Temperature Temperature Temperature at node 7 after 10 min = at node 7 after 20 min= at node 7 after 30 min = °C. °C. °C.

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The topic is heat transfer. Please help answer the question shown. Thank you.

Consider a uranium nuclear fuel element (k=35 W/m-K, p= 19,070 kg/m³, and cp=5 116 J/kg-K) of radius 10 cm that experiences a
volumetric heat generation at a rate of 4 x 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, p= 5 8055 kg/m³, and cp=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 at node 7 using the EES software considering both the
fuel rod and 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.
Temperature at node 7 after 10 min =
Temperature at node 7 after 20 min=
Temperature at node 7 after 30 min =
Uranium fuel rod
°C.
°C.
°C.
7
h = 1000 W/m²-K
T₂ = 50°C
Stainless steel cladding
Transcribed Image Text:Consider a uranium nuclear fuel element (k=35 W/m-K, p= 19,070 kg/m³, and cp=5 116 J/kg-K) of radius 10 cm that experiences a volumetric heat generation at a rate of 4 x 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, p= 5 8055 kg/m³, and cp=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 at node 7 using the EES software considering both the fuel rod and 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. Temperature at node 7 after 10 min = Temperature at node 7 after 20 min= Temperature at node 7 after 30 min = Uranium fuel rod °C. °C. °C. 7 h = 1000 W/m²-K T₂ = 50°C Stainless steel cladding
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