"One step in the manufacture of silicon wafers used in the microelectronics industry is the melt crystallization of silicon into
a crystalline silicon ingot. This processis carried out within a special furnace. When the newly solidified ingot is removed from the furnace, it is assumed to have a uniform initial temperature of 1600 K, which is below the crystallization temperature. At this temperature, the thermal conductivity of silicon is 22 W/(m•K), the density is 2300 kg/m3, and the heat capacity is 1000 J/(kg•K). The hot solid silicon ingot is allowed to cool in air maintained at a constant ambient temperature of 30°C. The diameter of the silicon rod is 15 cm. End effects are considered negligible. The convective heat transfer coefficient is 147 W/(m2•K). What temperature will exist 1.5 cm from the surface of the ingot after a cooling time of 583 sec (9.72 min)?" Consider the rod as acylinder placed vertically.
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