Mathematical and Computer Model of the Tree Crown Ignition Process from a Mobile Grassroots Fire

Abstract

Forest fires cause great damage to the environment and are difficult to predict and eliminate. Mathematical models of temperature regimes of forest fires can create a scientific basis for improving the effectiveness of firefighting measures. The study of fire propagation processes and temperature regimes during a fire is an urgent task that many researchers are engaged in. The processes of heat exchange in the process of fire are very complex and include many factors. For this reason, they are difficult to model. The equations of heat transfer processes themselves are also difficult to solve and obtain analytical solutions.The aim of this work is to create a mathematical model of the ignition of a needle from the flame of a moving ground fire. The solution of the set tasks was carried out by the method of direct integration.The model of the process of heating the lower part of the tree crown due to the moving grass fire described in this paper has the advantage that it is based on mathematical calculations that can be easily performed using the mathematical software package Maple. The program in the Maple package is offered, which, depending on the input data: the size of the fire area, the speed of fire spread, the distance from the ground to the bottom of the crown, calculates the air temperature. These results can be used to calculate and assess the operational situation during forest fires.