Simulation and Optimization of Vacuum Tube Solar Collector Water Heating System in Iran

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1 Online available since February 2016 at (2016) Copyright ORIC Publications Journal of Science and Engineering; Vol. 07 (01), 2016, ISSN: Simulation and Optimization of Vacuum Tube Solar Collector Water Heating System in Iran Majid Azimi 1, Seyed Sajad Mirjavadi 2, Ahmadreza Mohammadkarim 3* 1 School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran. 2 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. 3 Department of Energy System Engineering, Faculty of Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran, Iran * Received October 2015, Accepted December 2015 ABSTRACT The evacuated tube solar collectors with the free circulation water between the tubes and horizontal tank above it are economically cheaper than heat pipes collector systems. This type of solar system is widely used in the world. This paper is dedicated to simulating the vacuum tube solar water heating system with natural circulation water between the tubes under the different climatic conditions in Iran with TRNSYS16 software. The most important component diagram used in the simulation with the TRNSYS16 is Type71 for vacuum tube collector. Five nodes are stratified at different heights in horizontal tank for increasing the water in higher height of the tank. Initially we assume arbitrarily consecutive ten days in each twelve-months of the year. The values of the daily, monthly and yearly useful energy gain, efficiency and solar fraction are obtained. Also values of the outlet water temperature from each evacuated tube, ambient temperature and solar radiation are extracted. In order to improve the performance of the evacuated tube solar water heater, optimization of the efficiency this system is expressed by genetic algorithm Toolbox in MATLAB software. Keywords: Vacuum Tube Solar Collector, TRNSYS, Optimization, Efficiency Contents 1 Introduction Describing the circulation system and mathematical method TRNSYS simulation Results and discussion Conclusion All rights reserved. No part of contents of this work may be reproduced or transmitted in any form or by any means without the written permission of ORIC Publications,

2 NOMENCLATURE Parameter Value Unit Parameter Value Unit η η of water Dimensionless Dimensionless Dimensionless 1 INTRODUCTION The thermal performances of solar collectors are mentioned by Kalogeria [1, 2]. The structure and operation of several types of the most common solar collectors are reported in this paper. These collectors including: Flat Plate Collectors (FPCs), Evacuated Tube Collectors (ETCs), Parabolic Trough Collectors (PTCs), dish and Heliostat fields collectors (HFC) and Fresnel lens. The heating systems such as: FPCs and ETCs are generally designed with forced circulation of fluids between their tubes. In these thermal systems due to the pumps, there is no severe limitation for fluid flow circulation [3, 4, 5 and 6]. The water-in-glass Evacuated Tube Collectors are widely used in the world. The instantaneous efficiency and outlet water temperature of the collector in these systems are generally more than the flat plate collectors, because the heat losses of ETCs are lower than flat plate collector types [7, 8]. In these papers the efficiency of these collectors are expressed as linear regression of instantaneous efficiency against heat loss in selected hours in during chosen days. The vacuum tube solar collector water heating systems with natural circulation of fluid between the tubes and the horizontal tank above it are expressed by [9, 10, 11, 12, 13 and 14]. The characteristics of the optical efficiency are presented by experimental work [15]. The exergy and energy analysis of solar assisted heat pumps also is carried out by [15, 16]. In a few cases performance and efficiency of the vacuum tubes Solar Domestic Hot Water Systems (SDHWS) are done by overall heat losses of these systems. An overall heat loss coefficient of these collectors includes the irradiative and convective heat losses coefficients [17]. The performance of these types of the SDHWS are ideal, when the overall heat loss coefficients are minimized. The operation of the ETCs also is performed by U-tubes shape that its function is different from normal and common types of the vacuum tubes [18]. The performance of the vacuum tubes SDHWS are explained in a few works based on configuration of the integrated storage tanks [9, 19]. Some nodes are embedded in order to measure the temperature at different heights from the vertical tank. Vertical tanks are at ETCs with forced circulation of fluids or are accompanied with horizontal tank which increases the water outlet temperature of the horizontal tank [9]. The Tilt and Azimuth angles are investigated Journal of Science and Engineering / ISSN:

3 in some papers [20, 21 and 22]. These papers have shown that the inclination of collector effects on performance of the ETCs. The effects of Tilt and Azimuth angles in heat pipe (two-phase) evacuated tube SDHWS is commonly more than the single-phase ETCs SDHWS [20, 21]. Two common forms of the ETCs are including: Tilted- arranged and Horizontally-arranged, which are for the commercial-industry and domestic scales respectively. In Fig. 1. (a) Schematic of ETCs water heating system is shown. The nodes are mounted at different height of the vertical tank to measure the water temperature. Also the view of top section of the tube opening is depicted in Fig. 1. (b). Fig. 1. (a) Schematic of vacuum tube solar water heating system with Tilted-Arranged (b) Section of the tube opening 2 DESCRIBING THE CIRCULATION SYSTEM AND MATHEMATICAL METHOD A view of the fluid flow inside the pipes is displayed in Fig. 2. (a). The urban water circulates naturally in the tube throughout the day. This type of the solar thermal system starts producing the hot water using the sun heat during the day. Due to the different density between the cold and hot water, when the solar radiation encounters the black surface in inner tube of each vacuum tube the hot water of the tubes reaches the storage tank and replaced with cold water from horizontal tank to vacuum tubes. Outlet hot water at the highest height of the tank is used to load. The position of the solar irradiation in connection with each vacuum tube is shown in Fig. 2. (b). Aperture of the area in midday is greater than the other times. In the midday about %33 of absorber tubes of the vacuum tubes is exposed to the sun. Aperture of the area for each vacuum tube is obtained: That and are diameter of inner tube, length of each tube and number of the tubes respectively. Rate of the heat gain that reaches to each vacuum tube is given by: Journal of Science and Engineering / ISSN:

4 Therefor the total heat gain for all the tubes of the collector is: Instantaneous efficiency of the collector is written by: η η That is average of the inlet and outlet temperatures of the collector. η and are first and second heat loss coefficients, optical efficiency, ambient temperature and solar irradiation on tilted surface respectively. Also outlet water temperature of the collector is: η ( ) and are and respectively. are dimensionless number of Grassof, Nusselt, Prandtl. With considering as tilted angle of the collector, the dimensionless number of for the two concentric tubes that space between them is vacuum, is given by Eq. 6. having and, mass flow rate is given by: Also Solar Fraction (SF) of the evacuated tubes SDHWS is extracted from Eq. 8. It should be noted that the from Eq. 9. will be found Journal of Science and Engineering / ISSN:

5 3 TRNSYS SIMULATION The TRNSYS software is the most common program for simulating the thermal solar systems including: FPCs, ETCs, PTCs, Heat Pipe collectors and etc. The solar water heating system with single-phase vacuum tube solar collector is designed with TRNSYS16 software. The most important components in this simulation are: vacuum tube collector (Type71), horizontal tank (Type60k), weather data and daily load. Fig. 2. (a) Natural circulation of the water between the tube and tank (b) Solar radiation on absorber tube of the collector in different times 3.1. Load profile diagram in TRNSYS16 Performance of the daily load profile of the single-phase ETCs is shown in Fig. 3. This diagram of daily load contains three different curves at various times in a day. To obtain in a day we must to have some parameters such as: inlet temperature of the water to the tubes, outlet temperature of the water to the tank, mass flow rate of the water and times. Fig. 3. Daily load profile of the water-in-glass SDHWS Journal of Science and Engineering / ISSN:

6 3.2. Type109-TMY2 in TRNSYS16 Type109-TMY2 in TRNSYS16 software represents weather data in cities across the world. TRNSYS16 software is capable of simulating solar hot water system with different climatic conditions. This paper is considered three cites with different climatic conditions including: Tehran, Zahedan and Tabriz. In between these three cities, Zahedan city is the hottest city and solar radiation of this city is greater than two other cities. Tabriz city has cold and dry weather Type71 and Type60k in TRNSYS16 For the simulation single-phase and two-phase vacuum tubes SDHWS we must use Type71 and Type538 as collectors respectively. As water is the fluid between the tubes and tank with different of colds and hot streams, then Type71 is used for this simulation. Type60k is stratified with some nodes in different temperature levels to measured water temperature at different heights of the horizontal tank. Characteristics of the vacuum tube collector and horizontal tank is presented in Table System simulation diagram in TRNSYS16 Simulation of single-phase vacuum tube SDHWS with natural circulation is performed under the different climatic conditions. The yearly performance of the solar fraction and heat gain of this system in different cities is done in this paper. Table. 1. Characteristics Type71 and Tye60k Type71 (vacuum tube solar collector) Parameters Values Units Parameters Values Units Inner tubes 47 mm Length of tubes 1800 mm Cover tubes 58 mm Absorption Number of tubes 20 - Net weight kg Heat waste coefficients W/m 2 C Specific heat of water 4180 J/kgK Type60k (Horizontal Tank) Parameters Values Units Parameters Values Units Volume tank 200 Lit Tank loss -coefficient 0.3 Length of the tank 1.25 m Hot-side temperature 45 C Fluid density 997 Kg/m 3 Cold-side temperature 30 C Flow rate 30 kg/s Hot and cold sides flow rate 30 kg/hr Fluid thermal conductivity 1.4 Number of nodes 6 - Journal of Science and Engineering / ISSN:

7 Fig. 4. Diagram of the single-phase vacuum tube SDHWS in TRNSYS16 The curves of daily heat gain; outlet water temperature of the collector, G tilt and G coll are expressed in this simulation. Each ETC is including: 2 inlet flows and 1 outlet flow that urban water and cold water of the tank are inlet flows to collector. Also the water heated by solar irradiation on tilted surface of absorber tube is outlet flow from the collector. Diagram of this simulation is shown in Fig RESULTS AND DISCUSSION Performance of the single-phase vacuum tube SDHWS under the different climatic conditions in Iran country is investigated using TRNSYS16. For the better comparison, the daily curves of the collectible solar radiation, solar radiation on tilted surfaces of the collector and useful heat gain are drawn in warm and cold climates in Iran country. Also ambient and outlet water temperatures of the collector in two different climatic condition cities are shown in this paper. The values of the inlet, mean and outlet water temperatures in vacuum tube solar collectors are extracted with TRNSYS16 software. The parameters of the daily and monthly heat losses, instantaneous and yearly efficiencies of this solar thermal system are noted in this paper. The yearly solar fractions in this simulation in different cities are validated with the experimental work. Also performance optimization of the single-phase evacuated tube solar collector system efficiency under the climatic condition in Tehran city is done by Genetic Algorithm Toolbox in MATLAB software. Journal of Science and Engineering / ISSN:

8 4.1. Daily curves of the collectible and tilted solar radiations The values of the collectible and tilted solar radiations on the vacuum tubes solar collectors are shown in Fig. 5. The curves of the G coll and G tilt in Tabriz and Zahedan cities are drawn in selected warm and cold days. For example in Aug. 15 th, the peak value of the solar radiation in Zahedan city is about 3500 kj/hr.m 2. (a) (b) Fig. 5. The daily curves of the G coll and G tilt (a): Aug. 15 th (b): Feb. 14 th The area under the curves of the solar radiation in Zahedan city is more than Tabriz city. The pick values of the G tilt in Feb 14 th are 2330 kj/hr.m 2 and 1070 kj/hr.m 2 in Zahedan and Tabriz cities respectively. The daily curves of the G coll and G tilt in two cities are shown in Fig. 5. Journal of Science and Engineering / ISSN:

9 4.2. Performances of the nodes in Type60k Some nodes are stratified at different heights in horizontal tank. These nodes will cause water with different temperatures trend to values mentioned in Fig. 6. Performances of the water temperatures in the Type60k tank considering their sensors are shown in Fig. 6. T top is value of the hot water in highest height of the tank. The maximum and minimum values of the T top and T bottom in their best positions in Type60k are 72 C and 35 C respectively. The values of the T 2, T 3, T 4 and T 5 are different in the beginning. These nodes at different heights of the Type60k converge together and create the final value. The final value of the T top enters to water port in order to load and use for consumers. Fig. 6. Performances of the water temperatures nodes in Type60k 4.3. Daily curves of the outlet water temperatures and useful energy gains The performances of the ambient and outlet water temperatures in two-different climatic conditions are demonstrated in Fig. 7. These Figs including: curves of the outlet water temperatures of single-phase evacuated tubes SDHWS with natural circulation of the water between the tubes in Aug. 15 th and Feb. 14 th. The peak values of the outlet water temperatures in midday Aug. 15 th are 80 C (Fig. 7 (a)), whereas maximum of these values in midday Feb. 14 th are 70 C and 60 C in Zahedan and Tabriz city respectively (Fig. 7 (b)). The distance between two curves of the outlet water temperature of the collector in Aug. 15 th is lower than them distance in Feb. 14 th due to the low solar radiation intensity in Tabriz city in Feb. 14 th. Also performances of the useful energy gains and useful energy gains per aperture areas are drawn in two cities noted above. The values of the heat gains and useful energy gains per aperture areas in selected days in Aug. 15 th are slightly more than those values in Feb.14 th (Fig. 7 (c)). The values of these parameters in night are negative, because the hot water in horizontal tank consume by consumers. The difference between curves of the collectible heat gain in two cities in Feb.14 th is more than the difference in Aug. 15 th due to little solar radiation in days of the winter in Tabriz city (Fig. 7 (d)). Journal of Science and Engineering / ISSN:

10 (a) (b) (c) Journal of Science and Engineering / ISSN:

11 (d) Fig. 7. The curves of the ambient and outlet water temperatures of Type60k in Aug. 15 th (a) and Feb. 14 th (b). The curves of the useful energy gains per aperture area and collectible heat gains in Aug. 15 th (c) and Feb. 14 th (d) Yearly performances of the solar fraction and useful energy gain Useful energy gains and solar fractions performances of the single-phase water-in-glass SDHWS are investigated in consecutive ten days in each month of the year. These parameters are evaluated in Zahedan, Tabriz and Tehran cities and these curves are compaired with each other. Evaluations of ten selected days in each month of the year demonstrate the performances of this system in one year in three cities. Trends of the useful energy gains in three cities are similar together (Fig. 8(a)). The minimum and maximum values of the area under the curves of useful energy gains in three curves are and in Aug. and Feb. months respectively. Also the yearly curves of the solar fractions are shown in three cities (Fig. 8(b)). The minimum value of the solar fraction is in Tabriz city curve and the value is Maximum different values of the solar fractions from Feb. to Aug. is 0.78 in Tabriz city, due to different values of solar radiation intensity in Tabriz city from Feb. to Aug., Also trends of these three solar fractions curves in three cities are similar to the useful energy gains curves. Journal of Science and Engineering / ISSN:

12 (a) (b) (b) Fig. 8. (a) Yearly useful energy gain (b) Yearly solar fraction 4.5. Validation of the yearly efficiency with experimental work Six selected days in spring and summer seasons are considered. The values of the inlet, mean, outlet and ambient temperatures, solar radiations on tilted surfaces, instantaneous efficiencies and heat losses are obtained in specified times. These characterizations and monthly Journal of Science and Engineering / ISSN:

13 performances of the single-phase vacuum tube SDHWS that simulated using TRNSYS16 software can be seen in Table.2. These parameters are extracted in climatic conditions of Tehran city. Since the instantaneous efficiency of the single-phase water-in-glass vacuum tubes SDHWS is between 50%-60% [3, 9 and 10], the values of the heat losses in vacuum tubes solar collectors must be lower than If the values of instantaneous heat losses in these systems are higher than 0.025, values of the instantaneous efficiencies of these systems in the linear regression curves of the efficiency against heat loss will be lower than 0.5, that is not acceptable [9]. Table. 2. Daily and monthly performances of the single-phase vacuum tube solar collector Daily Performance Day Time: (hr) T in ( C) T m ( C) T out ( C) T a ( C) G (W/m 2 ) ɳ 11: May : : : Jun : : : : Jun : : Jul : : : Jul : : : Aug : : : Monthly Performance Month Efficiency Heat Heat Heat Month Efficiency Month Efficiency loss loss loss Jan >0.025 May <0.025 Sep <0.025 Feb >0.025 Jun <0.025 Oct <0.025 Mar <0.025 Jul <0.025 Nov <0.025 Apr <0.025 Aug <0.025 Dec >0.025 Also yearly values of the efficiencies in different climatic conditions are shown in Figs. 9. Values of the yearly efficiency curves in Zahedan, Tabriz and Tehran cities are extracted and validated with experimental work [10]. The trends of these curves in three cities of Iran are similar to experimental works. Values of the monthly efficiencies in five curves are low in cold Journal of Science and Engineering / ISSN:

14 months. In months with high solar radiation, values of the efficiencies reaches to The yearly efficiency curve of the Jakarta city is slightly more than four other cities that noted in Fig. 9. Fig. 9. Validation of the yearly efficiency curves in this work and experimental work [10] 4.6. Optimization of vacuum tube solar collector performance in Tehran city In order to improve the efficiency of the single-phase solar water heating system in Tehran city, performance of this system is optimized using Genetic Algorithm (GA) Toolbox in MATLAB software. Since objective function in GA must be minimum, reverse efficiency is considered as objective function in this paper. So the optimum value of the efficiency will became maximum. Diameter of inner tube, length of the tube, natural circulation velocity of the water and tilt angle of the collector are design variables, these parameters are noted with x 1, x 2, x 3 and x 4 respectively. These parameters and values of the lower and upper bounds are shown in Table. 3. Table. 3. Lower and upper bounds of the design variables Notation Design Variables Lower Bounds Upper Bounds Units x 1 Diameter of inner tube m x 2 Length of each vacuum tube m x 3 Circulation velocity of water Kg/s x 4 Tilt-Angle of collector C Journal of Science and Engineering / ISSN:

15 In equations, instead of phrases d, l, u and t we used x 1, x 2, x 3 and x 4 respectively. Considering the thermal conductivity of the genus tube is 50 W/m K, the Eq. 1. can be written bellowing: Also mass flow rate of the water from Eq. 7. can be modified as Eq. 11. (10) { ( ) ( ) } { } (11) The dimensionless parameter and from Eq. 6. and Eq. 5. Are written as Eq. 12. and Eq. 13. respectively. (12) (13) { ( ) ( ) } { } Considering that this type of the single-phase water-in-glass SDHWS is extremely low pressure, for this system is first constraint that it s values must lower than 0.03 for low-pressure vacuum tubes solar collector systems. Since the water flow between tubes and horizontal tank is laminar flow, the dimensionless parameter in this system is second constraint and those values must be lower than Two constraints of this optimization can be written following Eq. 14. and Eq. 15. (14) (15) Then objective function equation is given below, considering design variables and it s lower and upper bounds values, constraints and other parameters which are noted in equations. η (16) Genetic algorithm chooses the best values x 1, x 2, x 3 and x 4 in order to achieve the maximum efficiency of the single-phase ETCs. Also the generation number which in the objective function is optimized should be mentioned. Whilst the average distance between individuals that produced in each generation become close to the previous generation, objective function desires to reach the optimum value. In fourth generation, the average distance between individuals is gets close to zero number, so the objective function is minimized and it s value becomes Fig. 10(a). So the efficiency value of the optimum is The convergence curve of the Journal of Science and Engineering / ISSN:

16 average distance between individuals is shown in Fig. 10(b). Also optimum values of the design variables are 0.031, 1.682, and for x 1, x 2, x 3 and x 4 respectively Fig. 10(c). (a) (b) (c) Fig. 10. (a). Optimal value of the objective function (b). Optimal values of the design variables (c) Curve of the average distance between individuals Journal of Science and Engineering / ISSN:

17 Since heat loss values of the single-phase water-in-glass SDHWS should not be greater than due to the falling efficiency, the values of the heat losses in Dec. Jan. and Feb. months are not acceptable. The yearly average efficiency in other nine months has been found which is mentioned in Table. 2. The improvement percent can be calculated using Eq. 17. The values of the η η η η (17), η and are shown in Table. 3. Table. 4. Values of the average months and optimal efficiencies and improvement Parameter Value Unit η η % 5 CONCLUSION Performance of the single-phase vacuum tube SDHWS in different climatic conditions is investigated using TRNSYS16 software. The most important simulated components in this paper are: Typey71 for ETC and Type 60k for horizontal tank with five nodes within. The daily curves for the G coll, G tilt and useful energy gains in hot and cold days of the year in three cities are shown. Also the yearly performances trends of the useful energy gains, efficiencies and solar fractions are validated and these values are similar together. The inlet, mean, ambient and outlet water temperatures of the collector, instantaneous efficiencies and daily heat losses in six selected days in spring and summer seasons are measured. The values of the daily and monthly heat losses in single-phase vacuum tube SDHWS must be lower than 0.025, which makes the daily and monthly efficiencies in these systems become at least 0.5. Optimization of the thermal efficiency of this collector with objective function as reverse efficiency is carried out with Genetic Algorithm Toolbox in MATLAB. Design variables in this optimization including: inner tube, length of tube, velocity of natural circulation of the water between the tubes and tilt-angle of the collector that are optimized. Optimal efficiency is , and this value is compared to average yearly efficiency. Improvement percent of the efficiency in climatic condition of Tehran city became 12.4%. REFERENCES [1] Kalogirou A. Solar thermal collectors and applications, Progress in Energy and Combustion Science, 2004, 30: [2] Shukla R, Sumathy K, Erickson P, Gong J. Recent advances in the solar water heating systems: A review, Renewable and Sustainable Energy Reviews, 2013, 19: Journal of Science and Engineering / ISSN:

18 [3] Hayek M, Assaf J, Lteif W Experimental Investigation of the Performance of Evacuated- Tube Solar Collectors under Eastern Mediterranean Climatic Conditions, Energy Procedia, 2011, 6: [4] Zambolin E, Del Col D. An improved procedure for the experimental characterization of optical efficiency in evacuated tube solar collectors, Renewable Energy.2012, 43: [5] Caglar A, Yamali C. Performance analysis of a solar-assisted heat pump with an evacuated tubular collector for domestic heating, Energy and Buildings.2012, 54: [6] Hobbi A, Siddiqui K. Optimal design of a forced circulation solar water heating system for a residential unit in cold climate using TRNSYS, Solar Energy.2009, 83: [7] Zambolin E, Del Col D. Experimental analysis of thermal performance of flat plate and evacuated tube solar collectors in stationary standard and daily conditions, Solar Energy.2010, 84: [8] Sokhansefat T, Kasaeian A, Rahmani K, Mohasseb S. Comparing the Performance of Flat Plate Collector and Evacuated Tube Collector for Building and Industrial Usage in Hot and Cold Climate in Iran with TRNSYS Software, Ninth International Conference on Engineering Computational Technology, At Napoli, Italy,2014. [9] Mohammadkarim A.R, Kasaeian A.B, Kaabi Nejadian A. Performance Investigation of Solar Evacuated Tube Collector Using TRNSYS in Tehran, International Journal of Renewable Energy Research.2014, 4(2): [10] Budihardjo I, Morrison G.L. Performance of water-in-glass evacuated tube solar water heaters, Solar Energy.2009, 83: [11] Morrison G.L, Budihardjo I, Behnia M. Water-in-glass evacuated tube solar water heaters, Solar Energy, 2004, 76: [12] Budihardjo I, Morrison G, Behnia M. Natural circulation flow through water-in-glass evacuated tube solar collectors, Solar Energy, 2007, 81: [13] Morrison G.L, Budihardjo I, Behnia M. Measurement and simulation of flow rate in a water-in-glass evacuated tube solar water heater, Solar Energy, 2005, 78: [14] Jivan Shah L, Furbo S. Theoretical flow investigations of an all glass evacuated tublar collector, Solar Energy, 2007, 81: [15] Ozgener O, Hepbasli A. A review on the energy and exergy analysis of solar assisted heat pump systems, Renewable and Sustainable Energy Reviews, 2007, 11: Journal of Science and Engineering / ISSN:

19 [16] Mishra R.K, Garg V, Tiwari G.N. Thermal modeling and development of characteristic equations of evacuated tubular collector (ETC), Solar Energy.2015, 116: [17] Waheed Badar A, Buchholz R, Ziegler F. Experimental and theoretical evaluation of the overall heat loss coefficient of vacuum tubes of a solar collector, Solar Energy, 2011, 85: [18] Ma L, Lu Z, Zhang J, Liang R. Thermal performance analysis of the glass evacuated tube solar collector with U-tube, Building and Environment, 2010, 45: [19] Smyth M, Eames P.C, Norton B. Integrated collector storage solar water heaters, Renewable and Sustainable Energy Reviews, 2006, 10: [20] Tang R, Yang Y, Gao W. Comparative studies on thermal performance of water-in-glass evacuated tube solar water heaters with different collector tilt-angles, Solar Energy, 2011, 85: [21] Tang R, Gao W, Yu Y, Chen H. Optimal tilt-angles of all-glass evacuated tube solar collectors, Energy, 2009, 34: [22] Bracamonte J, Parada J, Dimas J and Baritto M. Effect of the collector tilt angle on thermal efficiency and stratification of passive water in glass evacuated tube solar water heater, Applied Energy.2015, 155: Journal of Science and Engineering / ISSN:

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