Radiative Heat Transfer for Structural Members Exposed to Fire: An Analytical Approach
An analytical approach, as a reduced form of the more general multi-flux and discrete ordinates method for radiative transfer, is proposed in this article with clarified theoretical basis. The main assumption inherent in the proposed method is that the radiation intensities along positive and negative paths are isotropic and have constant values in each direction. A realistic nonisothermal absorbing/emitting medium with isotropic scattering is analytically treated between fire sources and structural members. General energy equations, including possible heat generation within the medium, can be adopted to solve for radiative flux and temperature distribution along the radiation path. The usage of the 'optical length' can readily incorporate the compound and realistic extinction coefficient of a participating medium, including gas and particle absorption and particle scattering effects. Application of the proposed method to temperature predictions of unprotected steel members in fire yields good accuracy and reliable stability, especially for those with large section factors.