Question

4. Parabolic/cylindrical trough: (Total points 45) Suppose you are planning to make a cylindrical trough from metal sheet of size 5m X 7m. The metal sheet is aluminum coated, having 95% reflectance. You gave this sheet a semicircle shape along its width so that the arc length of semicircle becomes 5 m. If a collector pipe made of copper, with the length 7m and diameter 5cm (inner diameter 3cm) is at the focal point of this trough, receiving concentrated light, and if the irradiation of the sun light is 1000 W/m2, answer the following questions a. i. Radius of curvature of the trough. (Points 5) Aperture area of the trough. (Points 5) Light concentration ratio. (Points 10) Intensity of the light hitting the pipe surface. (Points 5) How long it'll take to reach the pipe temperature 450 °C? Copper has density of 8.96 g/cm Heat capacity of 0.385 kJ/(Kg. 0C). Consider the pipe is black painted with ~5% reflectance and no other losses, hence the remaining light is absorbed and converted into heat. (Points 20) ii. iii. iv. v. Rim of trough mirror Focal line Normal to aperture Cylindrical trough Rim angle Figure: 4.1 Schematic of a cylindrical trough 100 Al 8 60 Au 40 Ag 200 nm 500 nm m2 m Wavelength Figure: 4.2 Reflectance of different metal surfaces

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