Geometric effect of radiative heat exchange in concave structure with application to heating of steel I-sections in fire

In structural fire engineering, it is well-known that the radiative heat exchange in unprotected steel I-section is attenuated due to geometric effect. An analytical approach to formulate the geometric effect by employing view factors is presented in this paper for concave structures in general. In particular, the exact solution is extended to predict the net radiation flux and the temperature evolution for unprotected steel I-sections in fire, which are fully characterized by the I-section aspect (width-to-depth) ratio. The proposed method is validated by comparison to the conventional model in Eurocode 3, as well as to experimental investigations. The method predicts the transient temperature field inside the I-sections with reasonable accuracy, while Eurocode provision yields over-estimations. Besides, the effective emissivity is found to be insensitive to temperature, but rather controlled by the section aspect ratio.