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 process is 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)?