s1.3-11 - Problem 1.3-11: Nuclear Fuel Element Figure...

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Problem 1.3-11: Nuclear Fuel Element Figure P1.3-11 illustrates a spherical, nuclear fuel element which consists of a sphere of fissionable material (fuel) with radius r fuel = 5 cm and k fuel = 2 W/m-K that is surrounded by a spherical shell of metal cladding with outer radius r clad = 7 cm and k clad = 0.25 W/m-K. The outer surface of the cladding is exposed to fluid that is being heated by the reactor. The convection coefficient between the fluid and the cladding surface is h = 50 W/m 2 -K and the temperature of the fluid is T = 500ºC. Neglect radiation heat transfer from the surface. Inside the fuel element, thermal energy is being generated for the reactor. This process can be modeled as a volumetric source of heat generation in the material that is not uniform throughout the fuel. The volumetric generation ( g ′′′ ± ) can be approximated by the function: g r β ′′′ = ± where = 5x10 3 W/m 2 . fissionable material k fuel =2W/m-K r fuel =5cm r clad =7cm cladding k clad =0.25W/m-K g ± 2 50 W/m -K 500 C h T = Figure P1.3-11: Spherical fuel element surrounded by cladding a.) Determine an analytical solution for the temperature distribution within the fuel element. Implement your solution in EES and plot the temperature as a function of radius for 0 < r < r fuel . The inputs are entered according to: $UnitSystem SI MASS RAD PA K J $Tabstops 0.2 0.4 0.6 3.5 in "Inputs" r_fuel=5 [cm]*convert(cm,m) "radius of fuel element" k_fuel=2 [W/m-K] "conductivity of fuel element" r_clad=7 [cm]*convert(cm,m) "radius of cladding" k_clad=0.25 [W/m-K] "conductivity of cladding" h_bar=50 [W/m^2-K] "heat transfer coefficient" T_infinity=converttemp(C,K,500[C]) "temperature of fluid" beta=5e3 [W/m^2] "constant for volumetric generation"
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A differential control volume is shown in Figure 2 and includes conduction at r and r + dr at the inner and outer surfaces of the spherical shell as well as generation within the enclosed volume.
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s1.3-11 - Problem 1.3-11: Nuclear Fuel Element Figure...

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