IJECA-ISSN: 2543-3717. December 2021 Page 01 International Journal of Energetica (IJECA) https://www.ijeca.info ISSN: 2543-3717 Volume 6. Issue 2. 2021 Page 07-12 Simulation of different modes of heat transfer on a parabolic trough solar collector Loubna Benhabib 1* , Yacine Marif 2 , Zakia Hadjou Belaid 3 , Abdelmadjid Kaddour 4 , Boumediène Benyoucef 1 , Michel Aillerie 5 1 URMER Laboratory, Abou Bekr Belkaid University, Tlemcen, ALGERIA 2 LENREZA, Kasdi Merbah University , Ouargla, ALGERIA 3 Macromolecules Laboratory, Abou Bekr Belkaid University, Tlemcen, ALGERIA 4Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de Développement des Energies Renouvelables, CDER, 47133, Ghardaïa, ALGERIA 5 Université de Lorraine, CentraleSupélec, LMOPS, F-57000 Metz, FRANCE Email*: loubnabenhabibhadjou@gmail.com Abstract- The development of solar concentrator technology has just reached a very significant level. Using reflectors to concentrate the sun's rays on the absorber dramatically reduces the size of the absorber, reducing heat loss and increasing its efficiency at high temperatures. Another advantage of this system is that the reflectors are significantly less expensive, per unit area, than the flat collectors. To determine the performances of a cylindrical-parabolic concentrator, mathematical modeling of the heat balance on the absorber, the coolant, and the glass envelope was established using Matlab. The system of equations obtained is solved by the finite difference method. The results for a typical day are the variation in the temperature of the heat transfer fluid, the absorber tube, and the glass envelope. Thus, we examine the effect of the wind speed, flow rate on the temperature distribution of the coolant at the outlet. However, for a mass flow rate of the fluid of 0.1 kg / s, the outlet temperature of the fluid is 85 ° C with a thermal efficiency of 73%. Excluding the energy absorbed by the absorber tube is 75% of the solar intensity received on the reflector. Keywords: Parabolic trough collector, Solar thermal energy, Simulation, Heat transfer, Solar concentrator. Received: 26/04/2021 – Accepted:26/06/2021 I. Introduction Renewable energies have experienced the first phase of development during the oil shocks of 1973 and 1978. Then a period of decline after the counter-shock of 1986, before regaining a new lease of life in 1998 following the signing of the Kyoto protocol, which predicts, in particular, a 5.2% drop in greenhouse gas emissions from wealthy countries over the period 2002-2012 compared to 1990 [1]. Solar energy can be used to generate power using concentrated solar systems. It is based on spherical, parabolic or Fresnel lens-based mirror concentrators [2], which have the principle of focusing the incident solar radiation in a point or a line. The conversion efficiency is high, and Temperature can easily surpass 500 °C. These technologies offer a natural alternative to the consumption of fossil resources with a low environmental impact and a high potential for cost reduction, as well as the possibility of hybridization of these facilities, by utilizing direct solar radiation, which is considered the primary resource and is very significant on a planetary scale [3]. When it comes to the specific challenges of electricity generation, transmission, and distribution, alternative sources, as opposed to conventional ones, can be a feasible answer. In areas where electrical energy delivery is unreliable, including alternative energy generation sources, such as solar, can be a viable choice [4]. http://www.ijeca.info/ http://www.ijeca.info/ mailto:loubnabenhabibhadjou@gmail.com Loubna Benhabib et al IJECA-ISSN: 2543-3717. December 2021 0 Several studies have been conducted to anticipate, analyse, and estimate the performance of parabolic trough collectors under a variety of weather conditions and configurations. A comprehensive review is presented, that examines various models and simulation approaches of PTCs. This study constitutes a complementary application contribution to parabolic trough concentrators [5]. According to the literature a detailed heat transfer solar receiver model has been performed [6]. The proposed models are based on the detailed analysis of one-dimensional or two-dimensional heat transfer processes assumed by trough collectors. Other researchers [7] performed precise two-dimensional digital heat transfer of PTC using synthetic oil Therminol VP1 as heat transfer fluid (HTF). They came up with two software options based on the properties of the solar PTC they were using. The first was written in Matlab and was used to calculate the annual solar energy collected on the absorber pipe using several tracking modes that were available in the area. Because (EES) automatically detects all unknowns and groups of equations for the most efficient solutions, the second program code is written using a simultaneous equation solving software (EES) to evaluate the performance of the heat collector element (HCE) [8]. Figure 1. Different heat transfer modes II.1. Incident radiation Our study will focus on the equations of direct incident solar irradiance, as it is the resource of concentrating systems [9]. Modeling is done on a horizontal plane using two models. The data considered for the simulation in the Mediterranean countries provide from the site of Tlemcen city having the following coordinates Latitude 34.53 °, Altitude 806m, Longitude 1.33 ° [10] In the current approach, a simulation program will be developed under Matlab to deal with the different modes of heat transfer in the concentrator absorber by determining the evolution of the system's temperature. Different parameters are studied to explain their importance in the temperature variation. The results taken are for a sunny day of June 21 in the region of Tlemcen, north-western Algeria, and water as the heat transfer fluid. II. Material and methods The absorber was the essential element in the Direct solar radiation is calculated according to the Capderou model, and the expression gives it: [11] 𝐼𝑑 = 𝐼0. s0. 𝑠i𝑛ℎ𝑠. exp(−𝑇𝐿. 𝑚𝑎. 𝛿𝑅) (1) Where ε0 represents the earth-sun distance correction, it is expressed as follows [12]: s = 1 + 0.034 * cos( 360 * (𝑁 − 2)) (2) 365 With hs is the sun elevation angle, N is the number of days, and 𝐼0 is the constant solar (1367W/m²) The atmospheric mass 𝑚𝑎 , as well as the Rayleigh thickness δR, is given by [11, 12]: 𝑚𝑎 = [sin(ℎ𝑠 ) + 9.4 * 10−4(sin(ℎ𝑠) + 0.0678)−1.253]−(13) 𝛿−1 =6.6296 + (1.7513×𝑚𝑎 ) − (0.1202×𝑚2 ) + 𝑅 𝑎 composition of the cylindrical-parabolic concentrator, (0.0065×𝑚3 ) − (0.00013×𝑚4 ) (4) 𝑎 𝑎 whose role is to absorb the incident solar radiation for its conversion into heat before transmitted to the heat transfer fluid. We report in Figure1 the diagram of the process explaining the heat flow exchanged between components. However, the heat exchange coefficients are considered as known while considering the following assumptions: • The transfer by conduction between the absorber and the glass is considered negligible. • The flow of the incompressible fluid is in a one- dimensional direction. Or the Linke factor 𝑇𝐿is given by the expression [13]: 𝑇𝐿 = 𝑇0 + 𝑇1 + 𝑇2 (5) Where: 𝑇0 = (2.4 − 0.9 * 𝑠i𝑛𝜑) + 0.1 * (2 + 𝑠i𝑛𝜑) − (0.2 * 𝑧) − (1.22 + 0.14 * 𝐴ℎ𝑒) * (1 − 𝑠i𝑛(ℎ𝑠)) (6) 𝑇1 = 0.89𝑧 (7) 𝑇2 = [0.9 + (0.4 * 𝐴ℎ𝑒)] * 0.63𝑧 (8) With z is altitude, φ is latitude and 𝐴ℎ𝑒 winter-summer alternation. However, the expression of the energy absorbed by the absorber is given by the expression: [14] Loubna Benhabib et al IJECA-ISSN: 2543-3717. December 2021 𝑎𝑚 A .ρ .Cp . = 𝑞 + 𝑞 − 𝑞 (12) ab ab ab 𝑎𝑏𝑠 i𝑛𝑡 𝑢 𝑞𝑎𝑏𝑠 = 𝐴0. 𝐼𝑑. 𝛼0. 𝜌0. 𝛾. 𝐾 /𝐴0 = 𝐿 * W (9) The transmission-absorption coefficient 𝛼0is given according to the following expression [15]: II.3. The heat transfer coefficients  Heat transfer between glass envelope and atmosphere 𝘢0 = 𝖺ab.𝜏g 1−(1−𝖺ab).(1−𝜏g) (10) Convection and radiation are two transfer techniques for As for the modified angle of incidence is given by [16]: K=1 − 3.84. 10−5. (𝜃) − 143. 10−6. (𝜃)² (11) II.2. Heat balance The incident solar energy absorbed is not entirely transmitted to the heat transfer fluid. Some are dissipated in the form of thermal losses between the absorber and the glass envelope. Figure 2 shows several heat transfer analyses between collector components and between the collector receiver and its surrounding environment. transferring heat from the glass enclosure to the atmosphere; convection requires wind. The coefficient of radiation is given by [17]: ℎ𝑟(𝑒𝑥𝑡) = sg. 𝜎. ((𝑇𝑠𝑘𝑦 + 273.15)² + (𝑇g + 273.15)²) * (𝑇𝑠𝑘𝑦 + 𝑇g + 546.3) (16) With the expression of the sky temperature [18]: 𝑇𝑠𝑘𝑦 = 0.0552𝑇1.5 (17) Then the coefficient of convection is given by [19]: 1⁄6 2 𝖥 𝖥 1 1 ℎ𝑐(𝑒𝑥𝑡) = I 0.6 + 3.87 * I 𝑅𝑎𝑎 16 I I * 𝑎 I I 0.559 9⁄16 ⁄9I I 𝐷𝑔𝑒 [ [ (1+( 𝑃r𝑎 ) ) ] ] (18) • Heat transfer between the absorber and the glass envelope Convection and radiation are the two ways of heat transmission. The annulus pressure affects the convection mechanism. Temperature variations between the outer absorber surface and the inner glass surface cause radiation. With the expression of the sky temperature [20]: ℎ𝑟(i𝑛) = si𝑛𝑡. 𝜎. ((𝑇𝑎𝑏 + 273.15)² + (𝑇g + 273.15)²) * (𝑇𝑎𝑏 + 𝑇g + 546.3) (19) Figure 2. Heat balance of the absorber With si𝑛𝑡 = 1 (20) ( 1 1−𝗌𝑔 𝐷𝑎𝑏𝑒 𝗌𝑎𝑏 + 𝗌𝑔 )*( 𝐷𝑔i ) Then the coefficient of convection is given by :  For the glass envelope: ℎ = 2 𝑒ƒƒ (21) 𝑑𝑇 g g g 𝑑𝑡 𝑎𝑏𝑠.g i𝑛𝑡 𝑒𝑥𝑡  For the absorber pipe : 𝑐(i𝑛) With: 𝐷𝑎𝑏𝑒 .𝑙𝑛( 𝐷𝑔i ) 𝐷𝑎𝑏𝑒 𝑃𝑟𝑎 1⁄4 1⁄ A .ρ .Cp . 𝑑𝑇 = 𝑞 − 𝑞 − 𝑞 (13) 𝑑𝑡 𝜆𝑒ƒƒ = 0.386 * 𝜆𝑎 * ( ) 𝑃𝑟𝑎+0. 61 * (𝑅𝑎𝑐) 4 (22) 𝐷𝑔i 4 𝑅𝑎 = (𝑙𝑛( 𝐷𝑎𝑏𝑒 )) * 𝑅𝑎  For the fluid: 𝑐 3 −3/5 −3/5 5 𝑒ƒƒ (23) A .ρ .Cp .𝑑𝑇 + 𝑚 ....... 𝑑𝑇 = 𝑞 (14) 𝐿𝑒ƒƒ*(𝐷𝑎𝑏𝑒 +𝐷𝑔i ) Whose: f f f 𝑑𝑡 𝑑𝑥 𝑢 𝐿𝑒ƒƒ = 𝐷𝑔i−𝐷𝑎𝑏𝑒 2 (24) 𝑞𝑎𝑏𝑠.g = 𝐴0. 𝐼𝑑. 𝛼g. 𝜌0. 𝛾. 𝐾 (15) The boundary condition: 𝑇g,0 = 𝑇𝑎𝑚; 𝑇𝑎𝑏,0 = 𝑇𝑎,𝑒; 𝑇ƒ,0 = 𝑇𝑒 (Tam is the ambient temperature). 𝑅𝑎𝑒ƒƒ = 𝐺𝑟𝑎 * 𝑃𝑟𝑎 (25) • Heat transfer between the fluid and the absorber The flow type affects convective heat transfer from the inside surface of the absorber pipe to the fluid. We consider the case of turbulent flow [21] and is given by: Loubna Benhabib et al IJECA-ISSN: 2543-3717. December 2021 ℎ𝑢 = ƒ*𝑁𝑢ƒ 𝐷𝑎𝑏i 5 𝐷𝑎𝑏i 2⁄3 (26) Moreover, the solar power absorbed by the absorber tube reached 680W / m², Figure 4, which explains the existence of heat losses between the glass envelope and the absorber tube. These losses cause a decrease in the With: 𝑁𝑢ƒ = ( 8 ).(𝑅𝑒ƒ−1000).(1+( 𝐿 ) 2 ).𝑃𝑟ƒ . ( 𝑃𝑟ƒ ) 𝑃𝑟𝑎𝑏 0.11 rate of energy absorbed, which is of the order of 75%. 1+12.7.√ ƒ .(𝑃𝑟 ⁄3−1) 8 ƒ Knowing that: 5 = (1.84. log(𝑅𝑒 ) − 1.64) −2 for 𝐷 < 𝐿 and; (27) 1000 800 ƒ 𝑎𝑏i 5 = (1.8. log(𝑅𝑒 ) − 1.5) −2 for 𝐷 > 𝐿, ƒ 𝑎𝑏i 600 The physical proprieties of fluid (water) are considering variants. III. Solution procedure, Results and discussions 400 200 0 Matlab did the programming of these equations. We used the finite difference method to solve these equations. The process consists of giving a value of the variable and recalculating this variable with the equation, and finally, we compare the two deals. Depending on the desired precision, if the difference between the two calculated and proposed values is less than the fixed accuracy, this value is taken. Otherwise, the second value is taken, and the calculations are repeated until the difference between these two values becomes inferior to precision. The characteristics of the solar PTC are mentioned in Table.1 Table 1. Characteristics of the simulated PTC 700 600 500 400 300 200 100 0 4 6 8 10 12 14 16 18 20 22 Tlo (h) Figure 3. Variation of the solar intensity 4 6 8 10 12 14 16 18 20 22 Tlo (h) Figure 4. Variation of the absorbed energy Moreover, Figure 5 shows the variation in the outlet temperatures of the fluid, absorber and glass envelope. It is noted that the fluid outlet temperature is 55 ° C for a mass flow rate of 0.2Kg / s. On the other hand, according to Figure 6, it is deduced that the outlet temperature of the fluid varies as a function of the mass flow rate or the temperature increases by decreasing the latter. Following the use of the Capderou model for the calculation of the solar intensity and based on a solar tracking system for our solar system, we notice that the solar intensity at the level of the Tlemcen region and for a day sunny, reaches 900W / m²as shown in Figure 3. 21 Juin P a b s ( W h /m ²) S o la r i n te n s it y ( W /m ²) Absorber length (L) 7.8m Collector width (W) 5m Focal length (f) 1.84m The absorber external diameter (Dabe) 0.07m The absorber internal diameter of (Dabi) 0.066m The glass external diameter (Dge) 0.115m The glass internal diameter (Dgi) 0.109m Thermal conductivity of the absorber (λab) 54W/mK Thermal conductivity of the glass (λv) 1.2W/mK Absorption of the absorber (αab) 0.906 Glass transmissivity (τg) 0.95 Transmissivity-absorbance factor (α0) Emissivity of glass (𝗌𝑔) Reflection of reflector (𝜌0) Interception factor (𝛾) 0.864 0.86 0.93 0.92 Loubna Benhabib et al IJECA-ISSN: 2543-3717. December 2021 Tv Tab Tf Tf (°C) 90 In what follows Figure 7, shows the variation of the thermal efficiency as a function of the temperature of the 80 collector which is equal to 73%. This efficiency helps to 70 control the reliability of our system since it is the ratio 60 between the useful flux and the power absorbed through the absorber tube. We note that the thermal efficiency is 50 close to the experimental, whose value is 73.68% in the 40 air in the annular space and validated by SNL. This 30 difference only has to let us think of the existence of thermal losses. 20 10 8 10 12 14 16 18 20 22 Tlo (h) Figure 5. Variation of the outlet Temperature 90 80 70 60 50 40 30 20 10 8 10 12 14 16 18 20 22 Tlo(h) Figure 6. Variation of the outlet Fluid Temperature for different mass flow rate IV. Conclusion Our study relates to the study of the various existing heat transfers for a PTC sensor. For this, a mathematical simulation in Matlab language is carried out to solve the nonlinear equations. Our results are based on the study of outlet temperatures and influencing parameters. Among those proposed the mass flow rate of the fluid shows an important parameter introducing into the variation of the outlet temperature or we have seen that the water outlet temperature reaches a value of 85 ° C for a flow rate of 0.1 kg / s. however, the energy absorbed is 75% relative to the solar intensity received on the reflector. Concerning the thermal efficiency which explains the rate of the useful flux linked to the heat transfer fluid, it is 73% for our system under the conditions of the Tlemcen region for a sunny day. In contrast, the wind speed turned out to be negligible. In addition, the sun tracking system is essential and necessary for the operation of the PTC as it only uses direct solar radiation. 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 -0,1 25 30 35 40 45 50 55 60 outlet References [1] J. D. Balcomb, R. W. Jones, C. E. Kosiewicz, G. S. Lazarus, R. D. Mc Farland, W. O Wray, « PassiveSolar Design Handbook », Volume 3, American Solar Energy Society, 1982. [2] S. Mihoub, Effect of Design Parameters on The Performance of DSG Linear Fresnel Solar Power Plant, Int. J. Energy Clean Environ, Vol 22, No 2, 2021, pp. 65- 81. [3] K. Ogilvie, ‘L’Abc des Technologies de l’Energie Renouvelable’, Pollution Probe, Canada, September 2003 [4] S. Quezada-Garcia, H. Sanchez-Mora, A.M. Polo- R.I Labarrios,. Cazares-Ramirez, Modeling and simulation to determine the thermal efficiency of a parabolic solar trough collector system, Case Studies in Thermal Figure 7. 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Journal of Heat Transfer, Vol 101, 1979, pp. 108-113. [21] V. Gnielinski, On heat transfer in tubes. Int J Heat Mass Transf, Vol 63, 2013, pp. 134–40. . http://www.infoclimat.fr/ I. Introduction II. Material and methods  For the glass envelope:  For the absorber pipe :  For the fluid: III. Solution procedure, Results and discussions IV. Conclusion References