For the single-phase case, the natural circulation flowrate is found by integration of the loop momentum equation and coupling this to the energy equation. Thus, the primary temperature increase is given by the standard result,

(17)

where the fluid thermal expansion drives the convective flow around the loop. Also, from the heat balance across the HX, we have a second relation for the power, taking the primary to secondary temperature difference as close to that due to conduction across the tube wall only, with a correction coefficient for any surface, plugging, corrosion, and thermal resistance effects. To maximize the heat removal we assume the HX to not be limiting in capacity, and hence may take the core outlet temperature as saturated boiling, and the inlet temperature as close to the HX secondary temperature.

From the two expressions for the power, there is the following result for the maximum heat removal in a natural convection loop with onset of bulk boiling at the core exit is the limit,

(18)

The trends are somewhat counter intuitive for several reasons. The maximum heat removal is very sensitive to the HX design, relies on maximizing the primary to secondary temperature drop, and hence minimizing the core to HX elevation difference, and also maximizing the loop flow resistance.