On the flame shape in diffusion combustion of a liquid fuel film on a substrate

In this paper, we consider the classical Burke–Schumann problem as applied to the construction of a mathematical model of a diffusion flame spreading over a fuel film deposited on a thin substrate. This formulation is used to model the combustion of a gaseous fuel flowing from a thin slot (half-width $x_{in}$ and mixed with oxidizer flowing from a parallel slot (with the outer boundary $x_{out}$). The key parameters determining the position of the flame front in the space are identified: the Peclet number Pe, the stoichiometric parameter $A$ dependent on the equivalence ratio, and the geometric parameter $X_{in}=x_{in}/x_{out}$. The dependences of the flame length on these parameters, including $x_{out}\to\infty$, are analyzed. Comparison shows good agreement between calculated and experimental