Theoretical Model of Transient Regression of Thermoplastic Materials During Flame Spread: Vaporization; Permanent Mass Loss; Surface Shape

ABSTRACT This article examines a transient, one‐dimensional model of surface regression during opposed flow flame spread over finite thickness, non‐charring thermoplastics. Gas to solid conductive transfer from the flame drives sample heating. The solid degrades into volatile fuel molecules in two stages: (1) the pre‐vaporization heat‐up stage and (2) the vaporization/regression stage. The influence of the external (flame) heat flux on heat‐up and regression is examined. Regression stalls eventually because the sample bottom temperature, which is fixed, is lower than the sample top vaporization temperature. The moving boundary value problem is described by the energy equation subject to a variable top surface energetic boundary condition. The energy flux from the external source (flame) is taken as constant. The regressing solid is transformed to a fixed‐domain coordinate system in which it is coupled, nonlinearly, to the energetic boundary condition. This nonlinear system is solved numerically. Term‐by‐term evaluation of the numerical solution allows development of analytical energy balance formulas in the short and long time intervals of the regression stage. A physics based Peclet number analysis describes features of time dependent surface regression.