Sunrise Sunset and Day length Solar incidence angle

Sunrise, Sunset and Day length • Solar incidence angle for horizontal collector • For sunrise as well as for sunset the =90 o where ωs is the hour angle • Smax (day length or maximum number of sunshine hours) E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 1

E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki Estimation of solar radiation 2

Estimating solar radiation empirically: Global radiation Estimation of monthly average global radiation on horizontal surface Hga = monthly averaged daily global radiation on a horizontal surface Hoa = monthly averaged extra-terrestrial solar radiation at horizontal surface (at top of atmosphere) Sa and Smaxa = monthly averaged daily sunshine hours and maximum possible daily sunshine hours (the day length) at a given location. a and b = constant E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 3

Values of constant a and b Location a b Ahmedabad, India 0. 28 0. 48 Atlanta, Gerorgia, USA 0. 38 0. 26 Brownsville, Texas, USA 0. 35 0. 31 Buuenos Aires, Argentina 0. 26 0. 50 Charleston, S. C. , USA 0. 48 0. 09 Bangalore, India 0. 18 0. 64 Hamburg, Germany 0. 22 0. 57 Malange, Angola 0. 34 Miami, Florida, USA 0. 42 0. 22 Nagpur, India 0. 27 0. 50 New Delhi, India 0. 25 0. 57 Nice, France 0. 17 0. 63 Pune, India 0. 31 0. 43 Rafah, Egypt 0. 36 0. 35 Stanleyville, Congo 0. 28 0. 39 Tamanrasset, Algeria 0. 30 0. 43 E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki • The values of the constant is empirically obtained from know data • Ref: Lof J. A. et al, 1966 4

Estimation of Extra-terrestrial solar radiation • Hoa is equal to Ho if calculated on following days of month; January 17, February 16, March 16, April 15, May 15, June 11, July 17, August 16, September 15, October 15, November 14 and December 10. The monthly averaged daily solar extra-terrestrial radiation S is in W/m 2 the Ho will be W-Hour/m 2 E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 5

Problem • Example: Estimate the monthly average daily global radiation on the horizontal surface at Nagpur (21. 06 N, 79. 03 E) during month of March if the average sunshine hours per day is 9. 2. Assume values for a=0. 27 and b=0. 50 Given: Φ, a, b, Sa Required: δ, ωs, Smax, a, Hoa, n, S E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 6

• Solution: On March 16, n=75 • δ= -2. 4177 Day length=11. 8752 hr, Sunrise and sunset hours? • Ho=34140. 2 k. J/m 2 -day = 22442. 46 k. J/m -day E for • HEnergy 2 ga 12/27/2021 © IIT Bombay, C. S. Solanki 7

Monthly averaged daily Diffuse radiation Ref: Erbs et al. , 1982 • s = sunrise hour angle • KT = sky monthly averaged clearness index, = Hga / Hoa • Typically diffuse radiation is about 10 to 20% of the global radiation on horizontal surface E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 8

E for Energy 12/27/2021 Solar radiation on tilted surface © IIT Bombay, C. S. Solanki 9

Instantaneous Solar radiation on tilted surface Flux on the tilted surface is sum of direct, diffuse and reflected radiation • Tilt factor for beam radiation = ratio of radiation on tilted to horizontal surface • Thus if Ig is instantaneous global radiation on horizontal surface instantaneous radiation tilted surface is Ig*rb E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 10

Instantaneous Solar radiation on tilted surface • Tilt factor for the diffuse radiation Diffuse radiation • Tilt factor for the reflected radiation Reflected radiation Diffuse radiation on tilted surface Id*rd Diffuse radiation on tilted surface Ir*rr Where is the reflectivity of the surrounding in which collector is located -Total radiation on titled surface E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 11

Average daily radiation on tilted surface -Total average daily radiation on titled surface E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki • Ref: Liu el al, ASHRAE, 1961 12

Problem • Assignment: Calculate the monthly average hourly radiation between 11: 00 to 12: 00 (LAT) falling on a flat plate collector facing South with a slope 20 o located in Chennai for the month of March. It is given that monthly averaged hourly global and diffuse radiation in a given condition is 2500 and 1050 k. J/m 2 -hr. Assume ground reflectivity to be 0. 1. E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 13

Typical Solar Radiation E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki 14

Tables for Solar Radiation data • G-Global • D-diffuse Ref: C. S. Solanki, 2007, Prentice Hall of India kilo-Watt-hour/ m 2 -day). • GL- global at latitude Jan G D Feb GL G D Mar GL G D Apr GL G D GL City Ahmedabad 5 1. 2 6. 8 5. 9 1. 3 7. 3 6. 6 1. 6 7. 2 7. 3 1. 8 7. 2 Bangalore 5. 6 1. 6 6. 4 1. 6 7. 0 6. 8 1. 9 7. 0 6. 8 2. 2 6. 6 Bhubaneshw ar 5. 2 1. 4 6. 7 5. 9 1. 4 7. 0 6. 3 2 6. 8 6. 5 2. 4 6. 4 Bhopal 4. 8 1 6. 6 5. 9 1 7. 4 6. 3 1. 6 6. 9 Chandigarh 3. 6 1. 6 5. 4 4. 7 2 6. 2 5. 6 2. 4 6. 6 2. 6 6. 6 Chennai 5. 4 1. 8 7. 5 6. 3 1. 7 6. 9 6. 6 2 6. 8 2. 2 6. 6 1. 4 6. 6 2 6. 8 2. 4 6. 8 EDelhi for Energy 4. 3 12/27/2021 6. 3 © IIT Bombay, C. S. Solanki 5 6 7 1. 8 6. 9 15

Tables for Solar Radiation data • G-Global • D-diffuse Ref: C. S. Solanki, 2007, Prentice Hall of India • GL- global at latitude May G D Jun GL G D Jul GL G D Aug GL G D GL City Ahmedabad 7. 6 5 3. 4 4. 6 3. 3 4. 4 Bangalore 6. 4 2. 6 6. 0 3 5. 6 4. 6 2. 9 4. 4 4. 8 3 4. 7 Bhubaneshw ar 6. 4 2. 6 5. 8 5. 3 3 4. 8 4. 6 3 4. 8 3 4. 6 Bhopal 7. 2 2 6. 5 6. 2 2. 9 5. 5 4. 7 3. 2 4. 4 3. 1 4. 2 Chandigarh 7. 3 2. 8 6. 7 7 3. 2 6. 2 3. 2 5. 6 5. 8 3 5. 5 Chennai 6. 3 2. 4 5. 9 5. 5 2. 8 5. 1 5. 2 2. 9 4. 9 5. 6 2. 8 5. 4 Delhi 7. 2 2. 8 6. 6 3. 1 5. 3 5. 7 2. 9 5. 3 E for Energy 12/27/2021 2 6. 9 6. 6 © IIT Bombay, C. S. Solanki 6 6 3 5. 9 3 5. 1 5. 6 16

Global Solar Radiation in Jan. in MJ/m 2/day E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki Ref: Solar Radiation Handbook, 2008, SEC and Indian Meteorological Station 17

Global Solar Radiation in May in MJ/m 2/day E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki Ref: Solar Radiation Handbook, 2008, SEC and Indian Meteorological Station 18

E for Energy 12/27/2021 © IIT Bombay, C. S. Solanki Thank you for your attention 19