### SUMMARY

- Top of page
- SUMMARY
- INTRODUCTION
- ANALYSIS
- CALCULATING HEAT TRANSFER COEFFICIENT
- RESULTS AND DISCUSSION
- CONCLUSIONS
- ACKNOWLEDGEMENT
- REFERENCES

Parabolic trough solar collector usually consists of a parabolic solar energy concentrator, which reflects solar energy into an absorber. The absorber is a tube, painted with solar radiation absorbing material, located at the focal length of the concentrator, usually covered with a totally or partially vacuumed glass tube to minimize the heat losses. Typically, the concentration ratio ranges from 30 to 80, depending on the radius of the parabolic solar energy concentrator. The working fluid can reach a temperature up to 400°C, depending on the concentration ratio, solar intensity, working fluid flow rate and other parameters. Hence, such collectors are an ideal device for power generation and/or water desalination applications. However, as the length of the collector increases and/or the fluid flow rate decreases, the rate of heat losses increases. The length of the collector may reach a point that heat gain becomes equal to the heat losses; therefore, additional length will be passive. The current work introduces an analysis for the mentioned collector for single and double glass tubes. The main objectives of this work are to understand the thermal performance of the collector and identify the heat losses from the collector. The working fluid, tube and glass temperature's variation along the collector is calculated, and variations of the heat losses along the heated tube are estimated. It should be mentioned that the working fluid may experience a phase change as it flows through the tube. Hence, the heat transfer correlation for each phase is different and depends on the void fraction and flow characteristics. However, as a first approximation, the effect of phase change is neglected. Copyright © 2013 John Wiley & Sons, Ltd.

### INTRODUCTION

- Top of page
- SUMMARY
- INTRODUCTION
- ANALYSIS
- CALCULATING HEAT TRANSFER COEFFICIENT
- RESULTS AND DISCUSSION
- CONCLUSIONS
- ACKNOWLEDGEMENT
- REFERENCES

In general, solar collectors can be classified into three categories, Point collector (high temperature, order of 1000°C or more), line collector (intermediate temperature, order of 300°C or more) and plane collector (low temperature, order of 100°C or less). Point collectors usually consist of a parabolic mirror, which concentrates the solar radiation into a small area (point), or it consists of many mirrors directing the solar energy into a small region. Those mirrors are usually monitored electronically. This type of collector needs a sophisticated solar tracking mechanism and usually applied in power generation, metal melting, hydrogen production, etc. The second type of the collector is the line collector, which usually consists of a parabolic cylinder that directs solar radiation into a tube (line), located at the focal length of the collector. The tube is coated with solar absorbing material and covered with a glass tube. The gap between the glass tube and tube is fully or partially evacuated from air to reduce the heat losses. Also, for better performance, the absorber is covered with selective materials and the glass tube coated with anti-reflective material. This type of collector can reach 300°C or more depending on the concentration ratio, flow rate and solar intensity. The tracking mechanism for this type of collectors is simpler than the tracking mechanism for the point collectors. It has been applied to power generation in many locations around the world [1-5]. State of art reviews of the trough solar collector applications for power generation with history are given by Price *et al*. [6]; Fernandez-Garcia *et al*. [7] and Garcia *et al*. [8]. Using natural convection heat tube integrated with solar trough collector experimentally investigated by Zhang *et al*. [9]. They claimed that their system achieved a thermal efficiency of about 38%. Application of a trough solar collector for water disinfection is given by Malato *et al*. [10]. Also, it is an ideal device for water desalinations, where the salted water can be flashed after passing through the collector. The evaporated water can be condensed and used as fresh water after certain processes. Flat plate type of solar collectors usually consists of a flat plate to absorb solar radiation with a glass cover. In general, the flat plate collector does not need the solar tracing mechanism. This type of collector usually operates at temperature of order of 100°C. However, for vacuumed glass tubes and if the solar intensity is high, the temperature may reach about 150°C. The more attractive feature of this type of collector is that it does not need the solar tracking mechanism. The main application of this type of collector is for domestic water and space heating. Different types of solar collectors and their applications were reviewed by Kalogirou [11].

In this paper, the second type of the collector (line) is considered. However, the model developed can be applied even for flat plate with vacuumed tubed collector, by setting the concentration ratio to order of unity. Hence, the model developed in this research is targeted by both types of collectors.

Espana and Rodriguez [12] developed a mathematical model for simulating the performance of a trough collector. They assumed that the absorber is a bare tube exposed to ambient conditions. In other words, the absorbing tube is not covered with glass tube.

Grald and Kuehn [13] studied the thermal performance of a cylindrical trough solar collector with innovative porous absorber receiver. They solved fluid dynamic and energy equations using finite difference method. The system is designed to reduce the heat losses as much as possible by allowing cold water pass through the outer layer of the absorber, and hot fluid extracted from the core of the absorber. The estimated thermal efficiency of the system is about 60% for a low temperature difference between the fluid outlet temperature and ambient temperature. However, the efficiency of the system drops to about 30% for high temperature differences.

Kalogirou *et al*. [3] published an analysis for hot water flow through a trough solar collector with water flashing system. The results of analysis indicated that about 49% of the solar energy can be used for steam generation.

Odeh *et al*. [14] presented an analysis for water flow inside the absorber tube as an application for direct steam generation. The analysis considered phase change of the liquid water to steam. The convective heat transfer coefficient is assumed to be a function of steam quality and Shah's equation was used [15, 16]. The model predictions were evaluated against Sandia Laboratory tests of LS2 collector [1]. Odeh and Morrison [17] examined the performance of solar trough collector integrated with water storage system to compensate the intermittency of the solar energy. Performance of a combo system (photovoltaic and thermal) was reported by Coventry [18] by using a trough collector covered with photovoltaic materials with a concentration ratio of 37. It is found that the thermal efficiency of the system can reach 58%, and electric efficiency is around 11%. Yan *et al*. [19, 20] simulated the thermal performance of a solar trough system used for steam generation for a power-plant or to heat the feed water.

All the mentioned works did not illustrate the variation of the local heat losses from the collector, which is the subject of this work. It is essential to understand the variation of heat losses along the absorber tube to estimate the length of the collector for a better performance. It is expected that the heat losses increase as the collector length increases because the temperature difference between the collector and ambient increases. At a certain location along the collector, the balance between heat losses and collected energy may reach the equilibrium conditions. Hence, beyond that location, extra length of collector may be useless, or it has insignificant effect on the operation of the collector. For example, the length one of the trough solar collectors used for power generation in Spain is more than 100 m [21] and can reach about 785 m [22]. The current work analyzes heat transfer from a trough solar collector with single and double glass covers. The gaps between glass covers and between the glass cover and absorber are assumed to be evacuated from air. The main objective of the work to identify the losses associated with the trough solar collector, especially for high-temperature application. As a fact, the rate of heat losses increases as the temperature difference between a system and ambient increases. Hence, using a double glass cover may be beneficial to a certain temperature difference. Burkholder and Kutscher [23] showed that heat losses per unit collector length can reach about 250 W/m for collector temperature of 400°C.

### ANALYSIS

- Top of page
- SUMMARY
- INTRODUCTION
- ANALYSIS
- CALCULATING HEAT TRANSFER COEFFICIENT
- RESULTS AND DISCUSSION
- CONCLUSIONS
- ACKNOWLEDGEMENT
- REFERENCES

Schematic diagram of trough solar collector is shown in Figure 1. Solar radiation is mainly absorbed at the outer surface of the absorber tube as a heat. Part of the absorbed heat transfers to the working fluid by conduction through tube wall and convection from the inner surface of the tube to the fluid. Other parts of the heat transfers as a loss by radiation to the inner surface of the glass through the vacuum and then by conduction from the inner surface of the glass to the outer surface of the glass. The heat dissipated to ambient from the outer surface of the glass by two mechanisms, convection to the surrounding air and by radiation to the surrounding surfaces (buildings and sky). Figure 2 shows the thermal resistance diagram for the heat transfer process, for single glass cover (a) and double glass covers (b). Extra resistance is needed to be added to model double glass covers, after R_{4} in the diagram.

By assuming that the surrounding surface temperature is equal to the ambient air temperature, the model equation for a single glass cover can be expressed as:

- (1a)

And for double glass covers:

- (1b)

Energy balance for the working fluid can be formulated as,

- (2)

The left-hand side of the equation (1) represents the total solar energy absorbed by the outer surface of the tube per unit length. The first term on the right-hand side of the equation represents the rate of heat transfer to the fluid inside the tube, useful energy. The second term on the right-hand side of the equation (1) represented the heat losses to the ambient. The left-hand side of the equation (2) represents useful rate of heat transferred to rise the fluid temperature as it passes through the tube.

The above equations are coupled and nonlinear because the rate of heat transfer from the tube to glass takes places by radiation. Also, the rate of heat to the surrounding surfaces and sky takes place by radiation. However, the above equation can be combined into one equation by replacing the right-hand side of equation (2) into the first equations, yields

- (3)

Equation (3) contains two unknowns, T_{fb} and T_{to}; hence, there is need to solve equation (3) coupled with equation (1).

And

- (4-h)

It is fair to assume that R_{2}, R_{4} and R_{4d} are negligible compared with other thermal resistances. Then, inner surface temperature of the tube (T_{ti}) is equal to the outer surface of the tube (T_{to}). Also, the outer surface temperature of the glass tube (T_{go}) is equal to the inner surface temperature of the glass cover (T_{gi}). Hence, equations (1) and (2) simplify to,

- (5)

and

- (6)

respectively. Yet, the above equations are not easy to solve analytically because nonlinearity introduced by radiative heat transfer (see R_{3} and R_{6}). Hence, equations (5) and (6) are needed to be solved iteratively, using finite difference method. However, to close the solution, there is a need for another equation to find glass temperature (T_{g}), which is,

- (7)

### CALCULATING HEAT TRANSFER COEFFICIENT

- Top of page
- SUMMARY
- INTRODUCTION
- ANALYSIS
- CALCULATING HEAT TRANSFER COEFFICIENT
- RESULTS AND DISCUSSION
- CONCLUSIONS
- ACKNOWLEDGEMENT
- REFERENCES

The rate of heat transfer for turbulent forced flow in a tube is given by Dittus-Boelter correlation as [24],

- (8)

Where Nu=h d_{p}/k_{f}, Re= (4 m)/(μ d π).

Convective heat transfer coefficient from the outer surface of the glass tube to ambient air is calculated from the following correlation,

- (9)

Where V_{wind} is wind velocity in m/s, and h_{o} is in W/m^{2}.K.

For double glass cover, the resistance R_{3} can be replaced by two resistances (R_{3} and R_{3d}), hence, R_{3} in equations (5) and (7) replaced by,

- (10)

Where subscript g1 and g2 stand for first and second glass covers, respectively. Also, for double glass cover, τ in equation (1) should be replaced by τ^{2}.

### RESULTS AND DISCUSSION

- Top of page
- SUMMARY
- INTRODUCTION
- ANALYSIS
- CALCULATING HEAT TRANSFER COEFFICIENT
- RESULTS AND DISCUSSION
- CONCLUSIONS
- ACKNOWLEDGEMENT
- REFERENCES

The results are presented for the aperture diameter of 1 and 3 m. The range of flow rate investigated is from 0.005 to 0.05 kg/s. All the simulations were done for a constant solar intensity of 500 W/m^{2}. Table 1 summarizes other parameters used in the simulations.

Table 1. Typical values for properties used in the simulation, unless otherwise stated.Property | Value |
---|

Glass tube emissivity | 0.9 |

Glass tube transmissivity | 0.94 |

Absorber tube absorptivity | 0.94 |

Absorber tube diameter (m) | 0.05 |

Glass tube diameter (m) | 0.10 |

Absorber length (m) | 20 |

Ambient temperature (°C) | 30 |

Inlet fluid temperature (°C) | 30 |

Typical solar intensity (W/m^{2}) | 500 |

Aperture length (m) | 3.0 |

Figure 3a shows the fluid, absorber and glass cover temperatures variation along the collector for the flow rate of 0.005 kg/s. For such a low flow rate, it is possible for the fluid to reach temperature of about 230°C for the collector with aperture of 1 m and 20 m long. However, the heat losses increase as the length of the collector increases (Figure 3b). For a collector of 10 m long, the thermal efficiency of the collector is about 60%. As the length of collector increase, the heat losses increase because the temperature difference between the absorber and ambient increase (Figure 3), and efficiency decreases to 40% for a collector length of 20 m.

The outlet temperature of the fluid from the collector decreases as the flow rate increase to 0.01 kg/s (Figure 4a). The outlet fluid temperature for the specified collector reaches about 170°C for the flow rate of 0.01 kg/s compared with 230°C for the flow rate of 0.005. However, the losses decrease as the flow rate increase. Figure 4b illustrates the heat losses and efficiency of the collector as a function of collector length for the flow rate of 0.01 kg/s. The thermal efficiency of the collector of length 20 m is about 60% compared with 40% for flow rate of 0.005 kg/s. Further increasing the flow rate to 0.05 kg/s decreases the fluid outlet temperature and increases the efficiency of the collector, as shown in Figure 5a and 5b, respectively. For such a high flow rate, the outlet fluid temperature is only about 70°C. Such a low temperature is difficult to be utilized for power generation or water desalination processes. The efficiency of power cycle is dictated by Carnot efficiency,

- (11)

where T_{c} and T_{h} are cold and hot absolute temperatures bounding a system, respectively. Hence, as the absorber temperature (T_{h}) decreases, the efficiency of power cycle decreases. For instance, for temperature of 70°C (343 K) and for ambient temperature of 20°C (293 K), the maximum ideal efficiency of the cycle is about 14.6%. In fact, even such a low efficiency is not achievable in real cycle. In practical cycle, only about half of Carnot efficiency is usually achievable, i.e. about 7.0%.

Results for aperture of 3 m are shown in Figure 6a and 6b for flow rate of 0.01 kg/s. The outlet temperature of the fluid can reach 370°C. Nevertheless, the losses also are high, where the efficiency drops to about 45%. The maximum cycle efficiency working with fluid temperature of 370°C (643 K) and with ambient temperature of 20°C (293) is about 54%. Practical cycle efficiency may be about 30%.

In a summary, for high temperature application, the heat losses increase drastically as the length of the collector increases due to the fact that the temperature difference between the absorber and ambient increases. Therefore, it is suggested that increasing the thermal resistance is necessary at least for collector length greater than 10 m, as the results of losses analysis suggest. It is expected that using double glass covers with vacuumed gaps may decrease the losses and increase overall efficiency of the collector. It should be mentioned that with added extra glass layer, the optical losses of the system also increase because the glass absorbs and reflects part of the incident solar radiation. In simulating double glass cover, the left-hand side of equations (1) and (5) is multiplied by τ. In other words, the τ in the mentioned equations is replaced by τ^{2}.

The results for a collector with double glass covers with aperture of 1 m are presented for mass flow rate of 0.01 kg/s (Figure 7a and 7b). It is possible to reach fluid outlet temperature of 190°C, compared with 170°C for single glass cover collector, i.e. 20°C gain in the temperature. However, the gain in efficiency is only a few percent. The efficiency for aperture of 3 m is about 50%, and outlet fluid temperature is of about 400°C compared with 45% and 370°C for single glass cover system (Figure 8a and 8b). Hence, there is some gain by adding double glass layers compared with results of single glass layer collector. The results suggested that it is not economical or beneficial to add double glass cover to the first part of the collector (at least to the first 10 m). In the following section, the results of analysis for partial covering the collector with second glass cover will be presented.

The results show that using double glass covers for solar collectors of length of 10 or less is not that economical. However, it may be beneficial to use double glass covers for collector length larger than 10 m. Hence, it may be a good idea to use single glass cover for the first 10 m and double glass cover for any length beyond that.

Figure 9a and 9b show typical results for a collector with three meter of aperture. The first half (first 10 m length) of the collector is covered with one glass layer, and the second half is covered with double glass layers. The difference between results of Figure 8 and 9 are not that significant. Therefore, collector with partially covered with single glass is recommended for high temperature applications.

For a given conditions, it is noticed that there is a correlation between the mass flow rate and heat losses. For instance, for I = 500 W/m^{2} and D = 1.0 m, different mass flow rates multiplied by heat losses can be correlated within 6% as shown in Figure 10.

Furthermore, effects of absorber diameter on the rate of heat losses and efficiency of the collector are examined (Figure 11). As the absorber diameter increases, the heat losses increases, consequently, the collector efficiency decreases. This is due to the fact that as the surface area of the absorber tube increases, heat losses increase, where heat loss is function of surface area. Also, for a given mass flow rate, the fluid flow velocity decreases as the tube diameter increases. Hence, the Reynolds number also decreases, which decrease the convective heat transfer to the working fluid.