Modeling Fire Spread in a Real-Time Coupled Atmospheric- Vegetation Fire: An Analytical Approach
Authors
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Zhiri, A. B.
Department of Mathematics, Federal University of Technology, Minna. Nigeria.
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Olayiwola, R. O.
Department of Mathematics, Federal University of Technology, Minna. Nigeria.
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Yavalah, D. W.
Department of Mathematics Federal University Wukari, Taraba, Nigeria
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Ode, C. E.
Department of Mathematics, Federal Polytechnic, Bida, Nigeria
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Adebayo, H. O.
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Abstract
The ability to analyse the rate of fire spread outbreak in a real-time coupled Atmospheric-vegetation fire has become increasingly vital as forest fire fighters are building diverse kinds of models to combat the dangers/effects of fire spread across a given fire vicinity. This paper theoretically examines the analysis of fire spread in a real fire environment. A partial differential equations (PDE) governing the phenomenon is presented. The analytical solution of the model is obtained via direct integration and eigenfunction expansion technique, which displays the influence of the parameters involved in the system. The effect of change in parameters such as Frank-Kamenetskii number, Radiation number, Peclet energy number and Activation energy number are presented graphically and discussed. The results obtained show that Frank- Kamenetskii number, Radiation number, Peclet energy number, and Activation energy number all reduced transient state temperature.
Keywords: Combustion, Crown fires, Fire spread, Forest fire, Ground fire, Spotting fire