2002AugQualMATH - Ben Sauerwine Practice for Qualifying...

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Ben Sauerwine Practice for Qualifying Exams Problem Source: CMU August 2002 Qualifying Exam In a toy model of a nuclear reactor, the conservation law for the number of neutrons is described by: + = V S V rudV dS n j udV dt d ˆ v (1) where V is the volume of the reactor, S is the surface, and a normal unit vector. The neutrons are described by a number density u and a flux vector n ˆ j v . The constant r is a growth rate describing the rate of increase of neutrons (more neutrons result in more nuclear fissions which result in more neutrons). An equation for the flow of neutrons has the form u v j = v v (2) where v, a constant, is a diffusion coefficient. (a) Use the divergence theorem to derive the differential form of the conservation law (equation 1). Combine this with equation 2 to give an equation for the diffusion of neutrons. The divergence theorem states that = S V dS n F dV F ˆ v v v . Thus, I get from (1), ru u v u dt d ru u v u
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This note was uploaded on 04/07/2012 for the course PHYSICS 767 taught by Professor Dr.jaouni during the Spring '12 term at Abu Dhabi University.

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2002AugQualMATH - Ben Sauerwine Practice for Qualifying...

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