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ENGR 3820U Assignment 2 Quiz: 2013-03-06 Prepare the solution steps in detail. Try to derive a final expression for the result, then substitute...

This problem involves solving a system differential equations, Kind of lost here.

ENGR 3820U Assignment 2 Quiz: 2013-03-06 Prepare the solution steps in detail. Try to derive a final expression for the result, then substitute numerical values. Problem 1 A thin-foil consisting of 10 22 fissile nuclei, each of which have a microscopic fission cross section of 2x10 -21 cm 2 is irradiated uniformly in a neutron flux of 10 8 n/cm 2 /s, starting at t=0. There is only one group of delayed neutrons. The total neutron yield per fission is 2.33. The delayed neutron fraction is 0.001 and the half-life of precursors is one minute. The number of neutrons emitted by the sample per second is measured with a neutron detector. a) What does the detector indicate 20 minutes after the start of the irradiation? b) At 25 minutes the irradiation stops. What does the detector indicate two minutes later? Note: Assume that the number of nuclei that react with neutrons (through fission or otherwise) is negligible compared to the original number of nuclei present in the sample, and that neutrons emitted from the sample do not interact in the sample. Problem 2 Consider a homogeneous nuclear reactor for which all neutrons are born prompt. The reactor is cubical, with side equal to 4m. The neutronic parameters of the reactor are: s m v cm cm D a / 2200 5 . 2 003 . 0 1 1 The reactor is initially critical, operating at 3000 MW fission power. The energy liberated per fission is approximately 200MeV. The extrapolated size of the reactor can be approximated by its physical size. a) Find f .
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b) Calculate the volume-integrated flux in the reactor. c) Calculate total neutron population in the reactor. d) Calculate the neutron generation time and life time. e) Calculate the neutron flux at the center of the reactor. A control device is removed from the reactor at t=0, which causes the absorption cross section to decrease to 1 00299 . 0 cm a . f) Calculate the reactivity. g) Calculate the new generation time and neutron life time. h) Calculate the power after 0.001s, 0.01s, 0.1s, 1s. Now assume that, in fact, after 0.002 s, the control device is reinserted, and the absorption cross section returns to its initial value. i) Calculate the power at 0.002s, 0.005s, 0.01s, 0.1s, 1s, 10s, 100s, 1000s. Consider a second reactor similar to the one initially described, but in which a fraction % 5 . 0 of neutrons are delayed. There is only one delayed neutron group and the precursor decay constant is 0.2s -1 . Assume the same initial state, power, and control- device maneuvers as for the first reactor. Recalculate points h) and i) for this second reactor.
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