1. Solar Cooking Jordan Englünd Heat Transfer April 2008

2. Project Description Cooking with the sun: Easy and fun to do, but how long does it take to cook a hot dog with the sun to the proper temperature of 150 degrees F?

3. Proof of concept This technology is used all over the world for solar power plants.

4. Approach to problem Because of the complications of having a variable convective coefficient, the temperature range (55 K) has been divided into 5 smaller temperature ranges (11 K). The convective coefficient will be assumed to be constant over those ranges.

5. Problem Setup For each temperature range, the net energy transferred to the hot dog due to radiation from the sun and by free and natural convection will be calculated. Using lumped capacitance, the time needed to transfer enough energy to make the temperature change was calculated. The time needed for each of the 5 temperature ranges was added to get the total time to cook the hot dog.

6. Radiation q in = αGA dish – EA surface = αGA dish – εE b A surface = αGA dish – εσT f A surface where…  α = 0.675 1 (see figure to the right)  G = 1226 W/m 2 (see problem 12.7)  ε = 0.825 1  T sun = 5800 K 1 http://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=enhttp://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=en

7. Convection Heat transfer from convection was calculated by combining free convection and forced convection.  Forced convection was assumed to be due to a light summer breeze of 1 mph. Is it necessary to combine forced and free?  Gr = 3e 4  Re 2 = 8e 5  Forced convection was more significant, but both were included for accuracy (using equation 9.64 with transverse flow).

8. Free | Forced q = h ave A dog (T dog -T ∞ ) Nu D comes from equation 9.34 for a horizontal cylinder. q = h ave A dog (T dog -T ∞ ) Nu D comes from the Churchill equation (7.54): Wind speed: a light breeze of 1 mph. www.eng.nus.edu.sg

9. Properties Hot Dog: Length = 17 cm Diameter = 3.25 cm k dog = 0.52 1 ρ dog = 930 2 c p,dog = 2340 3 Initial temp: 75 F Final temp: 150 F Temp steps: 11 K Environment: Wind: 1 mph horizontal breeze Outside temp: 75 F Dish diameter: 0.3 m  at opening (parabolic) Sun: 5800 K, at 30 degrees from vertical (summer conditions) 1 http://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=en http://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=en 2 http://asae.frymulti.com/abstract.asp?aid=15409&t=2http://asae.frymulti.com/abstract.asp?aid=15409&t=2 3 http://www.engineeringtoolbox.com/specific-heat-capacity-food-d_295.htmlhttp://www.engineeringtoolbox.com/specific-heat-capacity-food-d_295.html

10. Results Using lumped capacitance the time needed to make each temperature step was calculated from the net heat transferred to the hot dog and then summed. Time to fully cook the hot dog: 10 minutes and 7 seconds

11. Appendix – Excel Calculator