Glasshouse Heat Balance

What is modelled

One well-mixed air node and one soil node exchange heat with the outside, the sun, a thermostatic heater and each other. Humidity follows a single water-vapour mass balance with condensation at saturation.

Equations

• Air node Ca dT/dt = Qsun,air + Qheater - UA (T - Tout) - ρ cp (n V/3600)(T - Tout) - H (T - Tsoil) - Lv E.
• Soil node with 77 % of the transmitted sun and a weak link to a 13 °C deep ground.
• Vapour dm/dt = E - (nV/3600)(m/V - ρv,out); saturation by the Magnus formula.
• Thermostat with ±0.35 K hysteresis.

Checks run in the page

• Passive cooling against the closed-form exponential.
• The air-node energy budget closes over 30 minutes.
• Magnus saturation pressure against steam-table values.
• The thermostat keeps air inside its band.

Honest simplifications

No CFD, no radiation exchange with the sky, no plant physiology and a uniform air node. Time runs at 120 simulated seconds per real second at 1x.

• Choose Cold night and watch the heater cycle while the energy graph climbs.
• Choose Sealed and humid: with almost no ventilation the humidity reaches saturation and condensation appears on the roof.
• Raise ventilation on a sunny day and compare the heat lost through the vents with the wall loss.