Question

Consider an Am-Be neutron source placed inside a spherical water tank with a radius of R The source (assuming point source) emits S neutrons per second. For this experimental setup, students should (a) State energy of the neutrons released from the source. (b) Write time-dependent two-group neutron diffusion equation for the source. (c) Give boundary conditions necessary to solve the equations you obtained in (b). (d) Draw fast and thermal fluxes as a function of radius without solving the equations

please, solve by explaning :)

Answer 1

a) An absorption or release of nuclear energy occurs in nuclear reactions or radioactive decay; those that absorb energy are called endothermic reactions and those that release energy are exothermic reactions. Energy is consumed or liberated because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation.

An absorption or release of nuclear energy occurs in nuclear reactions or radioactive decay; those that absorb energy are called endothermic reactions and those that release energy are exothermic reactions. Energy is consumed or liberated because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation.

Nuclear energy is released by the splitting (fission) or merging (fusion) of the nuclei of atom(s). The conversion of nuclear mass-energy to a form of energy, which can remove some mass when the energy is removed, is consistent with the mass-energy equivalence formula:

ΔE = Δm c²,

in which,

ΔE = energy release,

Δm = mass defect,

and c = the speed of light in a vacuum.

b)

The general neutron diffusion equation for the scalar flux of neutrons, ϕ(r,t), is given by

1v∂ϕ∂t−∇⋅D(r)∇ϕ(r,t)+Σa(r)ϕ(r,t)=νΣf(r)ϕ(r,t)+Q(r,t).

Our notation is standard: v is the neutron speed, D(r) is the diffusion coefficient, Σa is the macroscopic absorption cross-section, Σf is the macroscopic fission cross section, ν is the number of neutrons per fission, and Q(r,t) is a prescribed source.

c)

The boundary conditions we will consider for this equation are generic conditions,

A(r)ϕ(r,t)+B(r)dϕdr=C(r)for r∈∂V.

The initial condition is

ϕ(r,0)=ϕ0(r).