Steel balls 12 mm in diameter are annealed by heating to 1100 K and then slowly cooling to 380 K in an air environment for which [infinity] 325 K and 20 W/m2·K. Assuming the properties of the steel to be 40 W/m·K, 7800 kg/m3, and 600 J/kg·K, estimate the time required for the cooling process.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.