The flashback or propagation of premixed flames along the near-wall low-velocity region at the base of a laminar boundary layer of a reactive mixture has been studied numerically. The analysis, carded out using the constant density approximation for an Arrhenius overall reaction, accounts for the effects of the Lewis number of the fuel. The flow field, as seen by an observer moving with file front, includes the unknown flame front velocity U relative to the wall and the linear velocity gradient A at the base of the boundary layer. Due to this gradient, the flame front is curved with a radius of curvature lF = SL/A, proportional to the planar flame velocity SL. The front velocity is changed from SL by a factor which depends on the Karlovitz number, or non-dimensional wall velocity gradient, defined as the ratio between the thickness of the planar flame and the front curvature lF. The front velocity has been calculated in the limiting cases of adiabatic and isothermal walls. The front velocity changes from negative to positive when the Karlovitz number decreases below a critical value, determining the onset of flashback. This critical value, which decreases when the Lewis number of the fuel increases, is smaller for isothermal than for adiabatic walls. In this second case, when the flame is not quenched close to the wall, flashback is prevented by flame stretch associated with flame curvature.
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