API 521 has provided a fire radiation model that is often used in flare and other types of fire modeling

$$ q_{absorbent} = \sigma(\alpha_{surface} \cdot \varepsilon_{fire} \cdot T^4_{fire} - \varepsilon_{surface} - T^4_{surface}) + h(T_{gas} - T_{surface}) $$

$q_{absorbent}$ absorbed heat flux from the fire ($Wm^{-2}$ or $Btu \text{ } h^{-1}ft^{-2}$)
$\sigma$ Stefan-Blotzmann constant ($5.67\mathrm{e}{\text{-}8}$   $Wm^{-2}K^{-4}$   or   $0.1713e{\text{-}8}$   $Btu\text{ }h^{-1}ft^{-2}{^{\circ}R}^{-4}$)
$\alpha_{surface}$ equipment absorptivity (dimensionless)
$\varepsilon_{fire}$ fire emissivity (dimensionless)
$\varepsilon_{surface}$ surface emissivity (dimensionless)
$T_{fire}$ fire temperature ($K$ or ${^{\circ}R}$)
$T_{surface}$ equipment temperature ($K$ or ${^{\circ}R}$)
$h$ convective heat transfer coefficient fo air/fire in contact with the equipment ($Wm^{-2}K^{-1}$ or $Btu\text{ }h^{-1}ft^{-2}{^{\circ}R}^{-1}$)
$T_{gas}$ temperature of air/fire in contact with equipment surface ($K$ or ${^{\circ}R}$)

References

  1. API STD 521 (2014), Pressure Relieving and Depressuring Systems, 6th Edition, American Petroleum Institute.