One method for growing thin silicon sheets for photo-voltaic solar panels is to pass two thin strings of high melting temperature material upward through a bath of molten silicon. The silicon solidifies on the strings near the surface of the molten pool, and the solid silicon sheet is pulled slowly upward out of the pool. The silicon is replenished by supplying the molten pool with solid silicon powder. Consider a silicon sheet that is Wsi=85mmW si =85mm wide and tsi=150μmt si =150μm thick that is pulled at a velocity of Vsi=20mm/minV si =20mm/min. The silicon is melted by supplying electric power to the cylindrical growth chamber of height H=350 mm and diameter D=300 mm. The exposed surfaces of the growth chamber are at Ts=320KT s =320K, the corresponding convection coefficient at the exposed surface is h=8W/m2⋅Kh=8W/m 2 ⋅K, and the surface is characterized by an emissivity of εs=0.9ε s =0.9. The solid silicon powder is at Tsi, i=298KT si, i =298K, and the solid silicon sheet exits the chamber at Tsio=420KT sio =420K. Both the surroundings and ambient temperatures are T[infinity]=Tsur=298KT [infinity] =T sur =298K. (a) Determine the electric power, Pelec P elec, needed to operate the system at steady state. (b) If the photo-voltaic panel absorbs a time-averaged solar flux of q′
sol=180W/m2q sol′′
=180W/m 2 and the panel has a conversion efficiency (the ratio of solar power absorbed to electric power produced) of η=0.20η=0.20, how long must the solar panel be operated to produce enough electric energy to offset the electric energy that was consumed in its manufacture?