Heat-flux control = burnout when q'' exceeds CHF (jump to film boiling). Temperature control = traverse the full S-curve including the transition regime.
During the animation the operating point moves along the curve toward this target. 0% = near room temperature, 100% = maximum input.
Water at 1 atm (T_sat = 100°C) is fixed. Natural convection h_nc ≈ 1000 W/(m²·K) and film boiling h_fb ≈ 30 W/(m²·K) are assumed. The Zuber CHF is about 1.1 MW/m² for water at 1 atm.
Top = boiling curve (log q'' vs ΔT_e). Yellow dot = current operating point / red dashed = CHF and Leidenfrost / orange arrow = burnout jump. Bottom = heating surface (bubbles → vapor film).
Pool boiling heat flux $q''$ exhibits four distinct regimes as a function of wall superheat $\Delta T_e = T_w - T_\text{sat}$, as first mapped by Nukiyama (1934).
Natural convection ($\Delta T_e < 5$ K). $h_{nc}$ is the natural convection coefficient:
$$q'' = h_{nc}\,\Delta T_e$$Nucleate boiling ($5 \leq \Delta T_e < 30$ K). Simplified Rohsenow form:
$$q'' = C\,\Delta T_e^{3}$$Critical heat flux (Zuber, ≈ 1.1 MW/m² for water at 1 atm):
$$q''_\text{CHF} \approx 0.131\,\rho_v^{1/2}\,h_{fg}\,[\sigma g(\rho_l-\rho_v)]^{1/4}$$Film boiling (Bromley convection plus radiation):
$$q'' = h_{fb}\,\Delta T_e + \varepsilon\sigma_{SB}(T_w^4 - T_\text{sat}^4)/2$$Under heat-flux control, once $q''_\text{input} > q''_\text{CHF}$ the surface cannot remain in nucleate boiling and jumps discontinuously to the film branch, so the surface temperature $T_w$ soars by hundreds to a thousand degrees (burnout = hysteresis).
