The Solar World manufacturing facility in Portland, Oregon, is the largest producer of silicon-based solar cells in the United States. The manufacturing process begins with the melt crystallization of electronic grade silicon into a cylindrical ingot of poly crystalline silicon. The newly formed silicon ingots must then be cooled before they can be sliced into thin silicon wafers. In the present cooling process, a 30-cm-diameter by 3-m-long solid
silicon ingot is placed vertically within a flowing air stream as shown in the figure. Air maintained at 27°C flows normal to the ingot at a velocity of 0.5 m/s. Heat transfer from the ends of the ingot can be neglected. At some point in time during the cooling process, the surface temperature of the wafer is measured to be 860 K (587°C). Parts (a) through (d) all refer to this condition.
a. What is the fluid Reynolds number, Re?
b. What is the total cooling rate (Watts) from a single silicon ingot at this time in the cooling process?
c. What is the Biot number for the heat-transfer process?

Properties of silicon at 860 K: ρ_Si = 2300 kg/m³, C_p,Si = 760 J/kg · K; k_Si = 30 W/m · K.

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hot Si ingot air flow 860 K =T, V, = 0.5 m/sec Tm = 300 K L= 3.0 m D = 30 cm