Consider the manufacture of photovoltaic silicon, as described in Problem 1.42. The thin sheet of silicon is pulled from the pool of molten material very slowly and is subjected to an ambient temperature of T_∞
= 527°C within the growth chamber. A convection coefficient of h = 7.5 W/m² · K is associated with the exposed surfaces of the silicon sheet when it is inside the growth chamber. Calculate the maximum allowable velocity of the silicon sheet V_si. The latent heat of fusion for silicon is h_sf = 1.8 10⁶ J/kg. It can be assumed that the thermal energy released due to solidification is removed by conduction along the sheet.

Data From Problem 1.42

One method for growing thin silicon sheets for photovoltaic  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 W_si = 85 mm  wide and t_si = 150 μm thick that is pulled at a velocity of  V_si = 20 mm/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 T_s = 320 K, the corresponding convection coefficient at the exposed surface is h = 8 W/m² · K, and the surface is characterized by an emissivity of ε_s = 0.9. The solid silicon powder is at T_si,i = 298 K, and the solid silicon sheet exits the chamber at T_si,o = 420 K. Both the surroundings and ambient temperatures are T_∞ = T_sur = 298K.

Transcribed Image Text:

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