exteriorExchange

Heat from an outer surface to the outside: natural and wind-driven convection (Buildings TemperatureWind) or a fixed coefficient, and long-wave exchange with sky and ground

FastSmoothBuildings.Envelope.Functions.exteriorExchange, function (source)

Purpose

Heat flow rate Q from an outer surface to the outside: convection with the outdoor air and long-wave exchange with sky and ground. Used by OuterWall.

Equations

With a fixed coefficient hFix > 0,

Q = h_fix A (T − T_out) + Q_sky;

otherwise natural and forced convection,

Q = Q_nat + A h_F (T − T_out) + Q_sky,   h_F = 2.537 W R (2/A^1/4) (v² + 0.25²)^1/4,

Q_nat from naturalConvection with the coefficients cPos and cNeg of the outer face, Q_sky from skyExchange, R the roughness factor (1.67, rough) and W the wind direction modifier:

W = 0.75 + (0.5 s_dir − 0.25) s_v,

s_dir a smooth step from 0 to 1 when cos(azi + π − dir) rises above cos 100° (the wind blows on the surface; width 0.05), s_v a smooth step from 0 to 1 when the wind speed v rises above 0.25 m/s (width 0.125 m/s). W is 1 on the windward side, 0.5 on the leeward side and 0.75 without wind.

Smoothing

• The steps of W are x/√(x² + δ²) ramps.
• √v is regularised as (v² + 0.25²)^1/4: finite derivative without wind.

Relation to Buildings

The TemperatureWind law of the exterior convection of Buildings, with smooth steps; 2/A^1/4 is √(P/A) for a square surface of perimeter P = 4 √A.

Revisions

• October 2026: moved from trano's FastModel.Envelope.Functions.