Transient Heat Conduction in a Wall Exposed to a Fire: an Analytic Approach

Fire safety engineering requires a detailed understanding of fire behaviour and of its effects on structures and people. Currently, advanced numerical codes for the prediction of the fire behaviour are available. However, they often require heavy calculations and long times. In this context analytical solutions can be useful for a fast analysis of simplified schematizations. It allows a more effective final utilization of the advanced fire codes. In this contribution, for a separation wall exposed to a fire the temperature history is analysed of the unexposed wall surface. Due to the limitations of the model, the temperature in the fire room changes stepwise, with a final value typical of a post-flashover condition. Nevertheless, with an appropriate choice of the heat transfer coefficient, the thermal action on the surface exposed to fire becomes that due to a fire following the standard temperature-time curve. The solution is then obtained by applying the separation of variables to the heat conduction equation. The problem is made dimensionless and the results are analysed in order to validate their significance. This simplified model allows to obtain useful information on the magnitude of the temperature reached.