A cylindrical fuel rod (k = 30 W/m ∙ K) of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel rod generates heat uniformly at a rate of 100 MW/m³, and the average temperature of the cooling water is 75°C with a convection heat transfer coefficient of 2500 W/m²∙K. The operating pressure of the cooling water is such that the surface temperature of the fuel rod must be kept below 200°C to avoid the cooling water from reaching the critical heat flux (CHF). The critical heat flux is a thermal limit at which a boiling crisis can occur that cause overheating on the fuel rod surface and lead to damage. Determine the variation of temperature in the fuel rod and the temperature of the fuel rod surface. Is the surface of the fuel rod adequately cooled?

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T(ro) egen = 100 MW/m³ Cooling water 2500 W/m².K, 75°C Fuel rod ↑ D = 2 cm