 collectors) on the company's roof. 

The system consists of 6 collector blocks connected in 
parallel, with 4 collectors connected in series in each block. 
Simulation results show that a solar coverage of 50% per year 
can be achieved, which is very high and has sparked great 
interest in integrating this solar thermal process at selected 
locations. 

The  parametric study confirmed that the selected mass flow 
rate is in good agreement with the EN 12975-2 and ISO 9806 
standards. The results also showed that the amount and 
duration of water exposure during the day had a large impact 
on plant performance. Therefore, to keep up with the 
fluctuations of the sun, the best time to brew is in the afternoon 
or early evening. 

The sensitivity analysis shows that operating temperature, 
collector selection, and required power are the most important 
factors affecting system efficiency. The economic evaluation 
shows that the assisted solar process is competitive with the 
fossil heating process at an electricity price of 0.062€ /kWh, 
while the unassisted solar process may be more competitive 
when the electricity price reaches 0.12€ /kWh. In the current 
context of global warming, Algeria's energy transition is still 
hampered by the relatively high installation costs of renewable 
energy compared to the kWh price of fossil electricity. The same 
is true for most oil and gas production operations. In fact, the 
latter's current offer is unbeatable. Therefore, it is more urgent 
than ever to develop national economic development plans that 
promote energy and environmental transition and sustainable 
development. 

 

Nomenclature 

Ac1   Collectors’ area of the first collector   (m2) 
Ac2  Collectors’ area  of the second collector   (m2) 
Ac        Collectors’ area  (m2) 
Cp        Heat capacity of water  (kJ/kg°C) 
F          Fraction of the monthly heating load(-) 
F’        Corrected FR factor   (-) 
FR  Collector heat exchanger efficiency factor   (-) 



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F’R  Corrected  collector heat exchanger efficiency factor  (-) 
FRUg Collector overall energy loss coefficient (W/m2°C) 
Gh        Monthly averaged, daily radiation incident   (MJ/m2) 
𝐻𝐻𝛽𝛽 Monthly average daily radiation incident on collector surface 

per unit area (MJ/m2) 
hm    Sun height     (degree)  
Ig         Global solar radiation (W/m2) 
L          Monthly total heating load hot water  (kWh/m2) 
M         Actual mass of storage capacity   (kg) 
�̇�𝑚 Mass flow rate (kg/s) 
N          Days in month(-) 
Qu1 Solar useful heat gain rate of the first collector(W) 
Qu2    Solar useful heat gain rate of the second collector (W) 
Te        Inlet fluid temperature (°C) 
Ta        Ambient temperature (°C) 
Tref       An empirically derived reference temperature (°C) 
Tr         The mains water temperature (°C) 
TS        Storage temperature  (°C) 
𝑇𝑇𝑎𝑎��� Monthly average ambient temperature (°C) 
Td  The minimum desired temperature(°C) 
X        Modified sensibility factor of the thermal losses   (-) 
𝑋𝑋𝐶𝐶���  Dimensionless average daily critical level of the solar  

collector  (-) 
Y          Ratio of the absorbed solar energy to the cooling load  (-) 

Greek symbols 

Δt        Total number of seconds in month  (s) 
β      Collector tilt angle  (degree) 
ε        Heat exchanger effectiveness   (-) 
(τα)e    Monthly average transmittance-absorptance product (-) 

Abbreviations 

IAM    Incidence Angle Modifier  (-) 
TSV     True solar time  (hours) 

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	Design, optimization and economic viability of an industrial low temperature hot water production system in Algeria: A case study
	Karim Kacia0F , Mustapha Merzouka, Nachida Kasbadji Merzoukb, Mohammed Missoumc, Mohammed El Ganaouid, Omar Behare, Rabah Djedjigd
	1. Introduction
	2. Methodology
	2.1. Presentation of the case study
	2.2. Weather data and validation
	2.3. Determination of the solar collector’s parameters

	3. Results and discussions
	3.1. Solar field area and optimal configuration
	3.2. Solar fraction of the solar system
	3.3. Parametrical study

	4. Economical study
	6. Conclusion