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Thermal performance of a heat-pipe evacuated-tube solar collector at high inlet temperatures
Applied Thermal Engineering 154 (2019) 315–325
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Research Paper
Thermal performance of a heat-pipe evacuated-tube solar collector at high inlet temperatures
T
⁎
Mahmoud B. Elsheniti , Amr Kotb, Osama Elsamni Mechanical Engineering Department, Faculty of Engineering, Alexandria University, El-Chatby, Alexandria 21455, Egypt
H I GH L IG H T S
term for the collector thermal mass is added to the mathematical model. • AThenewmaximum relative error in exit temperature is reduced from 12.5% to 4.4%. • Collector efficiency is reduced at higher inlet temperatures and more series tubes. • There is an upper limit the number of series tubes to be used effectively. • A new collector efficiencyforexpression is proposed with average deviation of 4.2%. •
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar collectors Evacuated tube Heat pipe Thermal mass Solar cooling
The thermal performance of a heat-pipe evacuated-tube solar collector is investigated in the present paper. Hot water is targeted at a relatively high inlet temperature of 70–90 °C to predict the collector performance that utilized in solar cooling applications such as adsorption and absorption systems. A mathematical model of the system was developed and validated experimentally under weather conditions of Alexandria, Egypt. The theoretical model of the collector is enhanced by considering the effect of the thermal mass of the system, hence the maximum relative error between the experimental and theoretical results was reduced from 12.5% to 4.4%. The effects of the inlet water and ambient temperatures, number of evacuated tubes, water mass flow rate, and solar irradiance on both the exit water temperature and the collector’s efficiency were all considered in comprehensive studies. The results showed that the collector performance was strongly affected by all the above parameters but with different manners. For examples, at certain values of the water mass flow rate and solar irradiance, the exit temperature increases with the increase in the number of evacuated-tubes reaching a specified number above which the increase in the exit water temperature will be eliminated. However, the thermal efficiency is always better at lower numbers of tubes. Consequently, the total number of the evacuated tubes for different series and parallel arrangements can be minimized at specified operating conditions based on the model’s results, leading to minimal capital cost. In addition, an expression for predicting the collector efficiency was derived based on the mathematical model’s results to be used in calculating the exit water temperature at different operating conditions and number of evacuated tubes. This expression can be effectively used for modeling such type of collector employed in a thermally driven cooling cycle.
1. Introduction Nowadays, energy demand, global warming, ozone depletion and environmental pollution caused a rise in the urgent need for clean alternative energy sources instead of fossil fuel. Such problems [1] will increase energy prices till renewable energy sources provide considerable percent of energy to supply buildings, transport and industry. So, global markets are in dire need for energy conservation methods and
⁎
innovations in renewable energy sources, the key is in utilizing modern approaches and technologies to satisfy this need. One of these approaches is the use of solar collectors for domestic and industrial heating purposes. At present, the collectors used in solar applications are categorized into two main types; evacuated tube collector (ETC) and flat plate collector [2]. The main feature in evacuated tube collectors is eliminating both conduction and convection losses between the absorbing
Corresponding author. E-mail address: [email protected] (M.B. Elsheniti).
https://doi.org/10.1016/j.applthermaleng.2019.03.106 Received 1 October 2018; Received in revised form 15 February 2019; Accepted 23 March 2019 Available online 23 March 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 154 (2019) 315–325
M.B. Elsheniti, et al.
σ τ ϕ2 ϕ3
Nomenclature
A Ar CP D F g h h fg I k L M ṁ N P Q R R3f R3P T t Uloss
area (m2) single tube aperture area (m2) specific heat capacity (J/kg K) diameter (m) fill ratio gravitational acceleration (m/s2 ) convective heat transfer coefficient (W/m2 K) latent heat of evaporation (J/kg) insolation (W/m2) thermal conductivity (W/mK) length (m) mass (kg) mass flow rate (kg/s) number of evacuated tubes pressure (Pa) heat rate (W) thermal resistance (K/W) film boiling thermal resistance (K/W) pool boiling thermal resistance (K/W) temperature (°C or K) time (s) manifold heat loss coefficient (W/m2 K)
Subscripts a ab amb c e eff ex exit exp f g gi go HP i in l m man o p sat u v w
Greek symbols
α ε η μ ρ
Stefan Boltzmann constant transmittance condensation figure-of-merit (kg/s2.5 K0.75) boiling figure-of-merit (kg0.6/m0.2 s1.4 K)
absorptivity emissivity collector efficiency dynamic viscosity (Pa s) density (kg/m3)
air absorbed ambient condenser evaporator effective exit from a single evacuated tube exit from solar collector experimental header fluid glass inner glass tube outer glass tube heat pipe inner/inlet to a single evacuated tube inlet to solar collector liquid mean manifold outer absorber saturation useful vapor wall
an ETC integrated with coaxial heat pipe using air as a heat transfer fluid. They studied the effect of tilt angle, filling ratio and refrigerant type on the performance of the ETC at different air flow rates. They also concluded that the increase in the thermal efficiency with the modified heat pipe comparing to a collector without heat pipe reached 67%. Azad [13] experimentally compared the performance of two heat pipe solar collectors with the same effective area but different number of heat pipes, and a conventional flow-through collector. It was found that the heat pipe collector with the higher number of heat pipes have a higher thermal efficiency than to the other two collectors. Alammar et al. [14] numerically studied the effect of inclination angle and fill ratio on the performance of a thermosiphon heat pipe. It was found that the fill ratio and inclination angle of 65% and 90° resulted in the best thermal performance. The results showed a higher efficiency for HPETC than conventional solar collectors. Brahim et al. [15] studied the effect of adding fin arrays to the heat pipe condenser with two types of working fluid (methanol and water). They developed a time-dependent theoretical model of the system and compared it with the experimental results. The results indicated that the water system had a better performance than that of the methanol. Furthermore, the addition of fins to the heat pipe condensing surface increased the system overall efficiency. The optimal fins density was found to be double layers of 100mesh/inch. Zheng et al. [16] studied the effect of radiative characteristics of receiver's back surface on the thermal performance of HP-ETC. This influence is generally related to the back surface emissivity and temperature. The heat loss of the HP-ETC increases by increasing of the back surface emissivity. The variation of back surface emissivity can significantly affect the performance of the collector especially at higher temperature It is worth mentioning that most of the researchers have evaluated the performance of the collector for inlet water temperature range near
surface and outside ambient air. Evacuated tube collectors have been designed in various layouts such as water –in- glass, U-tube and heat pipe. In the later, a two phase heat pipe is used for transferring solar energy from the absorber to the fluid to be heated [3]. Heat pipe evacuated tube collectors (HP-ETC) are more thermally efficient than flat plate collectors, especially in cold climates [4]. Atiz et al. [5] experimentally studied the effect of ETC on solar pond performance. They noticed a significant increase in the temperature of the heat storage zone by using an ETC, which led to enhancement of the solar pond performance without a significant deterioration in the pond layers structure. Nkwetta et al. [6] experimentally compared the performance of heat pipe and direct flow evacuated tube collectors. The obtained results showed a better performance of heat pipe system than the direct flow configuration. Ismail and Abogderah [7] used methanol as the working fluid in heat pipe collector with 15° increase in slope than the conventional state to enhance condensation, and compared it with conventional solar collectors theoretically and experimentally. Also, studying the performance and evaluating the thermal efficiency of HPETC theoretically and experimentally was the main scope of study in the majority of researches made on this type of collector during the past few years [8,9]. Daghigh and Shafieian [10] developed a mathematical model of water heating system with HP-ETC according to thermal and exergy analysis to evaluate its performance. The system was experimentally tested and compared with the theoretical model results. The results indicated the optimal number of collector pipes to be 15. Also, the exergy efficiency increases with time with a maximum value of 5.4% at the end of the day. The maximum exit temperature of collector was reported to be about 64°C. Jafarkazemi and Abdi [11] developed a theoretical model of a HP-ETC with a dry condenser and circular fin. They compared the system heat gain and efficiency with the experimental results. Kabeel et al. [12] developed an experimental model of 316
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2.1. Collector
ambient 20–40 °C for water heating applications [17,18]. However, solar collectors are used recently in heat-driven cycles for certain applications such as solar absorption cooling, adsorption cooling, desalination and desiccant dehumidification systems. In such cycles, heating water after being used for the regeneration process is sent back to the solar collector at relatively high temperatures [19]. In solar adsorption refrigeration and desalination applications, the inlet water temperature to the collector is in range of 50–80 °C and exits in the range of 60–100 °C [19–21]. Four different solar collector types for a solar driven absorption cooling system were tested by Bellos et al. [22]. They found that the optimum generation temperature needed for the cooling system ranges from 90 to 120 °C and the ETC has the lowest land use and investment cost. There is a general agreement on that the performance of these systems is highly affected by the regeneration temperature [21,23,24]. On the other side, the increase in the collector inlet water temperature can somehow affect the collector efficiency and the number of the evacuated tubes needed for raising the collector exit temperature up to the required limit that ensures the optimum operation of such applications. In addition, there is no enough data in the literature about the effects of a relatively-high inlet water temperature coupled with different numbers of evacuated tubes on the HP-ETC performance. Therefore, a thorough mathematical model for a HP-ETC is developed in the present work to provide researchers and engineers who work on these thermally driven systems by the expected HP-ETC performance in their cycles under different operating conditions. The theoretical model's accuracy is enhanced by involving the thermal mass of the system and assessed by experimental tests that carried out for four different days in Alexandria, Egypt. The effect of the number of the evacuated tubes arranged series in a single-line has been investigated, while the results can be used effectively for replacement such single line of series evacuated-tubes by a number of parallel lines to match specified application requirements with a minimum total number of evacuated tubes.
The amount of solar radiation absorbed by the heat pipe evaporator surface (Qab) can be calculated using Eq. (1).
Qab = Iαp τgi τgo Ar
(1)
A portion of the absorbed heat will be dissipated to the ambient by convection and radiation heat losses (Qloss ) , which can be calculated using Eq. (2).
Qloss =
TP − Tamb R1
(2)
where R1 is the equivalent resistance of radiation losses between absorber – inner glass, inner-outer glass, and the convection and radiation losses of outer glass to the ambient. R1 and its decomposed resistances are explained as follows:
R1 =
R (go − amb) R convloss R (go − amb) + R convloss
+ R (gi − go) + R (P − gi)
(3)
TP − Tgi
R (P − gi) =
εp σAr (TP4 − Tg4i )
(4)
Tgi − Tgo
R (gi − go) =
εg σAi (Tg4i − Tg4o )
R (go − amb) =
R convloss =
(5)
Tgo − Ta 4 εg σAo (Tg4o − Tamb )
1 ha A o
(6)
(7)
The remaining amount of heat is transferred to the heat pipe (QHP ) , which can be calculated using energy balance equation as follows:
QHP = Qab − Qloss
(8)
2. Mathematical model 2.2. Heat pipe In this work, a gravity-assisted heat pipe has been used in the evacuated tube collector. A schematic drawing of collector components and operation is shown in Fig. 1. In the steady state operation, solar irradiance heats up the outer surface of the heat pipe evaporator, this heat is transferred to the evaporator’s inner surface by conduction, and vaporizes the heat pipe working fluid, which is considered pure water. The generated vapor flows naturally upwards by the buoyancy forces to the heat pipe condenser. The header fluid (water) absorbs the heat from the condenser as it passes over it and condenses the inside vapor. Then the condensate moves back to the evaporator by gravity and the cycle is repeated. Electrical-thermal analogy model is presented in Fig. 2 by considering the thermal resistance of each component in a single evacuated-tube to describe its thermal behavior. While Fig. 3 shows an illustrative schematic diagram of temperature points and heat vectors on a single evacuated-tube. The following assumptions are considered in the developed model:
The heat pipe can be modeled using number of thermal resistances R2 − 9 represented as follows: Evaporator wall thermal resistance (R2) is presented by:
ln R2 =
( ) Deo Dei
2πk w Le
(9)
A recommended method by ESDU [25] has been used to calculate
• Natural convection losses between the inner glass and the evaporator is neglected. • Thermal resistance across water-vapor interface in both evaporator and condenser is neglected. • Surface temperature of both absorber and evaporator are considered the same. • The conduction thermal resistances within the glass tube thickness are neglected.
Energy balance equations and thermal resistances for each component are presented in the following subsections.
Fig. 1. Schematic drawing of the heat pipe evacuated tube collector. 317
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Fig. 2. Electrical analogy for a heat pipe evacuated tube collector.
Otherwise,
R3 = R3P F + R3f (1 − F )
(13)
R4 and R6 are the thermal resistances across the liquid-vapor interface in the evaporator and the condenser respectively, and they are always small compared to the other resistances and are therefore neglected. Thermal resistance (R5) due to the pressure drop (ΔP ) of the vapor flow inside the heat pipe is expressed as:
Tsat ΔP hfg ρv QHP
R5 =
(14)
where ΔP can be calculated using the Darcy–Weisbach equation for laminar flow. Condensation thermal resistance in the condenser (R7) which can be calculated using Nusselt's theory filmwise condensation [26] by: 1 3 0.235QHP
R7 =
Dci
4 3
4 1 3 g 3L
c ϕ2
(15)
Condenser wall thermal resistance (R8) .
ln
Fig. 3. Schematic diagram of temperature points and heat vectors on single evacuated-tube.
R8 =
R3P
R9 =
1
Rtot =
4
Dei3 g 3 Le ϕ23 3 2 0.25
(11) 0.65
0.3
0.7
(17)
R9· ∑i = 2 Ri 9 ∑i = 2
Ri
Tco = Tp + (QHP Rtot )
0.23
ρ . k . Cpl . Pv hfg k ρ where ϕ2 = ⎛ μl l ⎞ and ϕ3 = l 0.25 l 0.4 0.1 0.23 are the boiling and ρv . hfg . μl . Patm ⎝ l ⎠ condensation figure of merit, respectively. Therefore, the boiling thermal resistance in the evaporator (R3) can be calculated according to the following condition: If R3p > R3f ,
R3 = R3P
Leff Aw k w
8
3 0.235QHP 4
(16)
2πk w Lc
So, the total equivalent resistance (Rtot ) of heat pipe and the condenser outer surfaces temperature (Tco) can be expressed by:
(10)
1
R3f =
Dco Dci
Thermal resistance along the heat pipe wall in axial direction (R9) can be calculated as:
the evaporation thermal resistance approximately by checking the thermal resistance of a combination of both, the liquid film in the evaporator (R3f ) and nucleate in the boiling pool (R3P ) . The two resistances can be expressed by:
1 = 0.4 ϕ3 g 0.2QHP (πDei Le )0.6
( )
(18) (19)
2.3. Header Energy balance is performed on the header in order to calculate the useful heat gain from the collector. Moreover, system thermal mass is also presented in the energy balance which used to be neglected in all
(12) 318
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previous theoretical models. Thermal mass of a system can be defined as the ability of the system components to store the heat. It is also defined as the resistance of system components to temperature changes, indicated by the time dependent variations in temperature during a full heating/cooling cycle. This affects the system by lowering its response to temperature changes. For example, at the late hours of the day, the system releases an amount of heat to the water that has been stored in it during the early hours of the day. This can cause a delay in water temperature reduction at the late hours of the day. The thermal energy balance of collector header can be expressed by:
QHP = Qu + Qmanloss + QTM
Table 1 Physical characteristics of evacuated tube collector.
(20)
where QTM represents the heat absorbed from/to the system within the time step Δt due to the thermal mass of each component in the system and can be calculated by:
QTM
(T − Tt − 1) = ∑ MCp t Δt
Heat pipe Heat pipe material
Copper
Working fluid Outer diameter (mm)
Water 16.2
Collector Tube outer diameter (mm) Absorber area (m2) Absorptivity Number of tubes/Collector Overall heat transfer coefficient from manifold to ambient (Uloss) (W/m2K)
58 2.06 0.93 15 0.06
η=
Condenser Length (mm) Inner diameter (mm)
100
Tube length (m) Glass thickness (mm) Glass transmittance Glass emissivity Absorber emissivity
1.8 4 0.88 0.02 0.08
15.8
̇ p f (Texit − Tin ) mC IAr N
(25)
MATLAB codes were developed to solve the above equations simultaneously, and the results were compared to the experimental data based on the water exit temperature.
(21)
Qmanloss is the manifold heat loss to environment which is calculated by:
Qmanloss = Uloss Aman (Tm − Tamb)
(22)
3. Experimental setup and procedure
where Tm is the mean water temperature between inlet and exit of each condenser, and Uloss is manifold heat loss coefficient provided by manufacturer data. Qu is the useful heat gain which can be calculated using:
̇ p f (Tex − Ti ) Qu = mC
This study aims to assess the change in system performance by varying inlet water temperature and mass flow rate as the main variables in the experiment. These tests were performed at Thermal Engineering Laboratory, Faculty of Engineering, Alexandria University (latitude 31.2° N and longitude 29.9° E). These experiments were used to validate the introduced mathematical model to help in predicting the performance of the heat pipe solar collector under investigation with different irradiance and climatic conditions. Fig. 4 shows a schematic diagram of the experimental setup and the collector’s characteristics are listed in Table 1. The experimental test cases on the solar system have been carried out using three modules of heat pipe evacuated tube collectors connected in series, each consists of 15 tubes as shown in Fig. 5. Fig. 6 shows the different used system components. A 2 kW electric heater and a radiator type heat exchanger equipped with air fan were used to adjust the inlet water temperature. The mass flow rate was also adjustable through a control valve. A cylinder storage tank with capacity of 60 L is provided. Solar irradiance is measured using CMP3 pyranometer with an accuracy of less than ± 5%. Thermocouples of T type are used to measure the inlet and the outlet water temperatures of the
(23)
where the exit water temperature of a single evacuated tube (Tex ) can be calculated using logarithmic mean temperature difference LMTD method as follows: −hf A
c
̇ f Tex = Tco − (Tco − Ti ) e mCp
(24)
where hf is the convection heat transfer coefficient between header water and condenser outer wall which is calculated using Echkert and Drake correlation for Re < 100 [27] and Churchill and Bernstein correlation for higher Re [28]. For N number of tubes in the collector, the inlet water temperature to the condenser can be considered as the exit water temperature from the previous one. The collector efficiency is calculated from the equation:
Fig. 4. Schematic diagram of system setup. 319
Solar Irradiance [W/m2]
1200
40 Day 1 (19 April 2018)
1000
30
800 600
20
400
10
200 0
0
Ambient Temperature [ ] Wind velocity [m/s]
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Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
40
Solar Irradiance [W/m2]
collector, the water tank, and the ambient temperature. The thermocouples are connected to data logger with 12-bit resolution after calibration to log the data. 4. Results and discussions The main objective of the present study is evaluating the performance of evacuated tube solar collector at relatively high inlet temperatures. The collectors should be connected in series and/or parallel to have such high level of temperatures. It is not practical to test all arrangements experimentally especially when number of modules becomes larger due to the space and cost limitation. The strategy of the present study comprises four stages; (i) developing a mathematical model of the solar collector that can be used to evaluate the series and/ or parallel connections; (ii) validation of the mathematical model by comparing its results with the measurements of smaller number of evacuated tube solar collector at various operating conditions; (iii) adopting the model to evaluate the performance of solar collectors at different mass flow rates, number of tubes, and various solar intensities; and eventually; (iv) proposing a generalized correlation for the collector thermal efficiency that links the mass flow and the exit temperature required for high temperature applications.
Day 2 (24 April 2018)
30 20 10 0
Ambient Temperature [ ] Wind velocity [m/s]
Fig. 7a. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 1.
Fig. 5. ETC at test site.
Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
Fig. 7b. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 2.
two days were selected in April and two days in July. These data will be used in the mathematical model to deduce the theoretical exit temperature and compare them with the experimental measurements.
4.2. Experimental validation of the mathematical model The leaving water temperatures from the three collectors arranged in series were examined by the experimental and theoretical models for the four days given above. At first, inlet water temperatures at the ambient levels were adapted and measured experimentally. They fluctuated between 32 °C and 34 °C with mass flow rate of 0.03 kg/s on the first day, and 36–40 °C with mass flow rate of 0.3 kg/s on the second day as shown in Figs. 8 and 9 respectively. Generally, there are good
4.1. Weather data The experimental test cases were carried out on four different days for different water mass flow rates, as well as for both low and high inlet water temperatures. The values of the ambient temperature, the solar irradiance, and the wind speed during these days are shown in Figs. 7a–7d. In order to have wide range of the operating conditions,
Fig. 6. System components at test site. 320
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1200 Day 3 (24 July 2018)
40
1000
30
800 600
20
400 10
200 0
0
agreements between the mathematical and experimental results. However, at the lower mass flow rate of 0.03 kg/s, it can be seen in Fig. 8 that incorporating system thermal mass to the theoretical model reduced the maximum relative error between the experimental and the theoretical values to 4.4% compared to 12.5% when the thermal mass of the collectors was not considered. In details, system thermal mass began to show significant effect after mid-day, as it considers the amount of heat released from the system that has been absorbed during the early hours of the day, when the temperature of the water starts to fall down. By neglecting thermal mass effect as the model presented in reference [10], the exit water temperature trend only follows the solar irradiance trend along the day and the theoretical exit temperatures are lower than the experimental values at the late hours of the day. While in case of the higher mass flow rate of 0.3 kg/s, it is obvious in Fig. 9 that system thermal mass effect is less influential on the results, yet more accurate, since the maximum error only dropped from 3.22% to 3%. This is because the water is not in contact with the system for long enough time to absorb heat from the system. Generally, the trend of changes in both experimental and theoretical results is the same and shows good agreement in values with a maximum error of 4.4%. This is indicative of the validity of the developed model to predict the performance of evacuated tube heat pipe solar collector. Secondly, experimental tests were carried out for relatively high inlet water temperature ranging from 70 to 85 °C to mimic the water temperature exiting from thermally driven systems. These tests were performed at both 0.065 and 0.11 kg/s water mass flow rates. Figs. 10 and 11 compare between the experimental and theoretical values of exit water temperature for both mass flow rates. It is worth mentioning that the fluctuations in the inlet water temperatures is due to the replacement of hot water inside the tank with cold water to maintain the inlet water temperature within the desired range. As it can be seen, theoretical and experimental results share the same trend with a maximum relative error of 3.6%. However, it should be noted that there is no noticeable effect for the thermal mass in these two cases on the accuracy of the theoretical results. Since the thermal mass effect does not significantly affect the results when the drop in the irradiance is shallow after mid-day as in Day 3 and Day 4. So, for these two cases, working with relatively higher mass flow rates coupled with a gentle drop in the irradiance at late hours reduces the role of thermal mass.
Ambient Temperature [ ] Wind velocity [m/s]
Solar Irradiance [W/m2]
M.B. Elsheniti, et al.
Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
Solar Irradiance [W/m2]
1200
40 Day 4 (27 July 2018)
1000
30
800 600
20
400
10
200 0 10:00
11:00
12:00
13:00
14:00
15:00
0 16:00
Ambient Temperature [ ] Wind velocity [m/s]
Fig. 7c. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 3.
Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
Exit Temperature [ ]
Fig. 7d. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 4. 60 Day 1 (m=0.03 kg/s)
55 50 45 40 35 30 10:00
11:00
12:00
13:00
14:00
15:00
16:00
Texit,theo (No TM)
Tin
4.3. Effect of the operating parameters on the exit temperature
Time [hour] Texit,exp
Texit,theo (TM)
The theoretical model has been also employed to investigate the effect of number of tubes on the exit water temperature. Fig. 12(a–d) show the change of exit water temperature with increasing number of evacuated tubes at different mass flow rates and solar irradiances, while the inlet water temperature is set to 80 °C in these cases. Generally, the change pattern of the exit temperatures with an increase in the number of tubes are ascending, but with different rates depending on the water mass flow rates. Nevertheless, for specific mass flow rate and solar
Fig. 8. Experimental and theoretical exit water temperature values with and without thermal mass effect in theoretical model on Day 1.
Exit Temperature [ ]
95
85 80 75 70 65 10:00
Fig. 9. Experimental and theoretical exit water temperature values with and without thermal mass effect in theoretical model on Day 2.
Day 3 (m=0.065 kg/s)
90
11:00
12:00
13:00
14:00
15:00
16:00
Texit,theo (NO TM)
Tin
Time [hour] Texit,exp
Texit,theo (TM)
Fig. 10. Experimental and theoretical exit water temperature values on Day 3. 321
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Exit Temperature [ ]
85
connected in series with mass flow rate of 0.05 kg/s. However, the same requirements can be achieved by another arrangement using 5 collectors connected in parallel each has 20 tubes and 0.01 kg/s mass flow rate. As a result, the total number of tubes is dramatically reduced to 100 tubes compared to 170 tubes in the first scenario, hence the overall cost is meaningfully reduced.
Day 4 (m=0.11 kg/s)
80 75 70 65 60 55
4.4. Effect of the operating parameters on the collector efficiency
50 10:00
11:00
12:00
13:00
14:00
15:00
16:00
Texit,theo (NO TM)
Tin
Fig. 13(a–f) shows the collector efficiency variations with the change in the function of (Tin − Tamb)/ I and ṁ at different number of evacuated-tubes. As it is seen in the figures, the efficiency decreases with increasing inlet water temperature and number of tubes. As by increasing these two parameters, this will lead to a decrease in the temperature difference between the condenser outer surface and the water in contact at each successive tube, which lower the heat transfer rate, hence the efficiency decreases. For instance, the efficiency drops from 42% to 27% by increasing number of tubes from 15 to 150 tubes at the same (Tin − Tamb)/ I and ṁ of 0.03 m2.K/W and 0.12 kg/s, respectively. Moreover, at a specified (Tin − Tamb)/I, increasing water mass flow rate up to 0.08 kg/s increases the rate of heat transfer between the header water and the condenser, and then the efficiency increases.
Time [hour] Texit,exp
Texit,theo (TM)
Fig. 11. Experimental and theoretical exit water temperature values on Day 4.
irradiance at smaller mass flow rates of 0.01 kg/s and 0.02 kg/s, increasing in the exit temperature is diminished with increasing the number of tubes (due to the temperature difference limit with the heat pipe). Therefore, there is an upper limit for increasing the number of tubes under which the collector can be effectively used. Also, it is noticed that this upper limit for the number of tubes is increased with increasing mass flow rate, yet the maximum achievable exit temperature is decreased. For instance, as shown in Fig. 12-d, at water mass flow rate of 0.01 kg/s and 800 W/m2 solar irradiance, the maximum number of tubes can be effectively used is approximately 150 tubes that corresponds to 119 °C exit water temperature. While this number of tubes is increased to be almost 180 tubes in case of 0.02 kg/s mass flow rate at the same solar irradiance. However, the maximum temperature in this case drops to be 112 °C. Moreover, these results are also useful for selecting the optimum network series and parallel connection configuration for the collectors. For example, assuming 700 W/m2 solar irradiance, if the required exit water temperature and mass flow rate for the application are 95 °C and 0.05 kg/s, respectively. Thus, from Fig. 12-c, one can use 170 tubes
130
110
100
100
90
90
80
80
70 50
100
150
200
70 0
Number of Tubes (a) 130 120 110 100 90 80 70 50
100
130 120 110 100 90 80 70 150
Number of Tubes (c)
50
100
150
200
Number of Tubes (b)
I=700 W/m2
0
Fig. 12. Variation of water exit temperature from the collector with number of evacuated tubes at different mass flow rates and solar irradiances (Tin = 80 °C).
I=600 W/m2
120
110
0
In applications such as solar adsorption and absorption systems, the exit temperatures from the solar collector and mass flow rates are desirable to be in specified ranges to assure an acceptable performance for the overall system. Therefore, relating all solar collector parameters including the number of the evacuated-tubes to the overall system modeling will be very beneficial to find out the best performance with minimum number of collectors. For this purpose, the results were used to derive a model-based correlation that relates the efficiency with ṁ , (Tin − Tamb)/ I and number of evacuated-tubes N as follows:
130
I=500 W/m2
120
4.5. Correlation for the collector efficiency
200
I=800 W/m2
0
50
100
150
Number of Tubes (d)
322
200
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M.B. Elsheniti, et al.
Fig. 13. Energy efficiency vs. water mass flow rate and (Tin − Tamb)/I. (For N = 15, 30, 45, 60, 90, 150).
Tin − Tamb ) + a3(N ) ṁ 2 I T − Tamb T − Tamb 2 ⎞ + a 4(N ) ṁ ( in ) + a5(N ) ⎛ in I I ⎠ ⎝
And the corresponding exit temperature can be calculated by:
ηcorr = a0(N ) + a1(N ) ṁ + a2(N ) (
Texit corr = Tin +
(26)
323
ηcorr INAr ̇ f mCp
(27)
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The best values of the coefficients a 0 → 5 when 15 evacuated-tubes module is utilized are listed in Table 2. To generalize Eq. (26), Fig. 14 relates the new a 0 → 5 required for higher number of evacuated-tubes with those given in Table 2. It should be noticed that the coefficient a4 changes within different scale, then it is represented separately on the right y-axis in Fig. 14. The comparison between the experimental and correlation-based values of both efficiency and the corresponding exit water temperature are given in Figs. 15 and 16. The predicted data alternate up and down the prefect predicted data line but within narrow range. The correlation results give an average percentage deviation of −4.22% and −0.73% for efficiency and exit water temperature, respectively (over predicting model). The absolute percentage deviation are 6.78% and 1.32%. Also, the maximum deviation in predicting the efficiency is 14.85%, while it is 6.5% for the exit water temperature. However, the maximum deviation drops for the exit water temperature to be 2% at higher exit temperatures of 70–90 °C.
Value
a0(15)
0.559
a1(15)
3.492
a2(15)
−7.424
a3(15)
−17.82
a 4(15)
−0.5527
a5(15)
35.22
12
0.4
8
0.2
4
0
0
-0.2
-4
-0.4
-8
[a4 (N) - a4 (15) ] /a4 (15)
Coefficient
0.6
i=1,2,3,5
[ai (N) - ai (15) ] /ai (15)
Table 2 Efficiency coefficients of 15 tubes module.
5. Conclusion
-12
-0.6 15
30
45
60
75
90
105
120
135
In this work, the performance of a heat-pipe evacuated-tube solar collector was investigated at a relatively high inlet water that coming from heat-driven cycles such as solar adsorption and absorption cooling cycles. Experimental tests were carried out for four days under the weather conditions of Alexandria city in Egypt and used to validate the mathematical model. The outcomes and net effects of the HP-ETC parameters on the system performance can be concluded as follows:
150
Number of tubes a0
a1
a2
a3
a5
a4
Fig. 14. The change in efficiency coefficients from 15 tubes module coefficients vs. Number of evacuated tubes.
0.55
• At low mass flow rates, adding the thermal mass effect of the system
+12%
0.5
ABS-PD=6.78 A-PD= - 4.22 MAX-PD=14.85
0.45
-12%
0.4 0.35 0.3
•
0.25 0.2 0.2
0.3
0.4
0.5
exp Predicted values
0% Deviation Line
+/- 12% Deviation Line
•
Fig. 15. Predictive correlation efficiency validation.
100 90
ABS-PD=1.32 A-PD= - 0.73 MAX-PD=6.5
Texit corr [ ]
80
•
+2% -2%
70
to the theoretical model can lead to a noticeable reduction in the maximum relative error of exit water temperature, as for example from the relative error of 12.5–4.4% at 0.03 kg/s. Although, the thermal mass gives accurate results, its effect is insignificant at higher flow rates. However, since low flow rates are recommended in solar systems, the inclusion of the thermal mass is essential for better predictions. Generally, at any number of evacuated-tubes, either a decrease in the inlet water temperature or an increase in the mass flow rate will lead to an increase in the collector’s efficiency, while the exit water temperature will decrease. Also, at certain values of the water mass flow rate and solar irradiance, there is a maximum number of evacuated-tubes above which the increase in the outlet water temperature is valueless. The results of developed model can be used effectively in selecting the optimum series and parallel arrangements for HP-ETC at a given operating condition, leading to a minimum total number of tubes. A new correlation in a generalized form for predicting efficiency of HP-ETC as a function of ṁ , (Tin − Tamb)/ I and number of evacuated tubes is proposed. Where the average percentage deviation from experimental values was −4.22%.
60 +6.5%
50
Acknowledgements - 6.5%
40
This work is funded by the Science and Technology Development Fund (STDF) program in Egypt under the UK-Newton Institutional Links Grants,” Development of Heat Driven Adsorption Desalination – Cooling System Using Advanced Metal Organic Framework Material” project ID 26148, in collaboration with University of Birmingham, UK.
30 30
40
50
60
70
80
90
100
Texit exp [ ] Predicted Values
0% Deviation Line
+/- 6.5 % Deviation Line
+/- 2% Deviation Line
Appendix A. Supplementary material
Fig. 16. Predictive exit water temperature validation.
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.03.106. 324
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References
applthermaleng.2016.07.163. [15] T. Brahim, H. Dhaou, A. Jemni, Theoretical and experimental investigation of plate screen mesh heat pipe solar collector, Energy Convers. Manage. 87 (2014) 428–438, https://doi.org/10.1016/j.enconman.2014.07.041. [16] H. Zheng, J. Xiong, Y. Su, H. Zhang, Influence of the receiver’s back surface radiative characteristics on the performance of a heat-pipe evacuated-tube solar collector, Appl. Energy 116 (2014) 159–166, https://doi.org/10.1016/j.apenergy. 2013.11.051. [17] L.M. Ayompe, A. Duffy, Thermal performance analysis of a solar water heating system with heat pipe evacuated tube collector using data from a field trial, Solar Energy 90 (2013) 17–28, https://doi.org/10.1016/j.solener.2013.01.001. [18] J. Bracamonte, J. Parada, J. Dimas, M. Baritto, Effect of the collector tilt angle on thermal efficiency and stratification of passive water in glass evacuated tube solar water heater, Appl. Energy 155 (2015) 648–659, https://doi.org/10.1016/j. apenergy.2015.06.008. [19] A. Alahmer, X. Wang, R. Al-Rbaihat, K.C. Amanul Alam, B.B. Saha, Performance evaluation of a solar adsorption chiller under different climatic conditions, Appl .Energy 175 (2016) 293–304, https://doi.org/10.1016/j.apenergy.2016.05.041. [20] E.S. Ali, K. Harby, A.A. Askalany, M.R. Diab, A.S. Alsaman, Weather effect on a solar powered hybrid adsorption desalination-cooling system: a case study of Egypt’s climate, Appl. Therm. Eng. 124 (2017) 663–672, https://doi.org/10.1016/j. applthermaleng.2017.06.048. [21] M.B. Elsheniti, O.A. Elsamni, R.K. Al-dadah, S. Mahmoud, E. Elsayed, K. Saleh, Adsorption refrigeration technologies, Sust. Air Condition. Syst. (2018) 71–95. [22] E. Bellos, C. Tzivanidis, K.A. Antonopoulos, Exergetic, energetic and financial evaluation of a solar driven absorption cooling system with various collector types, Appl. Therm. Eng. 102 (2016) 749–759, https://doi.org/10.1016/j. applthermaleng.2016.04.032. [23] F. Boudéhenn, H. Demasles, J. Wyttenbach, X. Jobard, D. Chèze, P. Papillon, Development of a 5 kW cooling capacity ammonia-water absorption chiller for solar cooling applications, Energy Proc. 30 (2012) 35–43, https://doi.org/10.1016/j. egypro.2012.11.006. [24] R.Z. Wang, Z.Y. Xu, Q.W. Pan, S. Du, Z.Z. Xia, Solar driven air conditioning and refrigeration systems corresponding to various heating source temperatures, Appl. Energy 169 (2016) 846–856, https://doi.org/10.1016/j.apenergy.2016.02.049. [25] N. Thompson, Heat pipes-performance of two-phase closed thermosyphons, Eng. Sci. Data Unit 81038 (1981). [26] B. Spang, W. Roetzel, Approximate Equations for the Design of Cross- Flow Heat Exchangers, Design and Operation of Heat Exchangers Vol. 18, Springer, Berlin Heidelberg, 1992, pp. 125–134. [27] E.R.G. Eckert, R.M.J. Drake, Analysis of heat and mass transfer, McGraw-Hill, 1972. [28] S.W. Churchill, M. Bernstein, A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow, J. Heat Transfer 99 (1977) 300–306, https://doi.org/10.1115/1.3450685.
[1] V.E. Pareto, M.P. Pareto, The Urban Component of the Energy Crisis, MPRA Paper, University Library of Munich, Germany, 2008https://doi.org/10.2139/ssrn. 1221622. [2] S.A. Kalogirou, Solar thermal collectors and applications, Prog. Energy Combust. Sci. 30 (2004) 231–295, https://doi.org/10.1016/j.pecs.2004.02.001. [3] S.M. Khairnasov, A.M. Naumova, Heat pipes application to solar energy systems, Appl. Solar Energy 52 (2016) 47–60, https://doi.org/10.3103/ s0003701x16010060. [4] F. Mahdjuri, Evacuated heat pipe solar collector, Energy Convers. 19 (1979) 85–90, https://doi.org/10.1016/0013-7480(79)90004-4. [5] A. Atiz, I. Bozkurt, M. Karakilcik, I. Dincer, Investigation of effect of using evacuated tube solar collector on solar pond performance, in: I. Dincer, C.O. Colpan, O. Kizilkan, M.A. Ezan (Eds.), Progress in Clean Energy, Vol. 2 Springer International Publishing, Cham, 2015, pp. 261–273. [6] D.N. Nkwetta, M. Smyth, F. Haghighat, A. Zacharopoulos, T. Hyde, Experimental performance evaluation and comparative analyses of heat pipe and direct flow augmented solar collectors, Appl. Therm. Eng. 60 (2013) 225–233, https://doi.org/ 10.1016/j.applthermaleng.2013.06.059. [7] K.A.R. Ismail, M.M. Abogderah, Performance of a heat pipe solar collector, J. Solar Energy Eng. 120 (1998) 51–59, https://doi.org/10.1115/1.2888047. [8] F. Jafarkazemi, E. Ahmadifard, H. Abdi, Energy and exergy efficiency of heat pipe evacuated tube solar collectors, Therm. Sci. 20 (2016) 327–335, https://doi.org/10. 2298/tsci130227150j. [9] K.C. Ng, C. Yap, T.H. Khor, Outdoor testing of evacuated-tube heat-pipe solar collectors proceedings of the institution of mechanical engineers, Part E: J. Proc. Mech. Eng. 214 (2000) 23–30, https://doi.org/10.1243/0954408001530182. [10] R. Daghigh, A. Shafieian, Theoretical and experimental analysis of thermal performance of a solar water heating system with evacuated tube heat pipe collector, Appl. Therm. Eng. 103 (2016) 1219–1227, https://doi.org/10.1016/j. applthermaleng.2016.05.034. [11] F. Jafarkazemi, H. Abdi, Evacuated tube solar heat pipe collector model and associated tests, J. Renew. Sust. Energy 4 (2012), https://doi.org/10.1063/1.3690958. [12] A.E. Kabeel, M.M. Khairat Dawood, A.I. Shehata, Augmentation of thermal efficiency of the glass evacuated solar tube collector with coaxial heat pipe with different refrigerants and filling ratio, Energy Convers. Manage. 138 (2017) 286–298, https://doi.org/10.1016/j.enconman.2017.01.048. [13] E. Azad, Experimental analysis of thermal performance of solar collectors with different numbers of heat pipes versus a flow-through solar collector, Renew. Sust. Energy Rev. 82 (2018) 4320–4325, https://doi.org/10.1016/j.rser.2017.10.015. [14] A.A. Alammar, R.K. Al-Dadah, S.M. Mahmoud, Numerical investigation of effect of fill ratio and inclination angle on a thermosiphon heat pipe thermal performance, Appl. Therm. Eng. 108 (2016) 1055–1065, https://doi.org/10.1016/j.
325
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Thermal performance of a heat-pipe evacuated-tube solar collector at high inlet temperatures
T
⁎
Mahmoud B. Elsheniti , Amr Kotb, Osama Elsamni Mechanical Engineering Department, Faculty of Engineering, Alexandria University, El-Chatby, Alexandria 21455, Egypt
H I GH L IG H T S
term for the collector thermal mass is added to the mathematical model. • AThenewmaximum relative error in exit temperature is reduced from 12.5% to 4.4%. • Collector efficiency is reduced at higher inlet temperatures and more series tubes. • There is an upper limit the number of series tubes to be used effectively. • A new collector efficiencyforexpression is proposed with average deviation of 4.2%. •
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar collectors Evacuated tube Heat pipe Thermal mass Solar cooling
The thermal performance of a heat-pipe evacuated-tube solar collector is investigated in the present paper. Hot water is targeted at a relatively high inlet temperature of 70–90 °C to predict the collector performance that utilized in solar cooling applications such as adsorption and absorption systems. A mathematical model of the system was developed and validated experimentally under weather conditions of Alexandria, Egypt. The theoretical model of the collector is enhanced by considering the effect of the thermal mass of the system, hence the maximum relative error between the experimental and theoretical results was reduced from 12.5% to 4.4%. The effects of the inlet water and ambient temperatures, number of evacuated tubes, water mass flow rate, and solar irradiance on both the exit water temperature and the collector’s efficiency were all considered in comprehensive studies. The results showed that the collector performance was strongly affected by all the above parameters but with different manners. For examples, at certain values of the water mass flow rate and solar irradiance, the exit temperature increases with the increase in the number of evacuated-tubes reaching a specified number above which the increase in the exit water temperature will be eliminated. However, the thermal efficiency is always better at lower numbers of tubes. Consequently, the total number of the evacuated tubes for different series and parallel arrangements can be minimized at specified operating conditions based on the model’s results, leading to minimal capital cost. In addition, an expression for predicting the collector efficiency was derived based on the mathematical model’s results to be used in calculating the exit water temperature at different operating conditions and number of evacuated tubes. This expression can be effectively used for modeling such type of collector employed in a thermally driven cooling cycle.
1. Introduction Nowadays, energy demand, global warming, ozone depletion and environmental pollution caused a rise in the urgent need for clean alternative energy sources instead of fossil fuel. Such problems [1] will increase energy prices till renewable energy sources provide considerable percent of energy to supply buildings, transport and industry. So, global markets are in dire need for energy conservation methods and
⁎
innovations in renewable energy sources, the key is in utilizing modern approaches and technologies to satisfy this need. One of these approaches is the use of solar collectors for domestic and industrial heating purposes. At present, the collectors used in solar applications are categorized into two main types; evacuated tube collector (ETC) and flat plate collector [2]. The main feature in evacuated tube collectors is eliminating both conduction and convection losses between the absorbing
Corresponding author. E-mail address: [email protected] (M.B. Elsheniti).
https://doi.org/10.1016/j.applthermaleng.2019.03.106 Received 1 October 2018; Received in revised form 15 February 2019; Accepted 23 March 2019 Available online 23 March 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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σ τ ϕ2 ϕ3
Nomenclature
A Ar CP D F g h h fg I k L M ṁ N P Q R R3f R3P T t Uloss
area (m2) single tube aperture area (m2) specific heat capacity (J/kg K) diameter (m) fill ratio gravitational acceleration (m/s2 ) convective heat transfer coefficient (W/m2 K) latent heat of evaporation (J/kg) insolation (W/m2) thermal conductivity (W/mK) length (m) mass (kg) mass flow rate (kg/s) number of evacuated tubes pressure (Pa) heat rate (W) thermal resistance (K/W) film boiling thermal resistance (K/W) pool boiling thermal resistance (K/W) temperature (°C or K) time (s) manifold heat loss coefficient (W/m2 K)
Subscripts a ab amb c e eff ex exit exp f g gi go HP i in l m man o p sat u v w
Greek symbols
α ε η μ ρ
Stefan Boltzmann constant transmittance condensation figure-of-merit (kg/s2.5 K0.75) boiling figure-of-merit (kg0.6/m0.2 s1.4 K)
absorptivity emissivity collector efficiency dynamic viscosity (Pa s) density (kg/m3)
air absorbed ambient condenser evaporator effective exit from a single evacuated tube exit from solar collector experimental header fluid glass inner glass tube outer glass tube heat pipe inner/inlet to a single evacuated tube inlet to solar collector liquid mean manifold outer absorber saturation useful vapor wall
an ETC integrated with coaxial heat pipe using air as a heat transfer fluid. They studied the effect of tilt angle, filling ratio and refrigerant type on the performance of the ETC at different air flow rates. They also concluded that the increase in the thermal efficiency with the modified heat pipe comparing to a collector without heat pipe reached 67%. Azad [13] experimentally compared the performance of two heat pipe solar collectors with the same effective area but different number of heat pipes, and a conventional flow-through collector. It was found that the heat pipe collector with the higher number of heat pipes have a higher thermal efficiency than to the other two collectors. Alammar et al. [14] numerically studied the effect of inclination angle and fill ratio on the performance of a thermosiphon heat pipe. It was found that the fill ratio and inclination angle of 65% and 90° resulted in the best thermal performance. The results showed a higher efficiency for HPETC than conventional solar collectors. Brahim et al. [15] studied the effect of adding fin arrays to the heat pipe condenser with two types of working fluid (methanol and water). They developed a time-dependent theoretical model of the system and compared it with the experimental results. The results indicated that the water system had a better performance than that of the methanol. Furthermore, the addition of fins to the heat pipe condensing surface increased the system overall efficiency. The optimal fins density was found to be double layers of 100mesh/inch. Zheng et al. [16] studied the effect of radiative characteristics of receiver's back surface on the thermal performance of HP-ETC. This influence is generally related to the back surface emissivity and temperature. The heat loss of the HP-ETC increases by increasing of the back surface emissivity. The variation of back surface emissivity can significantly affect the performance of the collector especially at higher temperature It is worth mentioning that most of the researchers have evaluated the performance of the collector for inlet water temperature range near
surface and outside ambient air. Evacuated tube collectors have been designed in various layouts such as water –in- glass, U-tube and heat pipe. In the later, a two phase heat pipe is used for transferring solar energy from the absorber to the fluid to be heated [3]. Heat pipe evacuated tube collectors (HP-ETC) are more thermally efficient than flat plate collectors, especially in cold climates [4]. Atiz et al. [5] experimentally studied the effect of ETC on solar pond performance. They noticed a significant increase in the temperature of the heat storage zone by using an ETC, which led to enhancement of the solar pond performance without a significant deterioration in the pond layers structure. Nkwetta et al. [6] experimentally compared the performance of heat pipe and direct flow evacuated tube collectors. The obtained results showed a better performance of heat pipe system than the direct flow configuration. Ismail and Abogderah [7] used methanol as the working fluid in heat pipe collector with 15° increase in slope than the conventional state to enhance condensation, and compared it with conventional solar collectors theoretically and experimentally. Also, studying the performance and evaluating the thermal efficiency of HPETC theoretically and experimentally was the main scope of study in the majority of researches made on this type of collector during the past few years [8,9]. Daghigh and Shafieian [10] developed a mathematical model of water heating system with HP-ETC according to thermal and exergy analysis to evaluate its performance. The system was experimentally tested and compared with the theoretical model results. The results indicated the optimal number of collector pipes to be 15. Also, the exergy efficiency increases with time with a maximum value of 5.4% at the end of the day. The maximum exit temperature of collector was reported to be about 64°C. Jafarkazemi and Abdi [11] developed a theoretical model of a HP-ETC with a dry condenser and circular fin. They compared the system heat gain and efficiency with the experimental results. Kabeel et al. [12] developed an experimental model of 316
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2.1. Collector
ambient 20–40 °C for water heating applications [17,18]. However, solar collectors are used recently in heat-driven cycles for certain applications such as solar absorption cooling, adsorption cooling, desalination and desiccant dehumidification systems. In such cycles, heating water after being used for the regeneration process is sent back to the solar collector at relatively high temperatures [19]. In solar adsorption refrigeration and desalination applications, the inlet water temperature to the collector is in range of 50–80 °C and exits in the range of 60–100 °C [19–21]. Four different solar collector types for a solar driven absorption cooling system were tested by Bellos et al. [22]. They found that the optimum generation temperature needed for the cooling system ranges from 90 to 120 °C and the ETC has the lowest land use and investment cost. There is a general agreement on that the performance of these systems is highly affected by the regeneration temperature [21,23,24]. On the other side, the increase in the collector inlet water temperature can somehow affect the collector efficiency and the number of the evacuated tubes needed for raising the collector exit temperature up to the required limit that ensures the optimum operation of such applications. In addition, there is no enough data in the literature about the effects of a relatively-high inlet water temperature coupled with different numbers of evacuated tubes on the HP-ETC performance. Therefore, a thorough mathematical model for a HP-ETC is developed in the present work to provide researchers and engineers who work on these thermally driven systems by the expected HP-ETC performance in their cycles under different operating conditions. The theoretical model's accuracy is enhanced by involving the thermal mass of the system and assessed by experimental tests that carried out for four different days in Alexandria, Egypt. The effect of the number of the evacuated tubes arranged series in a single-line has been investigated, while the results can be used effectively for replacement such single line of series evacuated-tubes by a number of parallel lines to match specified application requirements with a minimum total number of evacuated tubes.
The amount of solar radiation absorbed by the heat pipe evaporator surface (Qab) can be calculated using Eq. (1).
Qab = Iαp τgi τgo Ar
(1)
A portion of the absorbed heat will be dissipated to the ambient by convection and radiation heat losses (Qloss ) , which can be calculated using Eq. (2).
Qloss =
TP − Tamb R1
(2)
where R1 is the equivalent resistance of radiation losses between absorber – inner glass, inner-outer glass, and the convection and radiation losses of outer glass to the ambient. R1 and its decomposed resistances are explained as follows:
R1 =
R (go − amb) R convloss R (go − amb) + R convloss
+ R (gi − go) + R (P − gi)
(3)
TP − Tgi
R (P − gi) =
εp σAr (TP4 − Tg4i )
(4)
Tgi − Tgo
R (gi − go) =
εg σAi (Tg4i − Tg4o )
R (go − amb) =
R convloss =
(5)
Tgo − Ta 4 εg σAo (Tg4o − Tamb )
1 ha A o
(6)
(7)
The remaining amount of heat is transferred to the heat pipe (QHP ) , which can be calculated using energy balance equation as follows:
QHP = Qab − Qloss
(8)
2. Mathematical model 2.2. Heat pipe In this work, a gravity-assisted heat pipe has been used in the evacuated tube collector. A schematic drawing of collector components and operation is shown in Fig. 1. In the steady state operation, solar irradiance heats up the outer surface of the heat pipe evaporator, this heat is transferred to the evaporator’s inner surface by conduction, and vaporizes the heat pipe working fluid, which is considered pure water. The generated vapor flows naturally upwards by the buoyancy forces to the heat pipe condenser. The header fluid (water) absorbs the heat from the condenser as it passes over it and condenses the inside vapor. Then the condensate moves back to the evaporator by gravity and the cycle is repeated. Electrical-thermal analogy model is presented in Fig. 2 by considering the thermal resistance of each component in a single evacuated-tube to describe its thermal behavior. While Fig. 3 shows an illustrative schematic diagram of temperature points and heat vectors on a single evacuated-tube. The following assumptions are considered in the developed model:
The heat pipe can be modeled using number of thermal resistances R2 − 9 represented as follows: Evaporator wall thermal resistance (R2) is presented by:
ln R2 =
( ) Deo Dei
2πk w Le
(9)
A recommended method by ESDU [25] has been used to calculate
• Natural convection losses between the inner glass and the evaporator is neglected. • Thermal resistance across water-vapor interface in both evaporator and condenser is neglected. • Surface temperature of both absorber and evaporator are considered the same. • The conduction thermal resistances within the glass tube thickness are neglected.
Energy balance equations and thermal resistances for each component are presented in the following subsections.
Fig. 1. Schematic drawing of the heat pipe evacuated tube collector. 317
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Fig. 2. Electrical analogy for a heat pipe evacuated tube collector.
Otherwise,
R3 = R3P F + R3f (1 − F )
(13)
R4 and R6 are the thermal resistances across the liquid-vapor interface in the evaporator and the condenser respectively, and they are always small compared to the other resistances and are therefore neglected. Thermal resistance (R5) due to the pressure drop (ΔP ) of the vapor flow inside the heat pipe is expressed as:
Tsat ΔP hfg ρv QHP
R5 =
(14)
where ΔP can be calculated using the Darcy–Weisbach equation for laminar flow. Condensation thermal resistance in the condenser (R7) which can be calculated using Nusselt's theory filmwise condensation [26] by: 1 3 0.235QHP
R7 =
Dci
4 3
4 1 3 g 3L
c ϕ2
(15)
Condenser wall thermal resistance (R8) .
ln
Fig. 3. Schematic diagram of temperature points and heat vectors on single evacuated-tube.
R8 =
R3P
R9 =
1
Rtot =
4
Dei3 g 3 Le ϕ23 3 2 0.25
(11) 0.65
0.3
0.7
(17)
R9· ∑i = 2 Ri 9 ∑i = 2
Ri
Tco = Tp + (QHP Rtot )
0.23
ρ . k . Cpl . Pv hfg k ρ where ϕ2 = ⎛ μl l ⎞ and ϕ3 = l 0.25 l 0.4 0.1 0.23 are the boiling and ρv . hfg . μl . Patm ⎝ l ⎠ condensation figure of merit, respectively. Therefore, the boiling thermal resistance in the evaporator (R3) can be calculated according to the following condition: If R3p > R3f ,
R3 = R3P
Leff Aw k w
8
3 0.235QHP 4
(16)
2πk w Lc
So, the total equivalent resistance (Rtot ) of heat pipe and the condenser outer surfaces temperature (Tco) can be expressed by:
(10)
1
R3f =
Dco Dci
Thermal resistance along the heat pipe wall in axial direction (R9) can be calculated as:
the evaporation thermal resistance approximately by checking the thermal resistance of a combination of both, the liquid film in the evaporator (R3f ) and nucleate in the boiling pool (R3P ) . The two resistances can be expressed by:
1 = 0.4 ϕ3 g 0.2QHP (πDei Le )0.6
( )
(18) (19)
2.3. Header Energy balance is performed on the header in order to calculate the useful heat gain from the collector. Moreover, system thermal mass is also presented in the energy balance which used to be neglected in all
(12) 318
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previous theoretical models. Thermal mass of a system can be defined as the ability of the system components to store the heat. It is also defined as the resistance of system components to temperature changes, indicated by the time dependent variations in temperature during a full heating/cooling cycle. This affects the system by lowering its response to temperature changes. For example, at the late hours of the day, the system releases an amount of heat to the water that has been stored in it during the early hours of the day. This can cause a delay in water temperature reduction at the late hours of the day. The thermal energy balance of collector header can be expressed by:
QHP = Qu + Qmanloss + QTM
Table 1 Physical characteristics of evacuated tube collector.
(20)
where QTM represents the heat absorbed from/to the system within the time step Δt due to the thermal mass of each component in the system and can be calculated by:
QTM
(T − Tt − 1) = ∑ MCp t Δt
Heat pipe Heat pipe material
Copper
Working fluid Outer diameter (mm)
Water 16.2
Collector Tube outer diameter (mm) Absorber area (m2) Absorptivity Number of tubes/Collector Overall heat transfer coefficient from manifold to ambient (Uloss) (W/m2K)
58 2.06 0.93 15 0.06
η=
Condenser Length (mm) Inner diameter (mm)
100
Tube length (m) Glass thickness (mm) Glass transmittance Glass emissivity Absorber emissivity
1.8 4 0.88 0.02 0.08
15.8
̇ p f (Texit − Tin ) mC IAr N
(25)
MATLAB codes were developed to solve the above equations simultaneously, and the results were compared to the experimental data based on the water exit temperature.
(21)
Qmanloss is the manifold heat loss to environment which is calculated by:
Qmanloss = Uloss Aman (Tm − Tamb)
(22)
3. Experimental setup and procedure
where Tm is the mean water temperature between inlet and exit of each condenser, and Uloss is manifold heat loss coefficient provided by manufacturer data. Qu is the useful heat gain which can be calculated using:
̇ p f (Tex − Ti ) Qu = mC
This study aims to assess the change in system performance by varying inlet water temperature and mass flow rate as the main variables in the experiment. These tests were performed at Thermal Engineering Laboratory, Faculty of Engineering, Alexandria University (latitude 31.2° N and longitude 29.9° E). These experiments were used to validate the introduced mathematical model to help in predicting the performance of the heat pipe solar collector under investigation with different irradiance and climatic conditions. Fig. 4 shows a schematic diagram of the experimental setup and the collector’s characteristics are listed in Table 1. The experimental test cases on the solar system have been carried out using three modules of heat pipe evacuated tube collectors connected in series, each consists of 15 tubes as shown in Fig. 5. Fig. 6 shows the different used system components. A 2 kW electric heater and a radiator type heat exchanger equipped with air fan were used to adjust the inlet water temperature. The mass flow rate was also adjustable through a control valve. A cylinder storage tank with capacity of 60 L is provided. Solar irradiance is measured using CMP3 pyranometer with an accuracy of less than ± 5%. Thermocouples of T type are used to measure the inlet and the outlet water temperatures of the
(23)
where the exit water temperature of a single evacuated tube (Tex ) can be calculated using logarithmic mean temperature difference LMTD method as follows: −hf A
c
̇ f Tex = Tco − (Tco − Ti ) e mCp
(24)
where hf is the convection heat transfer coefficient between header water and condenser outer wall which is calculated using Echkert and Drake correlation for Re < 100 [27] and Churchill and Bernstein correlation for higher Re [28]. For N number of tubes in the collector, the inlet water temperature to the condenser can be considered as the exit water temperature from the previous one. The collector efficiency is calculated from the equation:
Fig. 4. Schematic diagram of system setup. 319
Solar Irradiance [W/m2]
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collector, the water tank, and the ambient temperature. The thermocouples are connected to data logger with 12-bit resolution after calibration to log the data. 4. Results and discussions The main objective of the present study is evaluating the performance of evacuated tube solar collector at relatively high inlet temperatures. The collectors should be connected in series and/or parallel to have such high level of temperatures. It is not practical to test all arrangements experimentally especially when number of modules becomes larger due to the space and cost limitation. The strategy of the present study comprises four stages; (i) developing a mathematical model of the solar collector that can be used to evaluate the series and/ or parallel connections; (ii) validation of the mathematical model by comparing its results with the measurements of smaller number of evacuated tube solar collector at various operating conditions; (iii) adopting the model to evaluate the performance of solar collectors at different mass flow rates, number of tubes, and various solar intensities; and eventually; (iv) proposing a generalized correlation for the collector thermal efficiency that links the mass flow and the exit temperature required for high temperature applications.
Day 2 (24 April 2018)
30 20 10 0
Ambient Temperature [ ] Wind velocity [m/s]
Fig. 7a. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 1.
Fig. 5. ETC at test site.
Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
Fig. 7b. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 2.
two days were selected in April and two days in July. These data will be used in the mathematical model to deduce the theoretical exit temperature and compare them with the experimental measurements.
4.2. Experimental validation of the mathematical model The leaving water temperatures from the three collectors arranged in series were examined by the experimental and theoretical models for the four days given above. At first, inlet water temperatures at the ambient levels were adapted and measured experimentally. They fluctuated between 32 °C and 34 °C with mass flow rate of 0.03 kg/s on the first day, and 36–40 °C with mass flow rate of 0.3 kg/s on the second day as shown in Figs. 8 and 9 respectively. Generally, there are good
4.1. Weather data The experimental test cases were carried out on four different days for different water mass flow rates, as well as for both low and high inlet water temperatures. The values of the ambient temperature, the solar irradiance, and the wind speed during these days are shown in Figs. 7a–7d. In order to have wide range of the operating conditions,
Fig. 6. System components at test site. 320
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1200 Day 3 (24 July 2018)
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1000
30
800 600
20
400 10
200 0
0
agreements between the mathematical and experimental results. However, at the lower mass flow rate of 0.03 kg/s, it can be seen in Fig. 8 that incorporating system thermal mass to the theoretical model reduced the maximum relative error between the experimental and the theoretical values to 4.4% compared to 12.5% when the thermal mass of the collectors was not considered. In details, system thermal mass began to show significant effect after mid-day, as it considers the amount of heat released from the system that has been absorbed during the early hours of the day, when the temperature of the water starts to fall down. By neglecting thermal mass effect as the model presented in reference [10], the exit water temperature trend only follows the solar irradiance trend along the day and the theoretical exit temperatures are lower than the experimental values at the late hours of the day. While in case of the higher mass flow rate of 0.3 kg/s, it is obvious in Fig. 9 that system thermal mass effect is less influential on the results, yet more accurate, since the maximum error only dropped from 3.22% to 3%. This is because the water is not in contact with the system for long enough time to absorb heat from the system. Generally, the trend of changes in both experimental and theoretical results is the same and shows good agreement in values with a maximum error of 4.4%. This is indicative of the validity of the developed model to predict the performance of evacuated tube heat pipe solar collector. Secondly, experimental tests were carried out for relatively high inlet water temperature ranging from 70 to 85 °C to mimic the water temperature exiting from thermally driven systems. These tests were performed at both 0.065 and 0.11 kg/s water mass flow rates. Figs. 10 and 11 compare between the experimental and theoretical values of exit water temperature for both mass flow rates. It is worth mentioning that the fluctuations in the inlet water temperatures is due to the replacement of hot water inside the tank with cold water to maintain the inlet water temperature within the desired range. As it can be seen, theoretical and experimental results share the same trend with a maximum relative error of 3.6%. However, it should be noted that there is no noticeable effect for the thermal mass in these two cases on the accuracy of the theoretical results. Since the thermal mass effect does not significantly affect the results when the drop in the irradiance is shallow after mid-day as in Day 3 and Day 4. So, for these two cases, working with relatively higher mass flow rates coupled with a gentle drop in the irradiance at late hours reduces the role of thermal mass.
Ambient Temperature [ ] Wind velocity [m/s]
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Ambient temperature
Wind Velocity
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40 Day 4 (27 July 2018)
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200 0 10:00
11:00
12:00
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Ambient Temperature [ ] Wind velocity [m/s]
Fig. 7c. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 3.
Time [hour] Solar Irradiance
Ambient temperature
Wind Velocity
Exit Temperature [ ]
Fig. 7d. Solar irradiance, ambient temperature and wind velocity variations during the experiment on Day 4. 60 Day 1 (m=0.03 kg/s)
55 50 45 40 35 30 10:00
11:00
12:00
13:00
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16:00
Texit,theo (No TM)
Tin
4.3. Effect of the operating parameters on the exit temperature
Time [hour] Texit,exp
Texit,theo (TM)
The theoretical model has been also employed to investigate the effect of number of tubes on the exit water temperature. Fig. 12(a–d) show the change of exit water temperature with increasing number of evacuated tubes at different mass flow rates and solar irradiances, while the inlet water temperature is set to 80 °C in these cases. Generally, the change pattern of the exit temperatures with an increase in the number of tubes are ascending, but with different rates depending on the water mass flow rates. Nevertheless, for specific mass flow rate and solar
Fig. 8. Experimental and theoretical exit water temperature values with and without thermal mass effect in theoretical model on Day 1.
Exit Temperature [ ]
95
85 80 75 70 65 10:00
Fig. 9. Experimental and theoretical exit water temperature values with and without thermal mass effect in theoretical model on Day 2.
Day 3 (m=0.065 kg/s)
90
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13:00
14:00
15:00
16:00
Texit,theo (NO TM)
Tin
Time [hour] Texit,exp
Texit,theo (TM)
Fig. 10. Experimental and theoretical exit water temperature values on Day 3. 321
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Exit Temperature [ ]
85
connected in series with mass flow rate of 0.05 kg/s. However, the same requirements can be achieved by another arrangement using 5 collectors connected in parallel each has 20 tubes and 0.01 kg/s mass flow rate. As a result, the total number of tubes is dramatically reduced to 100 tubes compared to 170 tubes in the first scenario, hence the overall cost is meaningfully reduced.
Day 4 (m=0.11 kg/s)
80 75 70 65 60 55
4.4. Effect of the operating parameters on the collector efficiency
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Texit,theo (NO TM)
Tin
Fig. 13(a–f) shows the collector efficiency variations with the change in the function of (Tin − Tamb)/ I and ṁ at different number of evacuated-tubes. As it is seen in the figures, the efficiency decreases with increasing inlet water temperature and number of tubes. As by increasing these two parameters, this will lead to a decrease in the temperature difference between the condenser outer surface and the water in contact at each successive tube, which lower the heat transfer rate, hence the efficiency decreases. For instance, the efficiency drops from 42% to 27% by increasing number of tubes from 15 to 150 tubes at the same (Tin − Tamb)/ I and ṁ of 0.03 m2.K/W and 0.12 kg/s, respectively. Moreover, at a specified (Tin − Tamb)/I, increasing water mass flow rate up to 0.08 kg/s increases the rate of heat transfer between the header water and the condenser, and then the efficiency increases.
Time [hour] Texit,exp
Texit,theo (TM)
Fig. 11. Experimental and theoretical exit water temperature values on Day 4.
irradiance at smaller mass flow rates of 0.01 kg/s and 0.02 kg/s, increasing in the exit temperature is diminished with increasing the number of tubes (due to the temperature difference limit with the heat pipe). Therefore, there is an upper limit for increasing the number of tubes under which the collector can be effectively used. Also, it is noticed that this upper limit for the number of tubes is increased with increasing mass flow rate, yet the maximum achievable exit temperature is decreased. For instance, as shown in Fig. 12-d, at water mass flow rate of 0.01 kg/s and 800 W/m2 solar irradiance, the maximum number of tubes can be effectively used is approximately 150 tubes that corresponds to 119 °C exit water temperature. While this number of tubes is increased to be almost 180 tubes in case of 0.02 kg/s mass flow rate at the same solar irradiance. However, the maximum temperature in this case drops to be 112 °C. Moreover, these results are also useful for selecting the optimum network series and parallel connection configuration for the collectors. For example, assuming 700 W/m2 solar irradiance, if the required exit water temperature and mass flow rate for the application are 95 °C and 0.05 kg/s, respectively. Thus, from Fig. 12-c, one can use 170 tubes
130
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Number of Tubes (a) 130 120 110 100 90 80 70 50
100
130 120 110 100 90 80 70 150
Number of Tubes (c)
50
100
150
200
Number of Tubes (b)
I=700 W/m2
0
Fig. 12. Variation of water exit temperature from the collector with number of evacuated tubes at different mass flow rates and solar irradiances (Tin = 80 °C).
I=600 W/m2
120
110
0
In applications such as solar adsorption and absorption systems, the exit temperatures from the solar collector and mass flow rates are desirable to be in specified ranges to assure an acceptable performance for the overall system. Therefore, relating all solar collector parameters including the number of the evacuated-tubes to the overall system modeling will be very beneficial to find out the best performance with minimum number of collectors. For this purpose, the results were used to derive a model-based correlation that relates the efficiency with ṁ , (Tin − Tamb)/ I and number of evacuated-tubes N as follows:
130
I=500 W/m2
120
4.5. Correlation for the collector efficiency
200
I=800 W/m2
0
50
100
150
Number of Tubes (d)
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Fig. 13. Energy efficiency vs. water mass flow rate and (Tin − Tamb)/I. (For N = 15, 30, 45, 60, 90, 150).
Tin − Tamb ) + a3(N ) ṁ 2 I T − Tamb T − Tamb 2 ⎞ + a 4(N ) ṁ ( in ) + a5(N ) ⎛ in I I ⎠ ⎝
And the corresponding exit temperature can be calculated by:
ηcorr = a0(N ) + a1(N ) ṁ + a2(N ) (
Texit corr = Tin +
(26)
323
ηcorr INAr ̇ f mCp
(27)
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The best values of the coefficients a 0 → 5 when 15 evacuated-tubes module is utilized are listed in Table 2. To generalize Eq. (26), Fig. 14 relates the new a 0 → 5 required for higher number of evacuated-tubes with those given in Table 2. It should be noticed that the coefficient a4 changes within different scale, then it is represented separately on the right y-axis in Fig. 14. The comparison between the experimental and correlation-based values of both efficiency and the corresponding exit water temperature are given in Figs. 15 and 16. The predicted data alternate up and down the prefect predicted data line but within narrow range. The correlation results give an average percentage deviation of −4.22% and −0.73% for efficiency and exit water temperature, respectively (over predicting model). The absolute percentage deviation are 6.78% and 1.32%. Also, the maximum deviation in predicting the efficiency is 14.85%, while it is 6.5% for the exit water temperature. However, the maximum deviation drops for the exit water temperature to be 2% at higher exit temperatures of 70–90 °C.
Value
a0(15)
0.559
a1(15)
3.492
a2(15)
−7.424
a3(15)
−17.82
a 4(15)
−0.5527
a5(15)
35.22
12
0.4
8
0.2
4
0
0
-0.2
-4
-0.4
-8
[a4 (N) - a4 (15) ] /a4 (15)
Coefficient
0.6
i=1,2,3,5
[ai (N) - ai (15) ] /ai (15)
Table 2 Efficiency coefficients of 15 tubes module.
5. Conclusion
-12
-0.6 15
30
45
60
75
90
105
120
135
In this work, the performance of a heat-pipe evacuated-tube solar collector was investigated at a relatively high inlet water that coming from heat-driven cycles such as solar adsorption and absorption cooling cycles. Experimental tests were carried out for four days under the weather conditions of Alexandria city in Egypt and used to validate the mathematical model. The outcomes and net effects of the HP-ETC parameters on the system performance can be concluded as follows:
150
Number of tubes a0
a1
a2
a3
a5
a4
Fig. 14. The change in efficiency coefficients from 15 tubes module coefficients vs. Number of evacuated tubes.
0.55
• At low mass flow rates, adding the thermal mass effect of the system
+12%
0.5
ABS-PD=6.78 A-PD= - 4.22 MAX-PD=14.85
0.45
-12%
0.4 0.35 0.3
•
0.25 0.2 0.2
0.3
0.4
0.5
exp Predicted values
0% Deviation Line
+/- 12% Deviation Line
•
Fig. 15. Predictive correlation efficiency validation.
100 90
ABS-PD=1.32 A-PD= - 0.73 MAX-PD=6.5
Texit corr [ ]
80
•
+2% -2%
70
to the theoretical model can lead to a noticeable reduction in the maximum relative error of exit water temperature, as for example from the relative error of 12.5–4.4% at 0.03 kg/s. Although, the thermal mass gives accurate results, its effect is insignificant at higher flow rates. However, since low flow rates are recommended in solar systems, the inclusion of the thermal mass is essential for better predictions. Generally, at any number of evacuated-tubes, either a decrease in the inlet water temperature or an increase in the mass flow rate will lead to an increase in the collector’s efficiency, while the exit water temperature will decrease. Also, at certain values of the water mass flow rate and solar irradiance, there is a maximum number of evacuated-tubes above which the increase in the outlet water temperature is valueless. The results of developed model can be used effectively in selecting the optimum series and parallel arrangements for HP-ETC at a given operating condition, leading to a minimum total number of tubes. A new correlation in a generalized form for predicting efficiency of HP-ETC as a function of ṁ , (Tin − Tamb)/ I and number of evacuated tubes is proposed. Where the average percentage deviation from experimental values was −4.22%.
60 +6.5%
50
Acknowledgements - 6.5%
40
This work is funded by the Science and Technology Development Fund (STDF) program in Egypt under the UK-Newton Institutional Links Grants,” Development of Heat Driven Adsorption Desalination – Cooling System Using Advanced Metal Organic Framework Material” project ID 26148, in collaboration with University of Birmingham, UK.
30 30
40
50
60
70
80
90
100
Texit exp [ ] Predicted Values
0% Deviation Line
+/- 6.5 % Deviation Line
+/- 2% Deviation Line
Appendix A. Supplementary material
Fig. 16. Predictive exit water temperature validation.
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.03.106. 324
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References
applthermaleng.2016.07.163. [15] T. Brahim, H. Dhaou, A. Jemni, Theoretical and experimental investigation of plate screen mesh heat pipe solar collector, Energy Convers. Manage. 87 (2014) 428–438, https://doi.org/10.1016/j.enconman.2014.07.041. [16] H. Zheng, J. Xiong, Y. Su, H. Zhang, Influence of the receiver’s back surface radiative characteristics on the performance of a heat-pipe evacuated-tube solar collector, Appl. Energy 116 (2014) 159–166, https://doi.org/10.1016/j.apenergy. 2013.11.051. [17] L.M. Ayompe, A. Duffy, Thermal performance analysis of a solar water heating system with heat pipe evacuated tube collector using data from a field trial, Solar Energy 90 (2013) 17–28, https://doi.org/10.1016/j.solener.2013.01.001. [18] J. Bracamonte, J. Parada, J. Dimas, M. Baritto, Effect of the collector tilt angle on thermal efficiency and stratification of passive water in glass evacuated tube solar water heater, Appl. Energy 155 (2015) 648–659, https://doi.org/10.1016/j. apenergy.2015.06.008. [19] A. Alahmer, X. Wang, R. Al-Rbaihat, K.C. Amanul Alam, B.B. Saha, Performance evaluation of a solar adsorption chiller under different climatic conditions, Appl .Energy 175 (2016) 293–304, https://doi.org/10.1016/j.apenergy.2016.05.041. [20] E.S. Ali, K. Harby, A.A. Askalany, M.R. Diab, A.S. Alsaman, Weather effect on a solar powered hybrid adsorption desalination-cooling system: a case study of Egypt’s climate, Appl. Therm. Eng. 124 (2017) 663–672, https://doi.org/10.1016/j. applthermaleng.2017.06.048. [21] M.B. Elsheniti, O.A. Elsamni, R.K. Al-dadah, S. Mahmoud, E. Elsayed, K. Saleh, Adsorption refrigeration technologies, Sust. Air Condition. Syst. (2018) 71–95. [22] E. Bellos, C. Tzivanidis, K.A. Antonopoulos, Exergetic, energetic and financial evaluation of a solar driven absorption cooling system with various collector types, Appl. Therm. Eng. 102 (2016) 749–759, https://doi.org/10.1016/j. applthermaleng.2016.04.032. [23] F. Boudéhenn, H. Demasles, J. Wyttenbach, X. Jobard, D. Chèze, P. Papillon, Development of a 5 kW cooling capacity ammonia-water absorption chiller for solar cooling applications, Energy Proc. 30 (2012) 35–43, https://doi.org/10.1016/j. egypro.2012.11.006. [24] R.Z. Wang, Z.Y. Xu, Q.W. Pan, S. Du, Z.Z. Xia, Solar driven air conditioning and refrigeration systems corresponding to various heating source temperatures, Appl. Energy 169 (2016) 846–856, https://doi.org/10.1016/j.apenergy.2016.02.049. [25] N. Thompson, Heat pipes-performance of two-phase closed thermosyphons, Eng. Sci. Data Unit 81038 (1981). [26] B. Spang, W. Roetzel, Approximate Equations for the Design of Cross- Flow Heat Exchangers, Design and Operation of Heat Exchangers Vol. 18, Springer, Berlin Heidelberg, 1992, pp. 125–134. [27] E.R.G. Eckert, R.M.J. Drake, Analysis of heat and mass transfer, McGraw-Hill, 1972. [28] S.W. Churchill, M. Bernstein, A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow, J. Heat Transfer 99 (1977) 300–306, https://doi.org/10.1115/1.3450685.
[1] V.E. Pareto, M.P. Pareto, The Urban Component of the Energy Crisis, MPRA Paper, University Library of Munich, Germany, 2008https://doi.org/10.2139/ssrn. 1221622. [2] S.A. Kalogirou, Solar thermal collectors and applications, Prog. Energy Combust. Sci. 30 (2004) 231–295, https://doi.org/10.1016/j.pecs.2004.02.001. [3] S.M. Khairnasov, A.M. Naumova, Heat pipes application to solar energy systems, Appl. Solar Energy 52 (2016) 47–60, https://doi.org/10.3103/ s0003701x16010060. [4] F. Mahdjuri, Evacuated heat pipe solar collector, Energy Convers. 19 (1979) 85–90, https://doi.org/10.1016/0013-7480(79)90004-4. [5] A. Atiz, I. Bozkurt, M. Karakilcik, I. Dincer, Investigation of effect of using evacuated tube solar collector on solar pond performance, in: I. Dincer, C.O. Colpan, O. Kizilkan, M.A. Ezan (Eds.), Progress in Clean Energy, Vol. 2 Springer International Publishing, Cham, 2015, pp. 261–273. [6] D.N. Nkwetta, M. Smyth, F. Haghighat, A. Zacharopoulos, T. Hyde, Experimental performance evaluation and comparative analyses of heat pipe and direct flow augmented solar collectors, Appl. Therm. Eng. 60 (2013) 225–233, https://doi.org/ 10.1016/j.applthermaleng.2013.06.059. [7] K.A.R. Ismail, M.M. Abogderah, Performance of a heat pipe solar collector, J. Solar Energy Eng. 120 (1998) 51–59, https://doi.org/10.1115/1.2888047. [8] F. Jafarkazemi, E. Ahmadifard, H. Abdi, Energy and exergy efficiency of heat pipe evacuated tube solar collectors, Therm. Sci. 20 (2016) 327–335, https://doi.org/10. 2298/tsci130227150j. [9] K.C. Ng, C. Yap, T.H. Khor, Outdoor testing of evacuated-tube heat-pipe solar collectors proceedings of the institution of mechanical engineers, Part E: J. Proc. Mech. Eng. 214 (2000) 23–30, https://doi.org/10.1243/0954408001530182. [10] R. Daghigh, A. Shafieian, Theoretical and experimental analysis of thermal performance of a solar water heating system with evacuated tube heat pipe collector, Appl. Therm. Eng. 103 (2016) 1219–1227, https://doi.org/10.1016/j. applthermaleng.2016.05.034. [11] F. Jafarkazemi, H. Abdi, Evacuated tube solar heat pipe collector model and associated tests, J. Renew. Sust. Energy 4 (2012), https://doi.org/10.1063/1.3690958. [12] A.E. Kabeel, M.M. Khairat Dawood, A.I. Shehata, Augmentation of thermal efficiency of the glass evacuated solar tube collector with coaxial heat pipe with different refrigerants and filling ratio, Energy Convers. Manage. 138 (2017) 286–298, https://doi.org/10.1016/j.enconman.2017.01.048. [13] E. Azad, Experimental analysis of thermal performance of solar collectors with different numbers of heat pipes versus a flow-through solar collector, Renew. Sust. Energy Rev. 82 (2018) 4320–4325, https://doi.org/10.1016/j.rser.2017.10.015. [14] A.A. Alammar, R.K. Al-Dadah, S.M. Mahmoud, Numerical investigation of effect of fill ratio and inclination angle on a thermosiphon heat pipe thermal performance, Appl. Therm. Eng. 108 (2016) 1055–1065, https://doi.org/10.1016/j.
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