We have used simple, basic heat transfer equations to estimate peak roof temperatures, based on the assumptions listed below. Lower peak roof temperatures contribute less thermal stress, and likely lead to longer roof lifetimes in some systems. Actually, we estimate and tabulate the maximum temperature rise above ambient air temperature. To obtain the absolute maximum roof temperature, add the maximum temperature rise in the table to your estimate of the maximum air temperature.
Assumptions are:
The maximum roof temperature is primarily determined by external heat transfers (as, for example, for an insulated roof.)
Heat storage effects in the roof are neglected. (Heat storage, as for example, in a concrete roof, does reduce peak roof temperatures, but the offset air conditioning load tends to appear in the evening hours, as heat is released from storage.)
Solar flux is Io = 1 kW per square meter of roof.
Sky temperature is 10 deg. C (18 deg. F)!
below air temperature.
The heat transfer coefficient for infrared radiative cooling is hr = 6.1 W /(sq. meter . deg. C) times the thermal emittance (this parameter is derived from the Stefan-Boltzmann constant).
The maximum temperature rise of an exposed black surface (solar reflectance = 0.05, infrared emittance = 0.90) is 50 deg. C (90 deg. F). This number is based on observations by a number of observers of the maximum temperature rise of black surfaces in full sun and with low wind speed. The uncertainty in this number is roughly 30%. This assumption allows us to mathematically solve for the heat transfer coefficient for roof cooling by convection, which is then found to be hc = 12.4 W/(sq. meter . deg. C). This is in the range that would be expected if we simply estimated this parameter from engineering textbooks on heat transfer. The weak temperature dependence of this parameter is henceforth neglected.
With these assumptions the heat transfer equatio!
n reads
(1-R)Io = (hc + hr) (max. temp. rise) + hr (10!
deg. C)
,
where R is the solar reflectance, and 10 deg. C is the sky temperature depression below air temperature. Thus the maximum temperature rise is found by solving this equation for each material, using the solar reflectance and infrared emittance values from the tables.
Materials with the highest SRI values are the coolest choices for roofing. Due to the way SRI is defined, particularly hot materials can even take slightly negative values, and particularly cool materials can even exceed 100.
