Vertical wall fire in a stratified ambient atmosphere

A mathematical model is presented for understanding the characteristics of a burning vertical wall immersed in a quiescent ambient atmosphere having nonuniform vertical distributions of temperature and oxidizer mass fraction. Such a stratified atmosphere occurs, for example, in the case of a room or aircraft cabin on fire. A set of partial differential equations and suitable boundary conditions describing a laminar boundary layer flow of exothermically reacting gases is solved using a finite difference method. Results for the local burning rate and maximum vertical velocity in the boundary layer are presented for many different cases of nonuniform ambient temperature and ambient oxidizer mass fraction. A comparison of these results with the results for the nonstratified atmosphere shows that the predicted burning rate for a thermally stratified case behaves like a linear combination of results for corresponding nonstratified cases; however, this is not true for compositionwise stratified cases. The stratification has a substantial effect on the velocity in the boundary layer.