Mathematical simulation of the impact of forest fire front on the enclosing structures of wooden building in rural settlement

Introduction. Forest fires lead to economic damage to the state, for example, damage and destruction of civil and in­dustrial buildings in rural areas. The purpose of the study is to develop physical and mathematical models of the forest fire front impact on the building enclosures. Research objectives: 1) formulation of physical and mathe­matical models; 2) software implementation of a mathematical model in a high-level programming language; 3) numerical study of heat transfer processes in building enclosures.

Methods. A low-intensity surface forest fire, a high-intensity surface forest fire, a crown forest fire, and a fire storm are considered. An element of a two-layer enclosing structure of a wooden building with a window opening is considered. The effect of convective heat flow is considered. Heat transfer processes in the building enclosures are described by a system of non-stationary heat conduction equations with the corresponding initial and boundary conditions. Two-­dimensional heat equations were solved using the locally one-dimensional method. For numerical implementation of the presented mathematical model, the finite difference method was used. Difference analogues of partial differential equations are solved by the marching method.

Results and discussion. Temperature distributions in a structurally inhomogeneous element of the building enclosures were obtained. The analysis shows that the temperature fields are almost the same for different seasons of forest fires. The noticeable difference is only near the contact of the enclosing structure with the soil. In general, higher temperatures are observed in the upper part of the building enclosures at the border with the roof of the building. The glass in the window opening is heated up to sufficiently high temperatures. This will lead to its destruction during the period of exposure to the forest fire front. The window opening is the most vulnerable area to flame in the building enclosures. In addition, as a result of numerical modelling, it was established that maximum temperature gradients occur in the cladding material.

Conclusion. Recommendations are proposed for improving the fire safety of buildings in rural areas and the application of the proposed physical and mathematical model were suggested.

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