The process of ablation often forms a key part in many mathematical models describing the combustion of a solid-phase fuel. The phrase was 5rst used to describe the thermal erosion of glaciers over 140 years ago. In recent times it has been applied to the thermal degradation of a solid when exposed to a large 6ux of heat. Two fundamental assumptions in the treatment are that mass is lost only from surface regions and that the temperature of the surface remains constant throughout the period of mass loss. The two critical parameters in this model are the critical temperature T p at which mass loss occurs and the heat required to convert matter from solid to gas at temperature T p .
In this paper we report mathematical models designed to simulate the loss of mass of a solid fuel (such as polyethylene) in cone calorimeter experiments. The models do not compromise on the thermal properties of the solid fuel or the heat loss mechanisms and consequently they require a numerical method of solution. Initially we explore a relatively simple ablation-based model. Although conceptually simple in approach, the model reproduces many qualitative features observed in experiments. We go on to consider a di4erent approach, where the thermal degradation of the solid is governed by a set of kinetic rate laws. We show that this approach removes many of the unrealistic features and assumptions of ablation-based models. Furthermore, we demonstrate that the agreement between theory and experiment is improved by this approach. We also show how the mathematical models may be used as aids in the interpretation of cone calorimeter data. For example, we show that a steady state measurement of mass loss rate is a more reliable indicator of a material response than a peak measurement. In fact we show how peak measurements are strongly a4ected by the thermal properties of the sample holder, but steady state measurements are insensitive to the particular choice of sample holder.