Chapter 1, Problem 1.42P

One method for growing thin silicon sheets for photo voltaic solar panels is to pass two thin strings of highmelting temperature material upward through a bath ofmolten silicon. The silicon solidifies on the strings nearthe surface of the molten pool, and the solid silicon sheet is pulled slowly upward out of the pool. The silicon isreplenished by supplying the molten pool with solid silicon powder. Consider a silicon sheet that is $W_{si}=85\text{mm}$ wide and $t_{si}=150\text{μm}$ thick that is pulled at a velocity of ${}_{si}=20\text{mm}/\min$ . The silicon is melted by supplyingelectric power to the cylindrical growth chamber ofheight $H=350\text{mm}$ and diameter $D=300\text{mm}$ . Theexposed surfaces of the growth chamber are at $T_s=320\text{K}$ , the corresponding convection coefficient at theexposed surface is $h=8\text{W}/{\text{m}}^{\text{2}}$ , and the surface ischaracterized by an emissivity of ${\in }_s=0.9$ . The solid silicon powder is at $T_{si,i}=298\text{K}$ , and the solid silicon sheetexits the chamber at $T_{si,i}=420\text{K}$ . Both the surroundingsand ambient temperatures are $T_{\infty }=T_{sut}=298\text{K}$ .

(a) Determine the electric power, $P_{elec},$ needed to operate the system at steady state.
(b) 1f the photovoltaic panel absorbs a time-averagedsolar flux of ${q^{″}}_{sol}=180\text{W}/{\text{m}}^{\text{2}}$ and the panel has aconversion efficiency (the ratio of solar powerabsorbed to electric power produced) of $\eta =0.20$ .how long must the solar panel be operated to produce enough electric energy to offset the electricenergy that was consumed in its manufacture?