solution

A steel sphere with a diameter of 7.6 cm is to be hardened by first heating it to a uniform temperature of 870°C and then quenching it in a large bath of water at a temperature of 38°C. The following data apply
surface heat transfer coefficient h = 590 W/(m2 K)
thermal conductivity of steel = 43 W/(m K)
specific heat of steel = 628 J/(kg K)
density of steel = 7840 kg/m3
Calculate: (a) time elapsed in cooling the surface of the sphere to 204°C and (b) time elapsed in cooling the center of the sphere to 204°C.
GIVEN
A steel sphere is quenched in a large water bath
Diameter (D) = 7.6 cm = 0.076 m
Initial uniform temperature (To) = 870°C
Water temperature (T?^?) = 38°C
Surface heat transfer coefficient (h) = 590 W/(m2 K)
Thermal conductivity of steel (k) = 43 W/(m K)
Specific heat of steel (c) = 628 J/(kg K)
Density of steel (I?) = 7840 kg/m3
ASSUMPTIONS
Constant water bath temperature, thermal properties, and transfercoefficient