Thermal-ignition Analysis in a Boundary Layer on a Hot Plate with an Unheated Inlet Section

The problem of thermal-ignition on a boundary-layer at a hot plate with an unheated inlet has been considered, and a local similar solution is derived. An explicit expression for the minimum ignition distance has been derived by using matched asymptotic analysis in the realistic limit of large activation energy. The unheated inlet section can reduce the flow velocity at the boundary-layer of the inlet of heating section, and then lead to easily ignited. It is shown that when the ratio between the length of unheated inlet section L_χ and the ignition distance on a isothermal hot plate χ I is large enough, the ignition distance χ_L,I is inversely proportional to the square root of L_χ. According to numerical results, the difference between the local similar solutions is less than 5% when χI=L_χ < 3. Although attention in this paper is confined to the flat-plate problem, it should be noted that this analytical method can be applied to more general cases, such as wedge flow ignition problems.