212 - ANTALYA Study of Heat Transfer by Low-Velocity Forced Convectionn of Parabolic Dish Solar Cylindrical Receiver Shiva Gorjian 1, Teymour Tavakkoli Hashjin 1, Barat Ghobadian 1, Ahmad Banakar 1 1 Department of Agricultural Machinery Mechanics, Tarbiat Modares University (T.M.U), Tehran, Iran Abstractt Solar energy can be used for substitution of the depleting fossil fuels in thermal applications and electricity generation throughh thermal route. For medium and high temperature applications, solar concentrators are required. Convectionn losses are an important determining factor in the performance of solar thermal power systems. Optimum sizing and selection of concentratorr and receiver for any thermal application calls for estimation of heat transfer at the required operating temperatures. In present study, an attempt has been made to estimate the wind induced convective heat transfer coefficients from the bottom side of a circular cylinder, while the remaining parts of this surface is kept insulated. Heat transfer rates are presented in terms of averagee Nusselt numbers. The effect of the receiver operating temperature and wind velocity magnitude on heat transfer coefficients has been studied. In addition, the effect of positive wind incidence angle (angle between heated surface and incoming wind flow) between and 9 on heat transfer rate has been investigated. The solutions covered the ranges of the Reynolds and Rayleigh numbers from 2.41 1 4 to 6.8 1 4 and 3.46 1 7 to.4 1 7 respectively. The calculations have been carried out based on empirical models. The results indicated that the heat transfer coefficient is strongly affected by Reynolds and Reyleilgh numbers. Keywords: Solar energy, Parabolic dish, Convective heat transfer, Reynolds number 1. Introduction In solar thermal systems, heat loss can significantly reduce the efficiency and consequently the cost effectiveness of the system. It is therefore vital to fully understandd the nature of these heat loss mechanisms. The solar parabolic dish collector is known as most efficient system among solar thermal devices. Generally a solar dish includes a paraboloid reflecting surface, a receiver, a tracking system, thermal energy utilization system and the working fluid which transfer the heat [1]. The entire radiation incident on the reflecting surface is reflected towards the focus. The reflecting surface may be mirrors or any specially treated metal surfaces. The reflected radiation is concentrated in a focal zone on a smaller area, thus ncreasing the energy flux in the receiving target. Solar receivers play an importantt role in light-heat conversion for the solar thermal power systems [2]. The thermal efficiency of the solar receiver is affected by various heat loss mechanisms. The working fluid in the receiver placed at the focus of the reflecting surface receives concentrated solar energy. The tracking system is designed to track the sun such that the aperture of the reflecting surface is orthogonal to the incident radiation. The concentration ratio (ratio of the aperture area to the receiver area) of solar dish determines the intensity of solar radiation received by the receiver. The increased heat flux makes solar energy suitable for utilization in medium and high temperature applications [3]. The solar parabolic dish collector maintains its optical axis always pointing directly towards the sun. The geometry of the concentrator allows reflecting the incident solar rays onto the receiver, which is located at the focal plane of the collector [2]. During its rotation, the receiverr experiences change in the complete behavior of the fluid and the heat transfer characteristics. The orientation of the receiver might alter the thermal performance of solar parabolic dish system in both natural and forced convectionn [4]. The estimation of heat losses from the receiver is an importantt input to the performance evaluation of the solar dish collector. The convection and radiation heat losses from the receiver substantially reduce the performance of the system. A moderate temperature rise leads to a considerablee heat loss, which may directly influence the performance of dish system [4]. A literature survey shows that, study on wind effect on the heat loss of solar cavity receivers is still in the early stage and no research has been done on the cylindrical receiver heat loss mechanism. Two wind directions, i.e., head-on and side-on wind have gained extensivee attention for cavity receivers [], [6] while a real wind in nature that is always parallel to the ground with a variety of directions has not been studied. Many studies have been conducted on the heat loss mechanisms of cavity receivers E-mail of Corresponding Author: m88_gorjian@rocketmail.com
which are often used for power production [7], [8]. The empirical correlation for predicting the forced convectionn heat loss of solar external (cylindrical) receivers has not been reported. In the present, quantitative analysis of wind effect on convection heat loss of medium-temperature solar cylindrical receiver particularly for heating water or purification of seawater has been carried out to further understand the convection heat losss mechanism. 2. Description of the parabolic dish collector Figure 1 shows the arrangement of the parabolic dish collector. The device comprises a parabolic dish concentratorr (PDC) with 1.8m aperture diameter and a cylindrical receiver unit on its focal point. The focal absorber receives the concentrated solar radiation and transforms it to thermal energy to be used in a subsequent process. The essential feature of a receiver is to absorb the maximumm amount of reflected solar energy and transfer it as heat, with minimumm losses, to the working fluid. The dish surface was covered with rectangular silver-backed glass segmentss with a thickness of 1 mm. A D=2 mm diameter and L=3 mm length circular cylinder made of stainless steel is placed at the focal point. It has the receiving surface of 3.2 m 2 with a geometric concentration of 1. The receiver is completely insulated except the part lit by the solar rays reflected by the parabolic surface. The bottom side of the receiver is covered with black chrome to increasee the absorption of solar radiation. This subsystem is tracked to hour angle variation by using stepper motor and declination angle variation by twisting the tracking setup to absorbb maximumm solar radiation on its focal region. The sun tracking mechanismm for this collector has two axes with a manual system. Insulation cover Cylindricall receiver Parabolic dish L D Tracking axis Black chrome coating Figure 1. Three-dimensional sketch of the solar cylindrical receiver of a parabolic dish. 3. The heat loss mechanism of the receiver In order to assess and subsequently improve the thermal performance of external receivers employed in parabolic dish solar concentrators, its associated heat lossess need to be determined with sufficient accuracy. The total heat losss rate of the receiver,, includes three contributions; conductive,, convective, and radiative. The total heat loss rate can be expressed as [3]: (1) Figure 2 shows the schematic diagram of various modes of heat loss mentioned above. In general, the conductionn and radiation modes of heat lossess can be determined relatively easily by the standardd methods described in the literature. On the other hand, the determination of convection loss is more complex [9]. In this study, the outer walls of the receiver are supposed to be adiabatic and the conductive heat loss from the outer surface of the receiver = Figure 2. Schematic diagram of different modes of heat transfer of the receiver. 2
Convection is the most complicated phenomenonn and yet also a major contributor of the total energy loss. Hence, its characteristic has been extensively investigated so as to find out effectivee measurements for the improvement of system efficiency [9]. The receiverr normally works in downward-facing or sideward-facing position in solar dish systems [4]. The range of tilt angle, which is defined as the angle between the normal direction of the bottom side of the receiver and the horizontal plane, in the current investigation is to 9. The wind is assumed to flow horizontally which is parallel to the ground. To distinguish the wind direction, the wind incidencee angle,, is defined as the angle between wind blowing direction and the axis normal to the bottom plane of the receiver [1]. The wind incidence angle varies azimuthally from to 9. The angle of does to the case of wind perpendicularly incident on the bottom side, is often referred to head-on wind. The angle of 9 corresponds to the case of wind blowing parallel to the aperture plane, is often called side-on wind [4]. The receiver will be exposed to the wind flow with different wind incidence angles (Fig. 3). θ θ Figure 3. Cylindrical receiver in different positions and definition of wind direction. For simulating different wind environments, a total of 4 wind directions (, 3, 6 and 9 ) and wind speeds in the range between (3. 7.2 /) for year-round in Tehran, capital city of Iran, are considered. The receiver is assumed to be used in medium-temperature systems (1 2, and the ambient temperature is equal to the air temperature of the location in different month of a year. The simplest physical model of such a flow is the two-dimensional forced convection flow along a flat plate and extensive studies have been conducted on this type of flow, especially in different angles of attack. A two-dimensional steady forced convection and heat transferr flow of a viscous, incompressible fluid over an isothermal finite plate which is the bottom side of the receiver has been considered. The main relevant dimensionless number is the number [11]: (2) where, is the velocity of the fluid flow, is the characteristic length of the flow situation for circular plates and is the kinematic viscosity of the flow. The ratio of is called the number (). The number () is the product of and number. Correlations for prediction of heat transfer coefficients are expressed in terms of number (), a dimensionless heat transfer coefficient, defined by [11]: (3) where is the convective heat transfer coefficient and is the conductivity of the fluid. Natural convectionn situationss show a strong dependencee on the number () which is a dimensionless ratio of buoyancy and diffusion effects, defined by [12]:. (4) where is the gravitational constant, is the temperature of the surface and is the temperature of the fluid.,, and are the thermal expansion coefficient, kinematic viscosity, and thermal diffusivity of the fluid respectively. In forced convection, the flow inducedd by density gradient is negligible compared with the fluid motion imposed by external devices, but in case of low flow velocity, the freee convection factor also plays an important role. A dimensionless parameter, number, predicts the relative importance of free convectionn with forced convection. For free convection, 1, for mixed convection (free-forced convection); 1 and for forced convection; 1. Calculating of this parameter is essential for the present study because the heat transferr caused by low-velocity wind flow [ 13]. The average convective heat transfer coefficient,, can also be expressed as follow [12]: () 3
3.1 Convective heat loss caused by side-on wind flow For the case of side-on wind, the bottom side of the receiver has been assumed as a flat plate which is exposed to the parallel flow. In this purpose, the equations have been used that were reported before by the other researchers. Thesee equations have been derived using analytical methods. The value of average number for laminar flow on a flat plate is equal to []:.664. / 1 (6)() And for turbulent flow is calculated as follow:.37. / 1 1 (7) 1.2.. where is the wind incidence angle, as mentioned before. (8) 3.2 Convective heat loss under head-on and oblique wind flow In the case of the head-on flow, Hess [1], has proposed an equation which is a function of number and the incidencee angle of the fluid. In this equation, it is assumed thatt the fluid flow is laminar and irrotational and the fluid is incompressible and inviscid. This equation can be applied to heat convection. The velocity of the flow on the side- facing the oncoming is given as follows [16]: 4. Results and discussion The two important parameters, and numbers for each month of a year and for three surface temperatures of the receiver were calculated under weather conditions of Tehran. The values of air temperature and wind speed for each month was obtained from NASA website for Tehran (Table1). The results showed that the wind flow is laminar and the convective heat transfer is forced. The solutions covered the ranges of the Reynolds and Rayleigh numbers from 2.41 1 4 to 6.8 1 4 and 3.46 1 7 to.4 1 7 respectively. All thermo-physical properties of air weree calculated in film temperature. The average temperature of the heated surface and the flowing fluid is the film temperature. For investigating the effect of the wind incidence angle on the convective heat transfer coefficient () and consequently on the convective heat loss rate ( ) of the receiver, the values of were plotted versus each month, for different receiver inclination angle while the receiver wall temperature is equal to 2 C (figs. 4 to7 ). Month Jan Table 1. The values of and of Tehran. Month 3 3. July 3.4..3 Aug 29. 2 4.9 1.3 6.4 Sep 2. 3 4.7 16.4 7.1 Oct 18. 4.7 22.1 7.2 Nov 11. 6 3.9 27. 6.7 Dec.6 3. ( ^2.) 4 4 3 3 2 2 1 1 Wind 2 4 6 8 Month of a year ( ^2.) 4 3 3 2 2 1 1 1 12 Wind, 3 2 4 6 8 1 12 Month of a year Figure 4. Values of under head-on wind flow. Figure. Values under 3 wind incidence angle. 4
3 2 ( ^2.) ( ) 2 2 1 1 Wind, 6 ( ^2.) 2 1 1 Wind 2 4 6 8 Month of a year 1 12 2 4 6 8 1 12 Month of a year Figure 6. Values of under 6 wind incidence angle. Figure 7. Values of under head-on wind flow. The equation (6) was used when the receiver was downward-facing and also was exposed to the side-on wind flow. In addition, the equation (7) was used when the receiver was exposed to the oblique and head-on wind flow in downward or sideward-facing position. In above diagrams, it is assumed that the wind direction is horizontal and the receiver is in different positions because of the tracking system. In this case, the wind direction would be oblique as the receiver is inclined. As the diagrams show, the head-on wind was found to cause higher convection heat loss than the side-on wind, which seems agreee to those reported by Xiao [4], for cavity receivers. Additionally, the free-stream wind with attacks the bottom side directly, causing larger magnitude air flow toward the plane, thus more convection heat loss may be expected. The maximum values were obtained for the angle of 3. Although the values of is higher for head-on wind in comparison with side-on wind, but the oblique wind causes more heat loss of the receiver. The inclined wind flow has two components on the bottom side of the receiver. One of them is normal to the bottom side and the other is parallel with this wall. For wind incidence angle between 9, there willl be more stream flow than one component such will exist for head-on and side-on wind flow. Consequently the values of should be higher than of the head and side wind flow. Therefore, the heat losss rate of the receiver has the maximumm of its value when the wind incidence angle has the amount of more than and less than 9. What is clear is that the values of are strongly affected by and numbers. In all graphs, higher values were obtained for the month with higher air temperature and wind speed values. The results related to the parallel flow, showed that increasing the wall temperature of the receiver will increase the value of, but this ncreasing has no importantt effect on the amount of convective heat loss (Table 2). In other words, there was no significant difference among the values of in the case of different receiver wall temperatures. The same results were obtained for the other wind directions. Table 2.. The values and numbers for side-on wind flow. 1 Month 1 Month.. Jan 16.19 1.88 July 128.88 19.92 126.7 2.34 8.84 8.89 2.72 18.99 21.49 22.63 22.79 21.99 Aug Sep Oct Nov Dec 121.81 119.84 12.8 11.94 1.86 18.81 18.42 18.41 16.77 1.89 2 Month 2 Month.. Jan 1.21 1.9 July 121.93 19.9 119.47 134.42.64.7 134.99 19.1 21.1 22.6 22.82 22.1 Aug Sep Oct Nov Dec 11.23 113.33 1.16.78 99.92 18.83 18.44 18.43 16.79 1.91 2 Month 2 Month.. Jan 94.99 1.92 July 11.82 19.96 113.26 127.49 133.4 133.62 128.2 19.3 21.3 22.67 22.84 22.3 Aug Sep Oct Nov Dec 19.4 17.61 18.34 99.39 94.74 18.84 18.4 18.4 16.81 1.92
4. Conclusion Whether from reality or a design standpoint, wind is one of the major concerns in the performance evaluation of a solar dish receiver. Therefore, based on the air property dependency on temperature, a study has been undertaken to investigate the role of wind on forced convection loss from a medium-temperature solar cylindrical receiver particularly for domestic applications. In most cases, the magnitude of heat loss is higher for the side-on wind than that of the head-on wind; the convection heat loss reaches the maximum value when the wind direction is perpendicular to the receiver bottom side. Results of the present study show that changing the wind angle or velocity can obviously affect the convective heat loss coefficient. The convection heat loss reaches the maximum value when the incidence angle of the wind is between to 9. Namely the variation of forced convection heat loss with wind speed and direction as well as the receiver inclination have been given in the peresent study using equations drived analytically. However, some unresolved issues still exist. Comparing the resultes of this reasearch with experimental data is strongly recomended. Refrences [1] V. R. Sardeshpande, A. G. Chandak, and I. R. Pillai, Procedure for thermal performance evaluation of steam generating point-focus solar concentrators, Solar Energy, vol. 8, no. 7, pp. 139 1398, Jul. 211. [2] S.-Y. Wu, L. Xiao, Y. Cao, and Y.-R. Li, Convection heat loss from cavity receiver in parabolic dish solar thermal power system: A review, Solar Energy, vol. 84, no. 8, pp. 1342 13, Aug. 21. [3] N. Bellel, Study of two types of cylindrical absorber of a spherical concentrator, Energy Procedia, vol. 6, pp. 217 227, Jan. 211. [4] L. Xiao, S.-Y. Wu, and Y.-R. Li, Numerical study on combined free-forced convection heat loss of solar cavity receiver under wind environments, International Journal of Thermal Sciences, vol. 6, pp. 182 194, Oct. 212. [] N. Sendhil Kumar and K. S. Reddy, Numerical investigation of natural convection heat loss in modified cavity receiver for fuzzy focal solar dish concentrator, Solar Energy, vol. 81, no. 7, pp. 846 8, Jul. 27. [6] S. Paitoonsurikarn and K. Lovegrove, Numerical Investigation of Natural Convection Loss in Cavity-Type Solar Receivers, 1984. [7] M. Prakash, S. B. Kedare, and J. K. Nayak, Investigations on heat losses from a solar cavity receiver, Solar Energy, vol. 83, no. 2, pp. 17 17,. 29. [8] K. S. Reddy and N. Sendhil Kumar, An improved model for natural convection heat loss from modified cavity receiver of solar dish concentrator, Solar Energy, vol. 83, no. 1, pp. 1884 1892, Oct. 29. [9] S. Paitoonsurikarn and K. Lovegrove, On the Study of Convection Loss from Open Cavity Receivers in Solar Paraboloidal Dish Applications, vol., pp. 161, 23. [1] C. Mahboub, N. Moummi, a. Moummi, and S. Youcef-Ali, Effect of the angle of attack on the wind convection coefficient, Solar Energy, vol. 8, no., pp. 776 78, 211. [11] F. P. Incropera, Fundamentals of Heat and Mass Transfer. John Wiley & Sons Canada, Limited, 1993, p. 992. [12] M. Favre-Marinet and S. Tardu, Convective Heat Transfer (Google ebook). John Wiley & Sons, 21, p. 448. [13] R. R., Heat And Mass Transfer, 2/E. Pearson Education India, 21, p. 472. [] C. P. Kothandaraman, Fundamentals Of Heat And Mass Transfer. New Age International, 26, p. 74. [1] J. L. Hess, Analytic solutions for potential flow over a class of semi-infinite two-dimensional bodies having circular-arc noses, Journal of Fluid Mechanics, vol. 6, no. 2, pp. 22 239, Sep. 1973. [16] A. A. Kendoush, Theoretical analysis of heat and mass transfer to fluids flowing across a flat plate, International Journal of Thermal Sciences, vol. 48, no. 1, pp. 188 194, Jan. 29. 6