Semi-Analytical Treatment of Wall Heat Transfer Coupled to a Numerical Simulation Model of Fire

Abstract

This analysis focuses on the importance of accurate description of walls' thermal behavior with particular relevance to fire safety cases. To accurately predict thermal loads on the walls in a complex fire situation, time dependent phenomena of thermal convection, diffusion, radiation, and heat transfer across the wall have to be taken into account. The heat transfer across the walls is often neglected as it requires fine grid resolution to approximate large temperature gradients. The analysis shows that this can lead to substantial errors and proposes a transient semi-analytical approximation of thermal wall behavior. Unsteady heat diffusion equation is solved by semi-analytical approximation of a temperature profile in a wall. The temperature profile is approximated in each time step and for each wall grid node separately using the temperature at the wall internal side and Biot number at the external side for boundary conditions. Wall heat transfer coefficient is calculated as a temperature profile derivative and then used in the coupled numerical model of the fire. The semi-analytical approach does not rely on a discretization procedure and the accuracy of its solutions is independent of grid spacing. Therefore, such semi-analytical technique is computationally less expensive and especially attractive for long transient calculations.

The present work was performed as a part of the project Under-Ventilated Compartments Fires (FIRENET) (Co. no. HPRN-CT-2002-00197). The project is supported by the EU Research Training Network FP5, which is gratefully acknowledged.