Zuber Critical Heat Flux (CHF / Boiling Crisis q″_max) Formula

Predicting boiler and nuclear-fuel burnout from Rayleigh-Taylor & Kelvin-Helmholtz vapor-jet collapse!

Exceeding the Critical Heat Flux (CHF, also called Departure from Nucleate Boiling or burnout) blankets a heated surface in an insulating vapor film, causing heater wall temperature to jump hundreds of kelvins in seconds! In 1958, Novak Zuber proved that CHF is governed purely by hydrodynamic Kelvin-Helmholtz instability of counter-flowing vapor jets and liquid return columns—independent of heater wall roughness: q″_max = 0.131 * h_fg * SQRT(ρ_v) * (σ * g * (ρ_l - ρ_v))^0.25 (giving kW/m^2 directly when latent heat h_fg is entered in kJ/kg and densities/surface tension in SI units)!

Compare saturated water at 1 atm (h_fg = 2,257 kJ/kg, ρ_l = 958.4 kg/m^3, ρ_v = 0.598 kg/m^3, σ = 0.0589 N/m) against dielectric/refrigerant R-134a immersion cooling (h_fg = 198.6 kJ/kg, ρ_l = 1,206 kg/m^3, ρ_v = 14.4 kg/m^3, σ = 0.0081 N/m): water tolerates up to 1,108.9 kW/m^2 (~1.11 MW/m^2), whereas R-134a hits CHF burnout at 307.9 kW/m^2!

Zuber Critical Heat Flux q″_max (kW/m^2)

Evaluates 0.131 * h_fg_kJ_kg * SQRT(ρ_v) * (σ * 9.80665 * (ρ_l - ρ_v))^0.25 across latent heat B2 (kJ/kg), liquid density B3 (kg/m^3), vapor density B4 (kg/m^3), and surface tension B5 (N/m).

=IF(OR(B2 <= 0, B3 <= B4, B4 <= 0, B5 <= 0), "Invalid Fluid Saturation Props", ROUND(0.131 * B2 * SQRT(B4) * ((B5 * 9.80665 * (B3 - B4)) ^ 0.25), 1))

Departure from Nucleate Boiling Ratio (DNBR = q″_max / q″_operating)

Divides Zuber CHF by actual operating heat flux B6 (kW/m^2) to audit thermal burnout safety margin.

=IF(OR(B2 <= 0, B3 <= B4, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Fluid Saturation Props", ROUND((0.131 * B2 * SQRT(B4) * ((B5 * 9.80665 * (B3 - B4)) ^ 0.25)) / B6, 2))

Further reading

• Microsoft Support — SQRT function