Heat generation is given as Q dot = 1 (kW/m^3)
Question 1 (35 Points)
Consider a spherical nuclear fuel of radius ri = 5 m with a thermal conductivity k = 20 W/m K contained in a vacuumed spherical furnace of radius ra = 10 m as shown below. These two spheres are concentric. The fuel steadily generates heat at a rate of Q dot (kW/m^3), which causes the entire spherical surface of the fuel (A1) to be at a temperature of T1. The emissivity of A1 is ε1 = 0.6. The upper half of the internal surface of the furnace is a black surface (A2) maintained at T = 300 K, while the lower half of the internal surface of the furnace (A3) is thermally insulated.
A,
T = 300 K, ε = 1.0
Vacuum
A1, k, T1 = ?
ε1 = 0.6
A3
Insulated
(a) Determine the heat loss at the fuel surface Qg (kW). (4 points)
(b) Find the values of the view factors F1u and F1u. (4 points)
(c) Determine the view factor F23 in terms of the symbolic parameters of ra and ri. (8 points)
(d) Determine the value of the surface temperature of the fuel T1 (K). (9 points)
(e) Determine the core temperature of the fuel (the temperature at the center of the sphere) T. (K). (10 points)
