In the following:
We use a critical mass flux model, to evaluate the flammability properties of thermally thin polymeric materials in radiative ignition experiments (such as the cone calorimeter). We also investigate the retardancy effect of inert, `glassy' and 'foamy' additives on the flammability properties of the polymer.
N. Waterhouseu, H.S. Sidhu, and M.I. Nelson. Polymer Combustion: The Critical Mass Flux Model. In M. Pemberton, I. Turner, and P. Jacobs, editors, EMAC 2002 Proceedings, pages 231--236. The Institution of Engineers, Australia, 2002. ISSN 1447-378X.
At MISG 2002, winemaker Beringer-Blass asked for several for a model of the open vat fermentation process used for making red wine. The quality and the character of the red wines rely partly on polyphenolic compounds that are contained within the grape skins and which are extracted during the fermentation process, contributing to the final colour flavour and texture. This is one example of a possible new and fruitful area for the application of classical applied mathematics. In this paper we will briefly outline the entire production process and identify where mathematical modelling has already been used and where it is still to be applied. The fermentation process and the extraction of polyphenolic compounds will be discussed in more detail to illustrate the utility of such modelling.
R.O. Weber, M.I. Nelson and S. Guy. Modelling wine production. In M. Pemberton, I. Turner, and P. Jacobs, editors, EMAC 2002 Proceedings, pages 237--240. The Institution of Engineers, Australia, 2002. ISSN 1447-378X.
We investigate the steady-state multiplicity exhibited by the reaction of a fuel/air mixture in a continuously stirred tank reactor. The chemical mechanism used is a modification of a scheme due to Sal'nikov. We consider four cases; corresponding to the choice of fuel fraction, inflow temperature, inflow pressure, or precursor decay rate as the primary bifurcation parameter. From the perspective of fire-retardancy, the case when the fuel fraction is varied is the most important. In this case the steady-state diagrams provide a basis for a systematic investigation into the effectiveness of gas-phase active fire retardants.
M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. I Adiabatic operation. Journal of Mathematical Chemistry, 31(2): 155-186, February 2002.
The retardancy effect of char formation upon the flammability of thermally thin products is investigated. The char is formed in a single-step non-competitive scheme and is assumed to be thermally stable. The criterion for ignition is that of a critical mass flux of volatiles from the solid into the gas phase. Both steady-state and transient formulations of the model are considered. In the high activation energy limit the critical heat flux efficiency in the steady-state model is proportional to c/(1-c), where c is the fraction of char formed. In the transient model the efficiency in reducing the maximum heat release rate, average heat release rate, and total heat released is given by c and is independent of activation energy and heat flux. The specific application that we have in mind for our model is piloted ignition in the cone calorimeter.
M.I. Nelson, J. Brindley and A.C. McIntosh. Ignition properties of thermally thin plastics: The effectiveness of non-competitive char formation in reducing flammability. Journal of Applied Mathematics and Decision Sciences, 6(3): 155-181, 2002.