Solar Thermal Course. Lecture 6 : Exercises on FPC

1. The solar radiation on a flat plate collector of 2.1 m2 of aperture is 800 W/m2. The collector is tilted 40º and south oriented. The angle of incidence of the radiation is 20º. The following data is also known: • Ambien temperature 12 ºC • Overall heat loss coefficient 4.32W/m2K • Absorber plate temperature 80ºC • Collector inlet temperature 28ºC • Mass flow rate: 0.014kg/s m2 • Glass cover: refraction index n=1.526, extinction coefficient by cover width (KL)=0.037 • Absorber absorptance: 0.92 • Specific heat of the fluid Cp=4180J/kgK • Air refraction index n=1 a) Which is the fluid outlet temperature? b) Which is the solar collector efficiency for the give conditions? 2. A flat plate collector with dimensions 1.5x3 m tilted 40º has the following specifications: • Overall heat loss coefficient: 5.6 W/m2K • Convection heat transfer coefficient between the tubes and the circulating fluid 200W/m2K • Glass cover refraction index 1.526 • Glass cover extinction coefficient by cover width (KL) 0.037 • Absorber absorptance 0.92 • Absorber width 0.5mm • Copper tubes of 10/8 mm (outer/inner diameter) and 12 cm of distance between tubes • Copper heat conductivity 385 W/mK • Heat capacity of the fluid: 4180 J/kgK If at some instant the normal irradiation on the collector surface is 850 W/m2, and the fluid at the inlet is at 45ºC, estimate the collector efficiency. Consider the mass flow rate of 0.0135kg/s m2 and the ambient temperature of 15ºC b) Which is the collector outlet temperature? 3. For the solar collector of exercise 2, if at some instant the radiation on the collector surface is of 850W/m2, but there is no fluid circulating through the collector, which is the stagnation temperature? What does this mean? 4. For the same collector of exercise 2, determine the critical radiation given an inlet temperature of 30ºC. What does this critical radiation mean? 5. In the following the table the ambient temperature, solar radiation on the collector surface, solar gains on the absorber plate and solar field inlet temperature are given. The solar field is made of 5 collectors of 2m2 tilted 40º and south oriented. For the solar collector, assume the overall heat loss coefficient to be UL=6.3 W/m2K and the plate efficiency factor (F’) to be 0.841. The mass flow rate through a single solar collector is 0.03kg/s. Assume that the controller turns off the pumps whenever the outlet temperature is less than the inlet temperature. Assume also that the thermal capacity of the fluid is 3720 J/kgK. Calculate the daily useful gains and the solar field efficiency for that particular day. Assume that the data given in the table can be considered constant for the whole hour. Time Ta[ºC] It[W/m2] S[W/m2] Tfi 7-8 1 15 12.45 30 8-9 3 125 103.8 33 9-10 5 280 232.6 37 10-11 7 460 382.3 38 11-12 8 496 407 40 12-13 7 475 395 45 13-14 6 320 266 44 14-15 6 250 207.8 40 15-16 6 110 91.4 35 16-17 5 7 5.3 25 6. Two flat plate solar collectors are considered to be installed for a low-temperature solar application where the solar field will be working between a temperature differences (Tfi-ta) of 15ºC up to 35ºC and for solar irradiation in the range of 350W/m2and 800 W/m2. Considering the working conditions which collector should be selected? Please, comment your answer. The solar collectors’ characteristics are: Ac[m2] ηopt FRUL1[W/m2K2] FRUL2 [W/m2K2] TSTG[ºC] Collector 1 2.25 0.792 5.3 0.0182 148 Collector 2 2.23 0.747 3.824 0.023 149.5 7. A flat plate collector of 4 m2 is tested indoors in order to determine its overall heat loss coefficient. In the test, thermal oil is used as heat transfer fluid (Cp=2035J/kgK) circulating with a mass flow rate of 0.052kg/s. The fluid enters the collector at 60ºC and at the outlet 49ºC is measured. The ambient temperature during the whole experiment was set to 15ºC. Which is the overall heat loss coefficient of the collector? 8. For a one-cover collector of dimensions 2.5x1.3m tilted 45º, determine the overall heat loss coefficient. The ambient temperature is 10ºC and the wind is blowing at 3m/s. The absorber plate thick is 0.5 mm and its emissivity is 0.92. The glass cover is at 35 mm from the absorber plate and has an emissivity of 0.88. The insulation is fiberglass (k=0.038W/mK) of 45mm thick at the back and 25 mm thick at the edges. The mean absorber plate temperature is 90ºC. Assume the convection heat transfer coefficient for the back of the collector to be 0.3W/m2K and for the edge of the collector to be of 2W/m2K. For the heat convection coefficient from the top of the collector the following correlation can be used: hw=2.8+3.0 V, where V is the wind velocity in m/s Assume that the sky temperature is the same as the ambient temperature. 9. A water heating collector with a aperture of 3.5 m2 is tested following the European standards with radiation nearly normal to the collector surface. The following table gives some results of the measurements Qu[W] It[W/m2] Tav [ºC] Ta[ºC] 2252 864 23.4 10 469 894 85.3 10 a.- Which is the collector efficiency curve? b. As the test was carried out following EU standards it might be necessary to convert the data for its use in a computer program which works with FrUL and Fr(τα). Please, evaluate them. c. A Second test was performed so as to evaluate the incidence angle modifier. To that end the collector was set to operate at the same temperature as the ambient and for radiation incidence angle different than normal. The following information comes from the test: ϑ It[W/m2] Qu[W/m2] 0 850 747 30 750 639 45 630 526 60 530 396