$13-69$ A long cylindrical black surface fuel rod of diameter $25mm$ is shielded by a surface concentric to the rod. The shield has a diameter of $50mm,$ and its outer surface is exposed to surrounding air at $300K$ with a convection heat transfer coefficient of $15\frac{W}{m^2}*K.$ Inner and outer surfaces of the shield have an emissivity of $0\mathrm{.}05,$ and the gap between the fuel rod and the shield is a vacuum. If the shield maintains a uniform temperature of $320K,$ determine the surface temperature of the fuel rod.

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