An analytical model based on radiative heating for the determination of safety distances for wildland fires

In a wildfire, radiative heat transfer is often the main thermal impact on people fighting the fire or on structures. Thus, the estimation of the radiation from the fire front and the heating of a target is of primary importance for forest and urban managers. An analytical formulation of this radiative heat transfer, based on a solid-flame assumption, is used. The realistic description of finite fire-front widths allows the proposal of a new criterion for the estimation of the radiative impact of the fire, which is based on the ratio of the fire-front width to the flame length, which is opposite to the classical approach of considering only the flame length. A numerical solution is necessary to calculate the safety distance for a fixed radiative threshold value, so an analytical approximation is proposed to obtain a simple and useful formulation of this Acceptable Safety Distance. A sensitivity analysis is conducted on the different physical and geometrical parameters used to define the flame front. This analysis shows that the flame temperature is the most sensitive parameter. The results of the analytical model are compared with the numerical solution of the flame model and previous approaches based only on flame length. The results show that the analytical model is a good approximation of the numerical approach and displays realistic estimations of the Acceptable Safety Distance for different fire-front characteristics.

► Acceptable Safety Distances are expressed by a simple analytical model.
► We proposed a new criterion to estimate the radiative impact of a fire.
► Good correlations are obtained between analytical model and numerical solutions.
► The most sensitive parameter is the flame temperature.