(Solved): 3.45 3-45 A sphere of outside diameter D=10cm maintained at a uniform temperature Ti=225C is ...

3-45 A sphere of outside diameter $D=10\mathrm{cm}$ maintained at a uniform temperature $T_i=225^{?}\mathrm{C}$ is exposed to an ambient at $T_{?}=25^{?}\mathrm{C}$ with a heat transfer coefficient for convection of $h=50\mathrm{W}/\left({\mathrm{m}}^2?{}^{?}\mathrm{C}\right)$. Calculate the thickness of the insulation $\left[k=0.08\mathrm{W}/\left(\mathrm{m}?{}^{?}\mathrm{C}\right)\right]$ required to reduce the rate of heat loss by 83 percent while the sphere is maintained at $T_i=225^{?}\mathrm{C}$. Answer: $0.5\mathrm{cm}$