Heat from the sealed containment can be used to provide useful work and it can be reabsorbed as particles coalesce in the reactor. For this reason, the rate of change of \(H\)eat from the containment is,
\(\cfrac{dH}{dt}=-\gamma.H+\delta.CH\)
where \(C\) is the \(C\)oolness around the containment, \(\gamma\) is the rate of re-absorption of \(H\)eat inside the containment and \(\delta\) the rate of production of \(H\)eat. Correspondingly the amount of \(C\)oolness around the containment changes with time,
\(\cfrac{dC}{dt}=\alpha.C-\beta.CH\)
where \(\alpha\) is the rate of \(C\)oolness introduced around the containment and \(\beta\) is the rate of \(C\)oolness taken up by the \(H\)eat.
Yes, this is the Lotka-Voltera equations as applied to cooling a heat producing reactor. \(H\)eat is the predator. This formulation allows for \(\gamma\) the \(H\)eat re-absorption rate and \(\beta\), the effective factor in the energy transfer from \(H\)eat to \(C\)old.
The control goals at the operating temperature of the sealed nuclear reactor are,
\(\cfrac{dH}{dt}=0\)
and
\(\cfrac{dC}{dt}=0\)
Goodnight.
Note: Is this set of control equations optimal?
