The shield of a nuclear reactor can be idealized as a slab with a face area...
The shield of a nuclear reactor can be idealized as a slab with a face area of 6 ft2 and a thermal conductivity k = 2 Btu / hr*ft*°F. Heat is generated in the shield at a steady rate S = S0 exp(-bx) [Btu / hr*ft3 ] where x = 0 denotes the inner surface close to the nuclear reactor and the outer surface is at x = L. The temperature is maintained at 300 °F at the inner surface (x = 0) and 80 °F at the outer surface x = L. Take the thickness of the slab L = 0.83 ft, S0 = 17,280 Btu / hr*ft3 , b = 5.5 ft-1 and k = 2.0 Btu / hr*ft*°F
a. Carry out a steady-state shell balance of energy to derive a differential equation for the heat flux variation in the slab.
b. Apply Fourier’s law of conduction to derive a differential equation for the temperature distribution T(x) in the slab. Apply the given boundary conditions to solve for T(x).
c. Determine the heat flow rate QH at the outer surface of the slab.
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The shield of a nuclear reactor can be idealized as a slab with
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