skyExchange

Long-wave exchange with sky and ground (Buildings SkyRadiationExchange)

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

Purpose

Long-wave heat flow rate from an outer surface to sky and ground, for OuterWall and Window.

Equations

With the sky view factor F = (π − til)/π (1 for a roof, 1/2 for a wall), the environment temperature

T_env = (F T_sky⁴ + (1 − F) T_out⁴)^1/4,

the ground being at the outdoor air temperature, and the exact grey-body exchange

Q = σ ε A (T⁴ − T_env⁴) = σ ε A (T² + T_env²) (T + T_env) (T − T_env),

written as the second form, a conductance times the temperature difference. A linearisation at T_env understates the loss of a sun-lit surface at 60 °C by a quarter.

Relation to Buildings

The view factor and the environment temperature of Buildings' SkyRadiationExchange.

Revisions

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