On the stability of one-dimensional diffusion flames established between plane, parallel, porous walls

A one-dimensional, non-premixed flame stability analysis is undertaken. Oscillatory and cellular flame instabilities are identified by a careful study of the numerically calculated eigenvalues of the linearized system of equations. The numerical investigation details the critical locations for changes in flame behaviour, as well as the critical values of various parameters that affect flame stability. A critical Lewis number, greater than unity, is identified as the value where unstable oscillations may begin to appear (Le > Lec) and for which cellular flames can exist (Le < Lec). Some prior discussions are clarified regarding the aforementioned critical values, as well as the role of convection in producing flame instabilities. The methodology of the stability analysis is discussed in detail.