I am looking for formulas and step by step explanations to find solve the following questions.

Problem 3. Consider a parabolic collector with the following parameters: - The collector has an aperture of 2 m wide - The rim angle is 45 - Specular reflectance of the concentrator is 0.87 - Assume the incident radiation at the aperture being equal to 800 W/m? - Light is parallel to the axis of the parabola. Concentroted image Using the Mon-Uniform Solar Disk model diagrams (Duffie and Beckman, Section 7.10), Flux intensity on the flat . receiver of o linear (a) Find the energy flux intensity in the center of the Intensity parabolic concentrator image (i.e. at the intersection of the focal plane with the parabola axis (point A): (b) Find the energy flux intensity at 2.5 mm from the center of the image (i.e. 2.5 mm from the parabola A B Distance axis [point B); 5IXE Tip 1: Study example 7.10.1 in Duffie & Beckman to better understand this problem. Tip 2: Equation 7.9.2 {Duffie, Beckmann, 2013) can be used to describe the relationship among the rim angle, focal distance, and aperture of a parabolic reflector. Problem 4. Estimate the transmittance for beam radiation at your location on July 22 at 11:00 am solar time. Assume the standard clear atmosphere conditions. Once you know the transmittance, as the next step, estimate the intensity of beam radiation (W/m?) at that time at your chosen location and its component on a horizontal surface. Tip 1: use Section 2.8 of Duffie and Beckman, 2013 book to guide your calculation. Example 2.8.1. is analogous to this problem and can be used for guidance. Tip 2: you can use Google Map tools to find altitude and latitude for your location. Tip 3: you can use the NOAA calculator to find solar zenith angle: https./faml.noaa.qgov/qrad/solcalc/azel. html {..or Equation 1.6.5 in Duffie and Beckman should give you the same result) Problem 1. For a parabolic trough concentrator illustrated below (not to scale), find the location where to place the receiver (tube). Consider the aperture width of 1 m and the height of the parabolic concentrator of 20 cm for this example. 20cm Problem 2. For a perfect parabolic reflector with an aperture of 1 m and rim angle of 307 (similar but not identical to the one shown in Problem 1): (a) calculate the image width it produces on a flat receiver placed perpendicular to the axis of the parabola; (b) estimate the geometric concentration ratio for this collector, using the image dimension you found (note that in case of parabolic concentrators, geometric concentration ratio may not be adeguate to describe the energy flux concentration); (c) estimate what rim angle would give you the highest geometric concentration ratio. Tip: Section 7.9 of Duffie and Beckman, 2013 book should help you to solve this