HW4 (1)

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University of Illinois, Urbana Champaign *

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436

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Mechanical Engineering

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Dec 6, 2023

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ABE 436 HW4 1. (10 pts) Find the local solar time (LST) on August 21 for the following local times and locations: a) 9:00 A.M. EDT, Norfolk, VA b) 1:00 P.M. CDT, Lincoln, NE c) 10:00 A.M. MDT, Casper, WY d) 3:00 P.M. PDT, Pendleton, OR e) 7:00 P.M., British Summer Time, London, England (British Summer Time is the U.K. equivalent of Daylight Savings Time, and is a Greenwich Civil time plus one hour) 2. (10 pts) Calculate the sun's altitude (β) and azimuth (Φ) angles at 10:00 A.M. solar time on September 21 at 40 deg N latitude. 3. (15 pts) Design an overhang to help shade a south-facing, sliding-glass patio door. You would like to shade the glass in the summer to help control the air-conditioning loads, and you would also like the glass to get full sun in the winter to help provide passive solar heating of the home. Suppose the sliding door has a height of 7 ft, the interior ceiling height is 9 ft, and the local latitude is 35 deg. a. What should be the overhang projection P to shade the entire glass door at solar noon during the solstice in June? b. With that overhang, where would the shade line, Y, be at solar noon on the winter solstice? 4. (15 pts) You are assigned to design a solar water heater (SWH) for a homeowner in Champaign, IL. The solar water collector will be installed on the roof facing west tilted at 40 deg. The efficiency of SWH is 70%. The energy usage per day is based on the DOE test procedure for hot water heaters, which assumes an incoming water temperature of 58°F (14.4°C), hot water temperature of 135°F (57.2°C), and total hot water production of 84.4 gallons per day, which is the average usage for a household of four people.
5. Please calculate the total required area (m 2 ) of solar water collector based on Jan. 21 in a sunny day (assume clear sky). Assume no thermal heat loss from the water tank to environment? (hint: need to find out the time for sunrise and sunset) . 6. (20 pts) A house owner in Champaign, IL (at 88 deg W longitude and 40 deg N latitude) installed solar PV panels (20 m 2 ) for his home. The panels are set on roof facing south and titled at 40 deg. What is the total electrical energy (kWh) produced over a day from these PV panels on September 10 (assume clear sky)? Assuming the efficiency of the PV panel is 20%. If all conditions remain the same, what are the total energy production for the following two setups? a. all panels are set on roof facing south and titled at 25 deg. b. all panels are set on roof facing west and titled at 40 deg. What do you learn from these calculations? 7. (10 pts) A PV cell has an active area of 250 mm by 160 mm and operates with an average conversion efficiency of 20%. a. Using an annual solar radiation data of 1068 kWh/m 2 , estimate the electrical energy, in kWh, that could be provided by the above cell. b. Calculate the number of such cells required to supply the 10,600 kWh per year of electricity needed by an energy-efficient household for lighting, AC and electrical appliances? What would be the total active area? c. On another location with the insolation at 800 kWh m -2 yr -1 , estimate what area of solar panels would be required to produce 10,600 kWh of electricity. d. What is the most obvious drawback of this form of electricity supply, as described? Water Collector 40
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