Consider a uranium nuclear fuel element (k = 35 W/m K, = 19,070 kg/m3 and

Consider a uranium nuclear fuel element (k = 35 W/m · K, ρ = 19,070 kg/m3 and c_p = 116 J/kg · K) of radius 10 cm that experiences a volumetric heat generation at a rate of 4 × 10⁵ W/m³ because of the nuclear fission reaction. The nuclear fuel element initially at a temperature of 500°C is enclosed inside a cladding made of stainless steel material (k = 15 W/m · K, ρ = 8055 kg/m³ and c_p = 480 J/kg · K) of thickness 4 cm. The fuel element is cooled by passing pressurized heavy water over the cladding surface. The pressurized water has a bulk temperature of 50°C and the convective heat transfer coefficient is 1000 W/m2·K. Assuming one dimensional transient heat conduction in Cartesian coordinates, determine the temperature in the fuel rod and in the cladding after 10, 20 and 30 min. Use implicit finite difference formulation with a uniform mesh size of 2 cm and time step of 1 min.

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2 3 •N نیا 4 Uranium fuel rod 156 7 h = 1000 W/m².K T%= 50°C Stainless steel cladding