Steady State Fenestration Heat Energy Flow and Loss

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Steady State Fenestration Heat Energy Flow and Loss

Heat Transfer Engineering
Thermodynamics and Heat Transfer Resources
HVAC System and Components Design and Engineering Data

Energy flows through fenestration via (1) conductive and convective heat transfer caused by the temperature difference between outdoor and indoor air; (2) net long-wave (above 2500 nm) radiative exchange between the fenestration and its surroundings and between glazing layers; (3) short-wave (below 2500 nm) solar radiation incident on the fenestration product, either directly from the sun through the fenestration. Simplified calculations are based on the observation that temperatures of the sky, ground, and surrounding objects (and hence their radiant emission) correlate with the outdoor air temperature. This is not the case for clear skies, particularly at night, which can be much colder than ambient air. The radiative interchanges are then approximated by assuming that all the radiating surfaces (including the sky) are at the same temperature as the outdoor air.

The basic equation for the steady-state energy flow through a fenestration is

Eq. 1
q = UA_pf (t_out - t_in ) + (SHGC) A_pf E_t + C (AL) A_pf ρ C_p (t_out - t_in)

Where

q = instantaneous energy flow (Btu/hr)
U = overall coefficient of heat transfer (U-factor) (Btu/hr -ft²-°F)
A_pf = total projected area of fenestration (product's rough opening in wall or roof minus installation clearances) (ft²)
t_in = indoor air temperature (°F)
t_out = outdoor air temperature (°F)
SHGC = solar heat gain coefficient, dimensionless
E_t = incident total irradiance (Btu/hr -ft²)
C = constant, 60 min/ hr
AL = air leakage at current conditions (cfm/ft²)
ρ = air density (lb/ft³)
C_p = specific heat of air (Btu/hr -°F)

The overall U-factor through a fenestration system using area weighted U-factors for each contribution is

Eq. 2
U-Factor (Thermal Transmittance)
U = ( U_cg A_cg + U_eg A_eg + U_t A_f ) / A_pf

where

cg = center of glass
eg = edge of glass
f = frame

References

ASHRAE Handbook - Refrigeration, ASHRAE: 2014.

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