Neutron flux for uniform parallelepiped¶

Neutron flux for a uniform rectangular parallelepiped reactor of side lengths \(a, b, c\) depends on the cartesian coordinates \(x, y, z\).

dimension_factor¶: Dimension factor that appears as a coefficient in the solution to the differential equation. See neutron_flux.

Symbol:: Phi_0
Latex:: \(\Phi_{0}\)
Dimension:: 1/(area*time)

x¶: position along the \(x\)-axis.

Symbol:: x_1
Latex:: \(x_{1}\)
Dimension:: length

y¶: position along the \(y\)-axis.

Symbol:: x_2
Latex:: \(x_{2}\)
Dimension:: length

z¶: position along the \(z\)-axis.

Symbol:: x_3
Latex:: \(x_{3}\)
Dimension:: length

length¶: length along the \(x\)-axis.

Symbol:: l_1
Latex:: \(l_{1}\)
Dimension:: length

width¶: length along the \(y\)-axis.

Symbol:: l_2
Latex:: \(l_{2}\)
Dimension:: length

height¶: length along the \(z\)-axis.

Symbol:: l_3
Latex:: \(l_{3}\)
Dimension:: length

neutron_flux¶: neutron_flux at a point with coordinates x, y, z.

Symbol:: Phi
Latex:: \(\Phi\)
Dimension:: 1/(area*time)

law¶

Phi = Phi_0 * cos(pi / l_2 * x_1) * cos(pi / l_1 * x_2) * cos(pi / l_3 * x_3)

Latex:: \[\Phi = \Phi_{0} \cos{\left(\frac{\pi}{l_{2}} x_{1} \right)} \cos{\left(\frac{\pi}{l_{1}} x_{2} \right)} \cos{\left(\frac{\pi}{l_{3}} x_{3} \right)}\]