Sustainable Cities and Society 38 (2018) 1–8
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Numerical investigation of solar chimney power plants performance for Saudi Arabia weather conditions
T
⁎
Mostafa A.H. Abdelmohimena,b, , Salem A. Algarnib a b
Mechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Egypt Mechanical Engineering Department, King Khalid University, Abha, Saudi Arabia
A B S T R A C T The solar chimney power plant is one form of renewable energy technology uses the benefit of high intensive solar radiation locations. The system consists of three main parts (collector, turbine, and chimney) where it can convert electric energy through three traditional mechanisms. In this study, the performance of the solar chimney power plant in six different locations in the kingdom of Saudi Arabia is investigated all over the year. A numerical model has been validated against published experimental data and carried out to investigate the performance. RNG K-∈ model is used to solve the momentum equation through the system. The discrete ordinate (DO) radiation model was adopted to solve the radiative transfer equation. The results show that a solar chimney power plant with 194 m chimney height and 244 m collector diameter is capable of producing monthly average 56 kW electric power over a year in Riyadh city. Bisha region of Saudi has found to be the best place to build a solar chimney power plant where the yearly average produced power is around 63 kW. The efficiency of the solar chimney power plant is affected by the value of both solar radiation and atmospheric temperature where the collector efficiency ranges between 10–29% around the year. The results indicated that the solar chimney power plant could be an important supplement for energy in Saudi Arabia.
1. Introduction With a very limited use of the abundant renewable solar thermal energy in Saudi Arabia, burning the fossil fuels and natural gas are heavily used to fulfill the electric energy demand. To reduce the dependency on fossil fuels and its associated CO2 emission, green technologies have to be adopted. Solar chimney power plant (SCPP) is one application of renewable energy technologies that can be utilized to reduce the use of conventional sources of energy. SCPP consists of three main parts; Solar collector, chimney, and wind turbines as shown in Fig. 1. The air temperature increases due to the heat gain from the collector, as a result of greenhouse effect. Buoyancy force drives a continuous flow of air from the collector perimeter into the chimney located at the middle of the collector roof. By setting a wind turbine in the path of air, electricity can be generated. Although the efficiency of the solar chimney power plant is low due to change of only a small portion of the collected solar energy into electricity, it makes up for this disadvantage by its economical, robust construction, and low cost of maintenance (Schlaich, 1995). Generating electricity by using SCPP has been proven as a reliable way by the prototype at Manzanares, Spain (Haaf, Friedrich, Mayr, & Schlaich,
⁎
1983; Haaf, 1984) where the chimney had a height of 195 m and a diameter of 10 m and the collection area (greenhouse) was 46,000 m2. The maximum power output was up to 50 kW. The performance of SCPP has been analytically and numerically estimated. The analytical method based on a one-dimensional thermal equilibrium analysis through the collector. Pasumarthi and Sherif (Pasumarthi and Sherif, 1998a, 1998b) represented an approximate model to investigate the effects of different parameters on air temperature and velocity distribution through the system. Larbi et al. (Larbi, Bouhdjar, & Chergui, 2010) estimated a performance analysis of the solar chimney power plant in the southwestern region of Algeria. Their analysis is based on the mathematical model developed by Schlaich et al. (Schlaich, Bergermann, Schiel, & Weinrebe, 2003). This mathematical modeling is based on momentum and energy balance equations, in the collector and in the chimney as well. Zhou et al. (Zhou, Yang, Xiao, & Hou, 2009) analyzed, by using a theoretical model, the maximum chimney height for convection avoiding negative buoyancy at the latter chimney and the optimal chimney height for maximum power output. The results show that maximum height gradually increases with the lapse rate increasing and go to infinity at a value of around 0.0098 K m−1. Guo et al. (Guo, Li, & Wang, 2014a)
Corresponding author at: Mechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Egypt. E-mail address:
[email protected] (M.A.H. Abdelmohimen).
https://doi.org/10.1016/j.scs.2017.12.013 Received 29 October 2017; Received in revised form 7 December 2017; Accepted 8 December 2017 Available online 13 December 2017 2210-6707/ © 2017 Elsevier Ltd. All rights reserved.
Sustainable Cities and Society 38 (2018) 1–8
M.A.H. Abdelmohimen, S.A. Algarni
Nomenclature Cp h I m˙ Pr rcoll Qv Δpt
T Ta Tsky uw v ηt ρ ρa β
Specific heat capacity (J/(kg K)) Convective heat transfer coefficient (W/(m2K)) the incident solar radiation (W/m2) the mass flow rate (kg/s) Prandtl number the collector radius (m) the volume flow rate (m3/s) the turbine pressure drop (Pa)
Air temperature (K) Atmospheric temperature (K) the equivalent temperature of the sky (K) the wind speed of the environment (m/s) Air velocity across the turbine (m/s) the turbine efficiency Air density (kg/m3) Atmospheric air density (kg/m3) the thermal expansion coefficient
climatic conditions of Saudi Arabia. The 3-D numerical simulation method incorporating the radiation and solar load according to the place and time of the year is used to simulate the SCPP in different cities of the Kingdom of Saudi Arabia. Six cities were selected to cover the impact of different climatic conditions of the kingdom.
developed a comprehensive theoretical model by taking into account the hourly variation of solar radiation. They represent the effects of the collector and chimney radii on the power output of the SCPP, and the results reveal that the power output increases almost linearly with the collector radius when the radius is small, then the trend becomes slower with the increase in collector radius. That means there is a limitation on the maximum collector radius, beyond which there is no further increase in the power output. On the other hand, the power output increases with the chimney radius. A thermodynamic analysis of a SCPP throughout a daily operation cycle including an unsteady theoretical model that take in consideration the soil heat storage is represented by Guo et al. (Guo, Wang, Li, & Wang, 2016) where different types of soil are used as a heat storage material in the unsteady simulations. The using of CFD commercial programs to predict the solar chimney power plant performance has been increased rapidly. a 2-D numerical model is represented by Pastohr et al. (Pastohr, Kornadt, & Gurlebeck, 2004). They studied the flow field and temperature distribution through the collector of the solar chimney. Xu et al. (Xu, Ming, Pan, Meng, & Zhou, 2011) used the same model with adding an energy storage layer and a turbine simulation model. Guo et al. (Guo, Li, & Wang, 2014b) represents a 3-D numerical simulation method including the radiation, solar load, and turbine models, they validate their model by comparing results with the experimental data of the Spanish prototype. They investigate the effects of variation of solar radiation, turbine pressure drop, and ambient temperature on the performance of the Solar chimney power plant. Many studies have investigated the performance of SCPP in the developing countries. The performance of SCPP have been analytically investigated in Iran (Sangi and Roozbeh, 2012), China (Dai, Huang, & Wang, 2003), rural areas of developing countries (Onyango et al., 2006), Egypt (El-Haroun, 2012), and Algeria (Larbi et al., 2010). However, little work on SCPP performance has been done under the climate conditions of Saudi Arabia. Hussain and Al-Sulaiman (Hussain et al., 2016) performed exergy analysis of SCPP performance under the hot-humid climate condition of Daharan, Saudi. Therefore, in the present work, the SCPP performance has been investigated under different
2. Geographical features of Saudi Arabia The typical geographical location of Saudi Arabia extends between E 34° and E 56° longitude, and N 16° and N 33° latitude. This location gives it a wide range of weather. Saudi Arabia has tropical and subtropical desert regions. The winds are generally dry, and almost all of the land is arid. Because of the dryness and the relatively cloudless skies, there are great extremes of temperature and solar radiation and wide variations between the seasons and regions. Fig. 2 shows the direct normal irradiation on the kingdom of Saudi Arabia. Over the last two decades, Saudi Arabia has experienced a large increase in energy consumption, which is four times higher than the world average per capita (Asif, 2016). Furthermore, the electric power demand in this region is expected to increase rapidly due to a heavily subsidized electricity cost structure and high population growth (Farnoosh, Lantz, & Percebois, 2014). Moreover, Saudi Arabia is located in the arid area, and its local ecosystem is fragile due to the extreme deficit of water. Due to that, there is a limitation of the construction of conventional thermal power stations, which depend heavily on water resource. Accordingly, it is a judicious choice to effectively utilize the local renewable energy resources to generate electric power. Saudi Arabia has an abundant resource of solar energy (Asif, 2016) where annual solar radiation and sunshine duration in Saudi Arabia are very high as compared with other places all over the world. Saudi Arabia is also rich in land resource and features a very low population density. The water shortage severely restricts the utilization of land resources. However, the large-scale installation of SCPP can provide an effective approach for exploiting the arid lands and deserts. Therefore, the construction budget for such a SCPP would be relatively low.
3. Numerical model and calculations 3.1. Physical model The Spanish prototype was selected as the physical model to verify the numerical method. A 3D model with the Spanish prototype has been created. Fig. 3 provides an overall view of the computational domain of the solar chimney power plant. As indicated in the measured data of the Spanish prototype (Haaf, 1984), soil temperature at 0.5 m depth underneath the ground remained unchanged with time. Therefore, a ground thickness of 3 m is believed to be sufficiently deep to facilitate the isothermal condition of the bottom boundary of the soil layer. The main dimensions of the studied geometry (Spanish prototype) are presented in Table 1. Fig. 1. Schematic illustration of a solar chimney power plant components (SCPP).
2
Sustainable Cities and Society 38 (2018) 1–8
M.A.H. Abdelmohimen, S.A. Algarni
Fig. 2. Direct normal irradiance on land of the Kingdom of Saudi Arabia.
3.2. Mathematical models
Table 1 Main dimensions of the Spanish prototype.
All simulations were conducted for steady flow using the finite volume-based solver FLUENT. An unstructured computational grid was developed using the Gambit grid generator with approximately 1.2 million computational cells for each case. A grid independence has been carried out to select the proper mesh. Body force weighted discretization is used for pressure, while second order upwind has been used for momentum, energy, turbulence kinetic energy, and turbulence dissipation rate. Standard wall functions are used to represent the near – wall treatment. Heat transfer in the SCPP system involves all three modes: conduction, convection, and radiation. The collector is the main part at which the radiation heat transfer occurs. There are many models available in FLUENT to solve the radiation heat transfer. The discrete
Mean collector radius Collector height at inlet Collector height at center Chimney height Chimney radius Ground thickness
122.0 m 2.0 m 6.0 m 194.6 m 5.0 m 3.0 m
ordinate model (DO model) has been selected to solve radiation heat transfer in the present simulation duo to its ability to calculate the radiation in semi-transparent media such as glass. This model is used by Guo et al. (Guo et al., 2014b) and validated with the experimental data
Fig. 3. the computational domain and the boundary conditions of the SCPP.
3
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of the Spanish prototype. In our study, the direction of the sun rays, which specified according to each city latitude and longitude, is represented by using the solar ray-tracing model provided by FLUENT. This assumption will represent more accurate results depending on the site of each city. The radiative transfer equation (RTE) for an absorbing, emitting, → and scattering medium at position r in the direction → s is
The quantities αk and αε are the inverse effective Prandtl numbers for k and ϵ, respectively. The main difference between the RNG and standard k-∈ models lies in the additional term in the ϵ equation given by
dI (→ r,→ s) σT 4 + (a + σs ) I (→ r,→ s ) = an2 ds π
where η ≡ Sk/ε, η0 = 4.38, β = 0.012 The effect of this term lets the RNG model be more responsive to the effects of rapid strain and streamline curvature than the standard k- ϵ model, which explains the superior performance of the RNG model for certain classes of flows. The Boussinesq model is used to represent the density change through the system. In that model, the density is defined by Eq. (9) in the buoyancy term in the momentum equation.
+
σs 4π
4π
∫ 0
' ' I ⎜⎛→ r,→ s ⎟⎞ Φ( ⎜⎛→ s,→ s ⎟⎞ dΩ' ⎝ ⎠ ⎝ ⎠
Rε =
(1)
The discrete ordinates (DO) radiation model solves the radiative transfer equation for a finite number of discrete solid angles, each associated with a vector direction → s fixed in the global Cartesian system (x, y, z). The DO model does not perform ray tracing. Instead, the DO model transforms Eq. (1) into a transport equation for radiation intensity in the spatial coordinates (x, y, z). Thus, Eq. (1) is written as
4π
∫ 0
' ' I ⎜⎛→ r,→ s ⎟⎞ Φ( ⎜⎛→ s,→ s ⎟⎞ dΩ' ⎝ ⎠ ⎝ ⎠
3.3. Boundary conditions Boundary conditions are set as shown in Table 2. Fig. 3 shows the boundary conditions for the studied domain. The boundary condition of the collector cover is called “mixed” that means both convection and radiation through the collector surface are taken in consideration. the bottom of the energy storage layer (Ground) is set as temperatureconstant boundary with 3 m thickness, whose temperature is 300 K (Guo et al., 2014b; Xu et al., 2011). While the temperature of the upper surface of the ground and the inner surface of the collector depend on the convection of the air inside the collector. Table 3 represents the material properties of the ground, collector cover, and chimney. The temperature outside the collector was set as the atmospheric temperature. while the external radiation temperature was set by using Eq. (10) which represents the equivalent temperature of the sky (Swinbank, 1963).
(2)
Tsky = 0.0552Ta1.5
(3)
u w ρCp ⎞ h = 3.87 + 0.0022 ⎛⎜ 2 ⎟ ⎝ Pr 3 ⎠ (4)
∂uj ∂x i
(5)
Gb is the generation of turbulence kinetic energy due to buoyancy, and may be given by,
μ ∂T Gb = βgi t Prt ∂x i
Δpt = 18.87v − 57.59
(6)
(7)
Place
Type
Value
Ground Cover of the collector
Wall (Opaque) Wall (Semitransparent) Wall (Opaque)
Thickness = 3 m, T = 300 K Mixed (Convection and radiation) Convection
Pressure inlet Pressure outlet
Pgage = 0 Pa, To = Ta Pgage = 0 Pa
Surface of the chimney Collector inlet Chimney outlet
Where Mt is the turbulent Mach number, defined as
Mt =
(12)
Table 2 Boundary conditions.
YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, and it may be given by:
YM = 2ρεMt2
(11)
where uw is the wind speed of the environment. Fig. 4 shows the monthly averaged wind speed for the selected cities. The pressure drop across the turbine can be determined in two ways: (1) specified using a constant value and (2) determined as a function of velocity across the turbine (Guo et al., 2014b). The second approach, i.e., a linear polynomial of velocity, was applied to determine the pressure drop across the turbine by using Eq. (12), which is represented by (Guo et al., 2014b).
In the above equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, and may be defined as
Gk = −ρui' uj'
(10)
The convective heat transfer coefficient from the collector roof to the environment is calculated by Pretorius and Kröger (Pretorius and Kröger, 2006).
∂ ∂ ∂ ⎡ ∂ε ⎤ ε ε2 αε μeff (ρε ) + (ρεui ) = + C1ε (Gk + C3ε Gb) − C2ε ρ ⎥ ∂t ∂x i ∂x j ⎢ ∂ x k k j⎦ ⎣ − Rε + Sε
(9)
where ρa is the density of atmospheric air at the atmospheric temperature Ta, and β is the thermal expansion coefficient.
The DO model solves for as many transport equations as there are directions → s . The solution method is identical to that used for the fluid flow and energy equations. The flow through the system is described by using the RNG k-∈ turbulence model due to the buoyancy force term in the momentum equation. The RNG-based k-∈ turbulence model is derived from the instantaneous Navier-Stokes equations, using a mathematical technique called “renormalization group” (RNG) methods. The analytical derivation results in a model with constants different from those in the standard k-∈ model, and additional terms and functions in the transport equations for k and ϵ (Choudhury, 1993). The Transport Equations (k and ϵ equations) for the RNG k-∈ Model have similar forms to standard k-∈ model with some additional terms. Eqs. (3) and (4) represent the k and ϵ equations in the RNG k-∈ model.
∂ ∂ ∂ ⎡ ∂k ⎤ (ρk ) + (ρkui ) = αk μeff + Gk + Gb − ρε − YM + Sk ∂t ∂x i ∂x j ⎢ ∂ xj ⎥ ⎣ ⎦
(8)
(ρ − ρa ) g ≈ −ρa β (T − Ta) g
σT 4 ∇ . (I (→ r,→ s )→ s ) + (a + σs ) I (→ r,→ s ) = an2 π σ + s 4π
Cμ ρη3 (1 − η / η0) ε 2 1 + βη3 k
k a2 4
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M.A.H. Abdelmohimen, S.A. Algarni
overestimation of updraft velocity and power output: (1) the physical model does not include supports in the collector such that its drag forces could not be included; and (2) the simulation is for steady flows, whereas the soil layer has thermal inertia in reality. February and October have the same solar radiation which is 430 W/m2. In Fig. 5 the present results show different updraft velocity and power for those months although they have the same radiation. This is because they have different values of atmospheric temperature and different sun ray directions. The atmospheric temperature of February is 277 K and for October is 286.2 K. The temperature rise through the collector in February is more than it in October. Those values cause lower efficiency of the collector in October than in February. So, the output power in February is more than in October although they have the same monthly average solar radiation.
Table 3 The properties of the used materials. Physical property (unit)
Glass
Ground
Chimney
Density (kg/m3) Thermal conductivity (W/m K) Specific Heat (J/kg K) Absorption coefficient (1/m) Transmission coefficient (1/m) Emmisivity
2700 0.96 840 17 1 0.9
1441 0.5 830 0.5 0.1 0.89
2100 1.4 880 0.5 0.1 0.71
9
Riyadh
Tabuk
Bisha
,aĨaƌůͲBaƟŶ
Sakakah
Jeddah
8 7
5. Results and discussion
6
Six cities of different locations in Saudi Arabia (Namely Sakakah, Riyadh, Tabuk, Jeddah, Hafar-Al-Batin, and Bisha) are selected to study the performance of SCPP in them. Those cities may be assumed that they cover most of the kingdom weather. Table 4 represents the latitude and longitude of the selected cities. Fig. 6 represents the variations of monthly average solar radiation in W/m2 for the selected cities. The values were used in the calculation of monthly average power generation. There is a slight difference between the solar radiation values of selected cities. It is clear also the highest solar radiation appears in Spring and Summer months. Bisha and Jeddah show higher solar radiation at winter months. Monthly average temperatures in the selected locations are shown in Fig. 7. Note the monthly average solar radiation and the average of the temperature are taken as an average of the last 22 years which are represented by NASA for the selected locations (NASA, 2016). Fig. 7 indicates that Riyadh and Hafar Al-Batin are the hottest cities in Summer months while Jeddah is the hottest city in other months. Tabuk is the coldest among all selected cities. Jeddah and Bisha show also a small difference between the higher and lower temperature. The output power of the solar chimney plant located in the six cities is presented in Fig. 8. The figure shows that the maximum power is produced in Tabuk and Jeddah at June with about 84.5 kW and 83.1 kW respectively. While from January to May and from September to December, Bisha gives the highest power as compared with other cities. The produced power is affected by two main parameters solar radiation and ambient temperature. the effect of those parameters can't be represented separately because the value of the ambient temperature is affected by the solar radiation in the selected locations. So, you can't assume high solar radiation with low temperature in a particular location. Guo et al. (Guo et al., 2014b) estimated that the variation of the ambient temperature has a negligible effect on the air temperature rise through the collector, but as the ambient temperature increases, the updraft velocity decreases. Fig. 9 shows the output power for the selected cities at different values of the solar radiation. Generally, the figure shows that as the solar radiation increases the output power of the SSPP increases. Fig. 10 represents the collector efficiency which is calculated by using Eq. (14). The figure shows that the collector efficiency increases as the solar radiation increases. In some cases, which has the same solar radiation, the same temperature rise, and the same location, the results are not the same because of the effect of the change in sun ray direction due to the month. Fig. 11 shows the yearly average power produced in each city. The figure shows that Bisha gives the highest yearly average power produced and Jeddah is the next city. By reviewing the solar radiation and atmospheric temperature of those cities, it can be seen that Bisha and Jeddah have high solar radiation and temperature in spring and winter months as compared with other cities. By taking the average of all months of the year Bisha and Jeddah will give more solar radiation. This will make the SSPP more stable and continuous in work in Bisha
5 4 3 2 1 0
Fig. 4. The monthly averaged wind speed for the selected cities according to what represented by NASA (NASA, 2016).
where v is the air velocity across the turbine. Eqs. (13) and (14) are used to calculate the turbine power output and the collector efficiency respectively.
P = ηt Δpt Q v ηcoll =
(13)
Cp m˙ ΔT 2 πrcoll I
(14)
Where ηt: is the turbine efficiency, Δpt: is the turbine pressure drop, Qv: is the volume flow rate m˙ : is the mass flow rate, ΔT: is the temperature rise through the collector, rcoll: is the collector radius I: is the incident solar radiation. The turbine efficiency was set as 0.8 (Gannon and von Backström, 2000; Pasumarthi and Sherif, 1998a; Pretorius and Kröger, 2006; Nizetic, Ninic, & Klarin, 2008). 4. Numerical model validation The used CFD simulation model is validated through comparison with the experimental data of the Spanish prototype (Schlaich, Bergermann, Schiel, & Weinrebe, 2005). The location of the Spanish prototype is defined by longitude 3° 23′ W and latitude 40° N which represents the location of Manzanares, Spain. The simulation is carried out at the monthly average solar radiation, the temperature average, and wind speed for the twelve months which represented by NASA at that location (NASA, 2016). Fig. 5a and b shows a comparison between the current simulation results and the experimental data of the updraft velocity and the output power respectively. The experimental data was represented by Guo et al. (Guo et al., 2014b) to validate their model. Their validation result also represented in the same figure. Fig. 5 shows that the simulation results are consistent with the experimental data, which indicates that the proposed numerical method is a suitable approach for investigating SCPP performance. As mentioned by Guo et al. (Guo et al., 2014b), two reasons may be responsible for the slight 5
Sustainable Cities and Society 38 (2018) 1–8
M.A.H. Abdelmohimen, S.A. Algarni
Exprimental data
9
Present work
Fig. 5. Comparison between the simulation result and experimental data for updraft velocity and output power. a) Updraft velocity b) Output power
Guo et al [13]
8 7 6 5 4 3 2 1 0 0
100
200
300
400
500
600
700
800
900
2
Solar radiaƟon (W/m )
a) Updraft velocity 70 Exprimental data
Present work
Guo et al [13]
60
50
40
30
20
10
0 0
100
200
300
400
500
600
700
800
900
Solar radiaƟon (W/m2 )
and Jeddah due to the small difference between the maximum and minimum output power along the year months.
Table 4 The latitude and longitude of selected cities. City
Latitude
Sakakah Riyadh Tabuk Jeddah Hafar Al-Batin Bisha
29° 24° 28° 21° 28° 19°
58′ 38′ 23′ 32′ 26′ 58′
16” 00” 03” 41” 04” 42”
Longitude N N N N N N
40° 46° 36° 39° 45° 42°
12′ 43′ 34′ 10′ 58′ 35′
01” 00” 48” 34” 25” 46”
6. Conclusion
E E E E E E
The study aims to numerically evaluate the performance of SCPP in selected cities of Saudi Arabia and to estimate the quantity of the produced electric energy. A numerical model has been carried out to evaluate the performance of SCPP. K-∈ model is used to solve the momentum equation through the system. The discrete ordinate (DO) radiation model was adopted to solve the radiative transfer equation. The numerical model is validated by comparing its results with the experimental data of the Spanish prototype in Manzanares, Spain. The performance of SCPP in six locations in Saudi Arabia were studied where the results showed that: 6
Sustainable Cities and Society 38 (2018) 1–8
M.A.H. Abdelmohimen, S.A. Algarni
90 1000
80 70
Riyadh
Tabuk
Bisha
Hafar Al-BaƟn
Sakakah
Jeddah
800 60 50
600
40 30
400
200
Riyadh
Tabuk
Bisha
Hafar Al-BaƟn
Sakakah
Jeddah
20 10 0 400
0
500
600
700
800
900
Fig. 9. The output power of the selected cities at different values of solar radiation.
Fig. 6. Monthly average solar radiation in the selected cities.
310
0.3
305
0.25
300
Riyadh
Tabuk
Bisha Sakakah
Hafar Al-BaƟn Jeddah
0.2
295 0.15 290 0.1
285 280 275
Riyadh
Tabuk
Bisha
Hafar Al-BaƟn
Sakakah
Jeddah
0.05 0 400
500
600
700
800
900
270
Fig. 10. The collector efficiency of the selected cities at different values of the solar radiation.
265
Fig. 7. Monthly average temperature in the selected cities.
60 80 50 70 40 60 30 50 20
40
Riyadh
Tabuk
Bisha
Hafar Al-BaƟn
Sakakah
Jeddah
10
30
0
20 10
Fig. 11. Yearly average power generated in the selected locations.
0
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Fig. 8. Monthly average power generation in the selected cities.
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