Oxygen index methods are widely used to measure the flammability of polymers and to investigate the effectiveness of fire-retardants. Using a dynamical systems model an oxygen index is identified with an extinction limit point. The action of the fire-retardant is investigated by unfolding this bifurcation point with a suitable continuation parameter which reflects the mode of action of the additive. The fire retardant mechanisms that we consider are non-competitive char-formation and dilution by addition of an inert filler. We investigate which types of material are best retarded by each mechanism.
M.I. Nelson. A dynamical systems model of the limiting oxygen index test. II Retardancy due to char-formation and addition of inert fillers. Combustion Theory and Modelling, 5(1):59-83, March 2001.
Microwave heating of porous solid materials has received considerable attention in recent years because of its widespread use in industry. In this study, the microwave power absorption term is modelled as the product of an exponential temperature function with a function that decays exponentially with distance. The latter describes the penetration of the material by the microwaves.
We investigate the phenomena of multiplicity in class A geometries, paying particular attention to how the penetration function effects the behaviour of the system. We explain why the phase-plane techniques which have been used in the case when the penetration term is constant do not extend to non-constant penetration.
M.I. Nelson, G.C. Wake, X.D. Chen, and E. Balakrishnan. Microwave heating of porous solids --- stability, power absorption function and multiplicity: I Infinite biot number and small penetration depth. ANZIAM Journal, 43(1): 87-103, 2001.
Oxygen index methods have been widely used to measure the flammability of polymeric materials and to investigate the effectiveness of fire-retardants. Using a dynamical systems framework we show how a limiting oxygen index can be identified with an appropriate bifurcation.
The effectiveness of fire-retardants in changing the limiting oxygen index is calculated by unfolding the bifurcation point with a suitable non-dimensionalised variable, which depends upon the mode of action of the additive. In order to use this procedure it is essential the model is non-dimensionalised so as to retain the variables of interest as distinct continuation parameters.
M.I. Nelson, H.S. Sidhu, R.O. Weber, and G.N. Mercer. dynamical systems model of the limiting oxygen index test. ANZIAM Journal, 43(1): 105-117, 2001.
The combustion of thermoplastics is modelled using a critical mass flux hypothesis as the ignition and extinction criteria. a featured neglected by most authors, is included. Polymer degradation is modelled as a single-step first order Arrhenius reaction term. A simple model for mass transport of polymer through the sample during pyrolysis is included. The degradation products are assumed to move out of the polymer instantaneously. The model consists of a nonlinear integral-differential advection-diffusion equation for the temperature in the thermoplastic, coupled to an ordinary differential equation, for the regression rate. Results are presented which quantify the effect that the thickness of the test sample has on the mass loss rate, or equivalently heat release rate, curve. From these we conclude that thermally thick samples are characterised by a region of steady burning which is independent of the initial sample thickness. The test method that we have in mind is the cone calorimeter.
J.E.J. Staggs and M.I. Nelson. A critical mass flux model for the flammability of thermoplastics. Combustion Theory and Modelling, 5(3), 399-427, September 2001.
The use of microwave heating to initiate combustion synthesis has been increasingly investigated in recent years because of its advantages over traditional methods. A simple mathematical model is used to model these experiments. The microwave power absorption term is modelled as the product of an Arrhenius reaction term with a function that decays exponentially with distance. The former represents the temperature-dependent absorption of the microwaves whereas the latter describes the penetration of the material by the microwaves. Combustion kinetics are modelled as a first-order Arrhenius reaction.
E. Balakrishnan, M.I. Nelson and X.D. Chen. Microwave assisted ignition to achieve combustion synthesis Journals of Applied Mathematics and Decision Sciences, 5(3): 151-164, September 2001.
The burning behaviour of thermally thin materials with high characteristic temperature is investigated using a previously developed dynamical systems model. Regimes of particular interest from the viewpoint of fire-retardancy are identified and exhibited in steady-state diagrams. We explain how regimes of practical interest can be identified from the limit-point bifurcation diagram and use this to determine the region of existence of these regimes as a function of the pyrolysis kinetics. This methodology provides a framework for the systematic investigation into the effectiveness of fire-retardants.
M.I. Nelson. Thermally thin materials with enhanced fire-resistant properties: A dynamical systems model. Combustion Science and Technology, 167: 82-112, 2001.