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Boiling curve q(dT), log-log: model (blue), your run (orange), CHF (green) and minimum (purple)
Raise the heat flux.
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How to use
Pick a preset or set the controls. In power mode the slider sets the heat flux the wire generates; turn on the auto-ramp and watch the orange trace climb the nucleate branch of the curve, then jump at the green critical-heat-flux line. In temperature mode the supply holds the wall superheat, so you can park on the transition branch that power control cannot reach. Change the pressure, wire diameter, surface condition and contact angle to see how the curve and the bubble size move. Space pauses, R resets. Things to try: (1) ramp at 1 atm and read the burnout flux against the green line; (2) repeat at 5 bar: CHF rises by about 80 per cent; (3) hold 25 K superheat, then 300 K, in temperature mode; (4) compare a 1 mm and a 10 mm wire (the Sun-Lienhard factor).
The 3D page has orbit/zoom, camera buttons and a guided tour. Its glass tank, hot plate, copper terminals, nichrome wire, insulating lid, power supply, thermometer unit and easel board were modelled in Blender with baked PBR textures and exported as one Draco GLB; Three.js r160 drives the bubbles, the vapour sheath, the glowing wire, the burnout flash and all screens from the same model as the 2D page.
The science
When a hot surface sits in a pool of liquid at its boiling point, the heat flux q it can hand over depends in a strongly non-monotonic way on the wall superheat ΔT = Twall − Tsat. Nukiyama (1934) found this by heating a wire electrically: raise the power slowly, and at one particular flux the wire suddenly glows and melts.
Free convection (small ΔT): q ≈ 600 ΔT1.25 W/m² (an empirical stand-in for the Churchill-Chu law). Nucleate boiling, Rohsenow (1952):
q = μl hfg √[g(ρl−ρv)/σ] · [ cp,l ΔT / (Csf hfg Prl) ]3
so q grows with the cube of ΔT. The critical heat flux (Zuber 1958, with the Sun-Lienhard correction for a small horizontal cylinder of radius R, R′ = R/√(σ/gΔρ)):
qCHF = [0.89 + 2.27 e−3.44√R′] · 0.131 hfg √ρv [σ g (ρl−ρv)]1/4 (1.1 MW/m² for water, 1 atm, flat plate)
Above it vapour columns merge into a blanket. Film boiling (Bromley 1950) on a horizontal cylinder of diameter D, with radiation added (ε = 0.8):
hc = 0.62 [ kv³ ρv(ρl−ρv) g h′fg / (μv D ΔT) ]1/4, h4/3 = hc4/3 + hr h1/3
The minimum film flux (Zuber/Berenson) qmin = 0.09 ρv hfg [σ g Δρ /(ρl+ρv)²]1/4 sets where the film collapses; between qCHF and qmin (transition boiling) the model interpolates log-log.
Dynamics. The wire is a lumped thermal mass per unit surface area, (ρ c D/4) dΔT/dt = qgen − qboil(ΔT). In power control qgen is fixed, and on the falling transition branch the equilibrium is unstable: the wire jumps to the film branch, whose temperature (above the 1673 K melting point of nichrome) destroys it. In temperature control qgen = K(ΔTset − ΔT) and every branch, including the transition, is stable.
Bubbles. Departure diameter Db = 0.0208 θ √(σ/gΔρ) (Fritz; θ in degrees) in nucleate boiling, growing toward 0.45 of the Taylor wavelength λ = 2π√(3σ/gΔρ) in film boiling. The emission rate follows from volume conservation, N = q A /(ρv hfg Vb): a 10 cm wire at the critical flux makes tens of thousands of bubbles per second, so the 3D view draws a sample (the HUD shows how many real bubbles one drawn bubble stands for). Decorative micro-bubbles are cosmetic.
Numerical checks run in the page. (1) Zuber flat-plate CHF vs the textbook 1.1 MW/m²; (2) the flux at which the time-stepped, ramped wire leaves the nucleate branch vs the analytic CHF; (3) the time-stepped steady superheat vs a bisection root of qboil(ΔT) = q; (4) the log-log slope of the nucleate branch (3); (5) the integrator's energy balance; (6) conservation of vapour volume by the discrete bubble emitter; (7) continuity of the curve at its regime edges.
Simplifications. Properties are approximate steam-table values interpolated in ln p between 0.5, 1.013, 2 and 5 bar. The pool is saturated (no subcooling). The wire is treated as isothermal (small Biot number), nucleation-onset hysteresis is ignored, and the transition branch is a log-log interpolation, not a correlation. The Zuber/Berenson qmin puts the film edge at a lower superheat than the measured Leidenfrost point of water (about 150 to 200 K). The vapour film in the 3D view is drawn 8 times thicker than computed.