Flame propagation in a closed channel with cold side walls

On the basis of complete nonsteady two-dimensional equations describing the motion of a reactive gas we have obtained a solution for the problem of flame propagation in a plane channel with cold side walls. We study in detail the process of flame quenching. The values of the critical Peclet numbers have been determined both numerically and analytically. We have ascertained the quantitative relationships governing flame propagation in the absence of quenching.