New formula for calculating time to ignition of semi‐infinite solids

An analytical closed form formula is presented for explicitly calculating time to reach ignition temperature of semi-infinite solids exposed to constant incident radiation and gas temperature as for example in the cone calorimeter. The non-linear boundary condition due to the emitted radiation from the surface being proportional to the surface temperature raised to the fourth power according to the Stephan-Boltzmann law is accurately considered. The formula works for a wide range of the parameter values like the thermal inertia of the solid, the emissivity of the exposed surface and the convective heat transfer coefficient. They are all assumed constant. The new formula contains a single constant coefficient, which has been derived by comparing results obtained by accurate numerical finite element simulations using two different codes, comsol and TASEF, as well as calculations based on a Duhamel superposition scheme. Thus, the formula can be classified as semi-empirical. It offers a simple approximate solution of a non-linear problem that requires cumbersome numerical calculation methods to obtain more exact results. Any exact analytical solution is not available. The new method is carefully verified by comparisons with numerical solutions. However, as it is an analysis of well-defined theoretical methods, any validation and comparisons with test data are not required and has therefore not been made.In comparison with other similar approximation formulas found in the literature, the accuracy as well as simplicity of applying the new formula is outstanding. Copyright (c) 2015 John Wiley & Sons, Ltd.