Mathematical Computing of Coniferous Tree Ignition by the Cloud-to-Ground Lightning Discharge using Joule-Lenz's Law

Abstract

The natural phenomenon of thunderstorm activity is one of many causes of a forest fire. Thunderstorms cause especially intensive fire danger situations within remote areas and highlands. As a rule, a cloud-to-ground lightning discharge is the fire source. The present study is based on the research results of electrical overloads in supply networks. Physical and mathematical formulation and numerical solution for the problem of a coniferous tree (pine) ignited by a cloud-to-ground lightning discharge are presented. The problem is considered in a cylindrical coordinate system in two-dimensional formulation. The features of current passage and heat transfer taking into account the reactive wood localization are investigated. The Joule-Lenz’s law is used to calculate heat production in a tree trunk. Parametric analysis has been conducted and tree trunk ignition conditions have been determined in a typical range for the influencing parameters of negative and positive discharges.