The Emmons problem: Role of an impermeable leading segment

While the presence of an impermeable leading segment is normally inevitable for a boundary layer diffusion flame established over a fuel surface, it also offers an opportunity to control and stabilize the flame by design. In this study, the classical Emmons’ problem with an impermeable leading section is investigated numerically and theoretically. The local similarity structure of the boundary layer is discussed and an explicit solution of the skin friction, local gasification rate, and flame characteristics is derived. It is shown that the existence of an impermeable leading section of length L reduces the skin friction and the gasification rate, while increases the flame height in the fuel plate section. This history effect of the flow on the boundary layer development is reduced as the streamwise distance, x, increases, and is negligible for x/L[Formula presented]10. The theoretical results agree well with the numerical results, both qualitatively and quantitatively.