A simplified analytical approach for the clear height in compartment fire based on a two-layer zone model

Compartment fire is an important research area in fire science and fire safety. Owing to its simplicity, the zone model remains attractive in studying compartment fire. Although computer software packages for the two-layer zone are in popular use, a basic understanding of the physical phenomena involved and the mathematical formulation thereon would benefit users of the zone model in terms of critical judgement of software outputs, which could be unreasonable, and insight of the general trends of important variables. In general, the differential equations based on a two-layer zone model have no analytical solutions and numerical methods are required. However, stiffness is present in using numerical methods to solve these differential equations, and reliable results are obtained only when very small time steps are used in computation. Nevertheless, in some special cases, analytical solution for the clear height in the zone model exists, as demonstrated in the present study. Predicted values of smoke layer height in the present approach are shown to be in good agreement with experimental results reported in the literature. The present work would provide insight into the tenability condition of a compartment on fire and is an important issue in fire safety management.