On Fractional Differential Equations Describing Fire Flashover

Abstract

It is demonstrated that compartment fire flashover can be described by non-linear dynamical model with two-dimensional phase space. System evolution is governed by two equations one of which is fractional differential and another ordinary differential.Relevant physical background is discussed in the course of the model development. The problem of paramount theoretical and practical interest is to separate two different behavior types of the system, that is quasi steady-state (controlled) fires and flashover (uncontrolled) fires. It is demonstrated that such a problem can be solved by quantitative analysis of presented set or equations, without resorting to their exact solutions. Critical conditions for compartment fire flashover are explicitly derived in much more general form compared to earlier studies.