Presets
Playback
Apparatus
Model checks
The science
What is modelled
A thin board with heat capacity per area ρc t and a hot-gas heat-transfer coefficient h on both faces behaves as a lumped body with time constant τ = ρ c t /(2h). As the conveyor carries it from zone to zone the air temperature steps, and the board temperature relaxes exponentially toward each new value. Lead-free SAC305 solder melts at about 217 °C, so the time the board spends above that liquidus decides whether joints wet properly.
Equations
ρ c t dT/dt = 2 h (Tzone(x = v t) − T), i.e.dT/dt = (Tzone − T)/τ.- Within a zone:
T(t) = Tz + (T0 − Tz) e−t/τ. - Biot number
Bi = h (t/2) / k; the lumped model needs Bi < 0.1. - Time above liquidus is the total time with T > 217 °C.
Checks run in the page
- RK4 board temperature against the exact exponential in one zone.
- Time above liquidus from sampling against the analytic crossing times.
- Lumped model against a one-dimensional through-thickness conduction solver at the same h.
- Heat balance: the convective heat delivered over the pass equals the stored heat of the board.
Honest simplifications
Uniform zone air temperature with sharp steps (real ovens blend between zones), a single board temperature without component thermal mass, constant h, and no radiation, flux outgassing or solder-paste behaviour. Profiles shown follow common paste datasheet ranges but are illustrative.
What to try
- Choose Lead-free profile and read the time above liquidus and the peak.
- Choose Too fast and see the board fail to reach the liquidus before leaving the hot zone.
- Choose Thick board and watch the Biot number read-out climb past 0.1 as the lumped model gets marginal.