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 equation 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.