For all problems in this homework, unless otherwise noted, assume the reactor is homo- geneous. Additionally, we can make the assumption the fuel (only 235U) is diluted in water, at atmospheric pressure (100 kPa) and room temperature (20 C). The fuel is so diluted the di usion coecient is that of water. Assume the neutrons are all thermal, with neutron energies at 0.0253 eV. The recoverable energy per ssion is 180 MeV.

1. Consider a 10 kW reactor in the shape of a cube, with a side length of 1 m. The reactor is critical. Determine:

(b) The neutron flux profile in the reactor (c) The neutron production rate in the reactor (d) The neutron leakage rate out of the reactor (e) The neutron absorption rate in the reactor (f) Do the values from c through e validate the reactor is critical?

2. Consider a spherical reactor with all parameters like that in Problem 1, with a radius of 1m. Determine a through f and in Problem 1.

3. Consider a 10 kW cylindrical reactor that has a height of 1 m. Determine a through f as in Problem 1 for radii of 0.01 m to 3 m in 0.1 m increments. This is best done in MATLAB. Plot the parts a through e as a function of the radius.