Chapter 5, Problem 5.78P

Spheres of 40-mm diameter heated to a uniform temperature of $400°\text{C}$ are suddenly removed from the oven and placed in a forced-air bath operating at $25°\text{C}$ with a convection coefficient of $300{\text{W/m}}^{\text{2}}\cdot \text{K}$ on the sphere surfaces. The thermophysical properties of the sphere material are $\rho =3000{\text{kg/m}}^{\text{3}},c=850\text{J/kg}\cdot \text{K,}$ and $k=15\text{W/m}\cdot \text{K}\text{.}$

1. How long must the spheres remain in the air bath for of the thermal energy to be removed?
2. The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?