Integral solution of a buoyant diffusion flame

Measurements of the rate of ambient air entrainment by axisymmetric diffusion flames suggest that entrainment occurs at a wrinkled laminar flame front in the lower regions of visible flame (Ref. 1). Entrainment of such flames requires a solution of the axisymmetric steady laminar diffusion flame which does not yield a self-similar solution. If one then considers the simple case of steady plane diffusion flame in semi-infinite fuel and oxidizer media separated by a flame sheet, an exact similarity solution can be obtained from equations of motion, energy and species conservation equations. This solution can also incorporate the differences in fuel and oxidizer densities resulting from either molecular weight differences or the temperature differences of oxidizer and fuel media. This problem was treated by G. C. Fleming and F. E. Marble to investigate the stability of such a flame front to periodic disturbances (Ref. 2). Inspired by their study, we chose to develop an integral solution to the same problem by appropriate selection of velocity, temperature and species profiles.