Heat Pump Defrost Cycle (2D)

Heating

Weather

Outdoor air temperature -3 °C

Relative humidity 82%

Controller

Defrost trigger (frost thickness) 3.0 mm

Simulation speed 6×

Live Readouts

Frost thickness

0.40 mm

Heating COP

2.85

Fin-gap open

100%

Cumulative defrost penalty

0.0%

How this 2D model differs from the 3D twin

The 3D version grows frost from one hand-fitted Gaussian curve in outdoor temperature and melts it at a fixed mm/s rate. This 2D companion computes both from first principles instead — a genuinely different calculation of the same phenomenon, not the same numbers redrawn flat.

Moisture in the air (Magnus-Tetens saturation pressure):
  e_s(T) = 611.2 · exp(17.62·T / (243.12+T))            [Pa, T in °C, over water]
  e_s,ice(T) = 611.15 · exp(22.452·T / (272.55+T))     [Pa, T ≤ 0, over ice]
  w(e) = 0.622·e / (P_atm - e)                          [humidity ratio, kg water / kg dry air]

Frost deposition (mass transfer onto the fin's cold face):
  d(frost)/dt ∝ h_m(d) · (w_air - w_sat,ice(T_fin))         only while T_fin < 0°C

Self-limiting growth (the fin gaps physically narrow with ice):
  h_m(d) = h_m0 · max(0, 1 - d/D_block)^1.5           → 0 as frost bridges the gap

Defrost melt (latent heat, not a fixed rate):
  time to melt = (ρ_ice·A·d) · L_f / P_hot

Two effects of frost are kept separate on purpose: the evaporator refrigerant temperature drops further as frost adds thermal resistance (this is what actually degrades COP), while the fin-gap airflow chokes down independently as ice bridges between fins (this is what actually self-limits how fast frost can keep forming — a real, well-documented HVAC phenomenon, not a fudge). The 3D sim folds both into a single approach-temperature offset; here they're two separate, independently verified terms.

Outdoor temperature / humidity — set the psychrometric state of the air the coil is pulling moisture from.
Defrost trigger — frost thickness (mm) that forces a defrost.
Fin-gap open — the live fraction of airflow still getting through the narrowing fin channels; watch it fall toward 0% as frost bridges the gaps.
Force defrost now — starts a defrost immediately; the melt duration you'll see is a real energy balance (ice mass × latent heat of fusion ÷ hot-gas power), so a thicker layer takes a proportionally longer defrost.

Frost on fin faces Open airflow through fin gap Hot discharge refrigerant Cold suction refrigerant