Chapter 5, Problem 5.9P

A solid steel sphere (AISI 1010), 300 mm in diameter, is coated with a dielectric material layer of thickness 2 mm and thermal conductivity $0.04\text{W/m}\cdot \text{K}\text{.}$ The coated sphere is initially at a uniform temperature of and is suddenly quenched in a large oil bath for which $T_{\infty }=100°\text{C}$ and $h=3300{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Estimate the time required for the coated sphere temperature to reach $140°\text{C}\text{.}$  Hint: Neglect the effect of energy storage in the dielectric material. since its thermal capacitance $\left(\rho cV\right)$ is small compared to that of the steel sphere.