Greenhouse Heat and Moisture Balance

What is modelled

A greenhouse is a box that lets sunlight in and keeps warm, moist air from escaping. In steady state the heat that enters has to leave: part is used to evaporate water from the crop (transpiration), part is carried out by the ventilation air and part leaks through the cover. At the same time the water the crop transpires must leave as vapour in the ventilation air, or it condenses. These two balances fix the inside temperature and humidity together.

Equations

• Heat τ I + qL = λE + ρ cp Φ (Ti − To) + Uc (Ti − To) per square metre of floor, with ventilation flow Φ = ACH × height / 3600.
• Moisture E = ρ Φ (wi − wo), plus condensation if the air is saturated.
• Penman-Monteith transpiration λE = [Δ Rn + ρ cp VPD / ra] / [Δ + γ(1 + rs/ra)], with the Magnus saturation pressure es = 0.6108 exp(17.27 T / (T + 237.3)).

Checks run in the page

• Closure of the energy balance of the solved state.
• Closure of the moisture balance including condensation.
• The Magnus formula against the tabulated value, and the dew point round trip.
• The limit of a very high ventilation rate, where inside equals outside.

Honest simplifications

The house is treated as one well-mixed air volume in steady state, with a single resistance for the whole crop, a fixed transmissivity and fixed aerodynamic resistance, no heating or cooling plant, no thermal mass, no leaf temperature different from the air and no latent heat released by condensation. It shows the balances, not a climate-control design.

• Compare Sunny day, small vents with Same day, vents wide open and watch the inside temperature fall towards the outside one.
• Press Sealed and humid to see the air saturate and condensation drip from the roof.
• Press Winter night with grow lights to see lamps alone keep the house above freezing.