A new approach to modeling heat transfer in compartment fires

Abstract Heat transfer models most often used in fire engineering practice to predict the temperature of structural elements exposed to fires in compartments adopt a radiation component which assumes that the fire is separated from the surrounding surfaces by perfectly transparent media. As a result the predicted temperatures usually differ significantly from the measured values. This paper describes a relatively simple heat transfer model which accounts for the emission and absorption of radiation by some of the combustion products of simulated real fires using wood as fuel. The model is validated by comparing the predicted results with published data of experimentally observed temperatures of unprotected structures with different sizes exposed to fires of different severities in a compartment. Good correlation between calculated and observed temperatures are obtained for the majority of cases under consideration. Notation A area, m2 E total emissive power, W/m2 F transfer factor, dimensionless F i-k shape (view)factor for radiation from surface i to surface k, dimensionless P perimeter of a structural element exposed to fire, m P/A s massivity, m-1 T temperature, K V volume, m3 a/f air-to-fuel ratio c p specific heat at constant pressure, J/kg K h coefficient of convective heat transfer, W/m2 K q heat flux, W/m2 t time, s x mass fraction of a chemical constituent in liquid or solid fuels Greek letters α total absorptivity e total emissivity θ temperature, °C ρ density, kg/m3 σ Stefan–Boltzmann constant, W/m2 K4 Subscripts and superscripts b black body c carbon, convective g gas h hydrogen i surface i k surface k o oxygen s enclosure inner surface, steel, stoichiometric v volumetric