gapConductance

Conductance of a vertical gas gap between two panes per unit area: convection of the gas (Buildings.HeatTransfer.Windows.BaseClasses.GasConvection and convectionVerticalCavity) and long-wave exchange between the two panes, opaque to it, at their temperatures (Buildings exchanges exactly)

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

Purpose

Heat transfer coefficient h_gap of a vertical gas gap between two panes, per unit area, at the temperatures of the panes: convection of the gas and long-wave exchange between the two faces. The window computes the conductance of each gap with it at every time, so the U-value of the glazing follows the temperatures as in Buildings.

Equations

Density of the gas at atmospheric pressure, at the mean temperature T_m = (T_a + T_b)/2:

ρ = p M / (R T_m),   p = 101325 Pa, R = 8.314462618 J/(mol K).

Rayleigh number, with the temperature difference regularised at 0.1 K and bounded below by 100:

Ra = smoothMax(ρ² x³ g c √((T_a − T_b)² + 0.01) / (T_m μ k), 100, 10),   μ = μ_a + μ_b T_m.

Nusselt number: the correlations of Wright (1996) for the vertical cavity, blended over 100 around Ra = 10⁴ and 5·10⁴, against the correlation of the tall cavity of ISO 15099,

Range	Nu1
Ra > 5·104	0.0673838 Ra1/3
104 < Ra ≤ 5·104	0.028154 Ra0.4134
Ra ≤ 104	1 + 1.7596678·10−10 Ra2.2984755

Nu = smoothMax(Nu₁, 0.242 (Ra x/h)^0.272, 0.1).

Conductance, the long-wave part exact for two grey parallel faces opaque to long-wave radiation:

h_gap = Nu k/x + σ (T_a² + T_b²) (T_a + T_b) / (1/ε_a + 1/ε_b − 1).

Smoothing

• |T_a − T_b| is replaced by √((T_a − T_b)² + 0.01): differentiable when both panes are at the same temperature.
• The branches of Wright's correlation are joined by regStep over 100 (Buildings joins them the same way), the bounds by smoothMax.

Relation to Buildings

Buildings.HeatTransfer.Windows.BaseClasses.GasConvection with convectionVerticalCavity for the convection. Buildings solves the long-wave exchange between the panes with their radiosities; here it is the closed form above, equal for panes opaque to long-wave radiation.

Validation

The free-floating BESTEST cases with double glazing: the zone temperatures within 0.38 K of Buildings on average (0.80 K with a constant gap conductance).

References

• J. L. Wright (1996). A correlation to quantify convective heat transfer between vertical window glazings. ASHRAE Transactions 102(1), 940–946.
• ISO 15099:2003. Thermal performance of windows, doors and shading devices — Detailed calculations.

Revisions

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