Solving of the integral model equations of fire at its prolonged duration
DOI:
https://doi.org/10.33408/2519-237X.2017.1-1.18Keywords:
compartment fire, integral model of fire, program in the system MathematicaAbstract
Purpose. The aim of the paper is to analyze the leading equations of the integral model of the fire in the compartment for prolonged time.
Methods. The approaches for solving of the ordinary differential equation were used.
Findings. It has been noted that the exponential dependence of the temperature on the mass of the fire load (divide to air mass in the compartment), m, which is used for the initial stage of the fire, gives too rapid rise already at this stage and cannot be extrapolated to prolonged fire for time more than some minutes. The equation for dynamics of relative gas medium density ρ/ρ0 has been formulated in terms of the parameters m′, q, and p which represent the rate of fire load burning, combustion heat and a combination of the geometric dimensions of the compartment and opening, respectively.
Application field of research. The obtained results can be used for calculation of fire hazards both in the compartment with fire and adjacent compartment.
Conclusions. The leading equations of the integral model of fire in the compartment for prolonged stage have been analyzed. A program to solve corresponding equation using Mathematica 9 system has been written.
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