A theoretical model to calculate the thermal radiation from localized fire to vertical surfaces located inside and outside the flame

Abstract

This paper presents a theoretical model to calculate the radiative heat fluxes from localized fires to vertical surfaces. The fire volume is modeled as a series of concentric hollow cylinders (CHCs), each treated as an isothermal graybody with uniform height and width. New methods for determining the emissivity of individual CHC elements, as well as the view factors and transmissivity between each CHC and the target surface, are introduced. The radiative contributions from each CHC element using a simplified view factor approach and incorporating transmissive radiation losses through Beer's law and Kirchoff's law to account for medium absorption. The proposed model is validated against experimental data from the literature and verified through three-dimensional (3D) simulations using the Fire Dynamics Simulator (FDS). Comparisons with experimental data and simulation results indicate that the model provides conservative and reliable predictions for vertical surfaces both inside and outside the flame. Compared to the other classic flame models, the proposed model demonstrates improved accuracy outside the flame. Furthermore, the model fills a critical methodological gap by enabling the calculation of radiative heat fluxes not only on vertical surfaces within the flame but also on vertical surfaces with arbitrary normal directions at any position in space. This makes the model a valuable tool for advancing structural fire engineering design and risk assessment in localized fire scenarios.