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A Study on Mathematical Modeling for Analyzing Real-Time Coupled Atmospheric Wildland Fire Spread
Abstract:
The propagation of wildland fires poses significant challenges to both reserved and unreserved vegetation in various developed and developing nations. The consequences of fire spread encompass severe environmental hazards, including the loss of human lives, property, animals, and valuable resources. This research introduces an approximate analytical solution to real-time coupled atmospheric wildland fire analysis. The solution investigates the impact of crucial variables such as temperature, oxygen concentration, volume fractions of dry organic matter, moisture, and coke.
The analytical solution is derived through a combination of direct integration and eigenfunction expansion techniques, revealing the intricate interplay among the system’s parameters. By assessing changes in parameters such as the Frank-Kamenetskii number, Radiation number, Peclet energy number, Peclet mass number, Activation energy number, and Equilibrium wind velocity, this study presents graphical representations and comprehensive discussions.
The findings unveil that the Frank-Kamenetskii number correlates with temperature reduction, while the Radiation number and Peclet energy number lead to decreases in temperature, oxygen concentration, and volume fraction of coke, while increasing volume fractions of dry organic matter and moisture. The Activation energy number, on the other hand, diminishes temperature and volume fraction of coke, while enhancing volume fractions of dry organic matter and moisture. Moreover, both the Peclet mass number and Equilibrium wind velocity amplify oxygen concentration.
These observations underscore crucial insights: increasing the Radiation number extracts heat from the combustion zone, and decreasing wind velocity restricts oxygen availability to the fuel. Sustained fuel ignition depends on the continuous supply of heat and adequate oxygen. This trio of elements—heat, fuel, and oxygen—must coexist for combustion to transpire. Modulating any of these elements alters the fire’s intensity. Equipped with this understanding, firefighters are better prepared to effectively manage wildfires
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