A long cylindrical black surface fuel rod of diameter 25 mm is shielded by a surface concentric to the rod. The shield has diameter of 50 mm, and its outer surface is exposed to surrounding air at 300 K with a convection heat transfer coefficient of 15 W/m² . K. Inner and outer surfaces of the shield have an emissivity of 0.05, and the gap between the fuel rod and the shield is a vacuum. If the shield maintains a uniform temperature of 320 K, determine the surface temperature of the fuel rod.

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Vacuum - D₂ - D₁ Air, h, To Shield A2, T2, 82 Fuel rod A₁, T₁, 1 Tsurr