Surface temperature calculation model in SRI calculation (ASTM E1980)

As discussed in What is SRI, solar reflectance index (SRI) can be understood as the surface temperature on a 0 – 100 scale. We have an online SRI calculator, which calculates the surface temperatures and SRIs under 3 standard conditions. This post aims to explain the surface temperature calculation model in SRI calculation according to ASTM E1980.

Surface temperature calculation model

Below is the surface temperature calculation model in ASTM E1980.

The absorbed solar radiation (the term on the left hand side) is splitted to 3 components:

  • Low-wave radiation to sky (the first term on the right hand side)
  • Convection to air (the second term on the right hand side)
  • Conduction to materials beneath the surface (ignored)

For the quantities in the equation below:

  • Solar absorptance (α) and emissivity (ε) are material properties (tested in the laboratory)
  • Solar flux (I), sky temperature (Tsky), convective coefficient (hc), air temperature (Ta) are the standard conditions defined in ASTM E1980
  • Stefan Boltzman constant (σ) is a constant [5.66961 × 10-8 W/(m2K4)]
  • Surface temperature (Ts) is the unknown to be solved

The equation can be solved iteratively to get the surface temperature. ASTM E1980 also provides an alternative solution to the equation.

Standard conditions

For the standard conditions, the following are defined in ASTM E1980:

  • Solar flux (I): 1000 W/m2
  • Sky temperature (Tsky): 300 K
  • Air temperature (Ta): 310 K
  • Convective coefficient (hc): 5, 12, or 30 W/(m2K), corresponding to low-, medium- and high-wind conditions

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