MATHEMATICAL MODELLING FOR ANALYSING FIRE SPREAD IN A REAL-TIME COUPLED ATMOSPHERIC WILDLAND FIRE

Abstract

Wildland fire spread is one of the most challenging problems faced by reserved or unreserved vegetation in many developed and developing nations, because it can lead to serious environmental hazards in claiming lives, properties, animals and some other valuable treasures. This thesis establishes an approximate analytical solution that is capable of analysing fire spread in a real-time coupled atmospheric wildland fire, in determining the effect of temperature, oxygen concentration, volume fraction of dry organic substance, volume fraction of moisture and volume fraction of coke. The analytical solution is obtained via direct integration and eigenfunction expansion technique, which depicts the influence of the parameters involved in the system. The effect of change in parameters values such as Frank-Kamenetskii number, Radiation number, Peclet energy number, Peclet mass number, Activation energy number and Equilibrium wind velocity are presented graphically and discussed. The results obtained show that Frank-Kamenetskii number reduces the temperature. Radiation number and Peclet energy number reduces the temperature, oxygen concentration and volume fraction of coke while they enhances volume fractions of dry organic substance and moisture. Activation energy number reduces the temperature and volume fraction of coke while it enhances volume fractions of dry organic substance and moisture. Also, Peclet mass number and Equilibrium wind velocity both enhance oxygen concentration. The inference drawn from this is that an increase in Radiation number will remove heat from the burning scene. Similarly, reducing wind velocity will limit the oxygen contact with fuel. With continuous supply of heat, the ignition of additional fuel will continue as long as there is enough oxygen present. Thus, it is obvious that these three elements (heat, fuel and oxygen) must be present before combustion can occur. Varying anyone of the elements will vary the intensity or otherwise of the fire. Armed with this knowledge, the fire fighters are better equipped to manage fire.