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Original Articles

Thermally Thin Materials with Enhanced Fire-Resistant Properties: A Dynamical Systems Model

Pages 83-112 | Received 13 Sep 2000, Accepted 16 Feb 2001, Published online: 06 Apr 2007

References

  • Babrauskas , V. ( 1984 ). Development of the cone calorimeter - a bench-scale heat release rate apparatus based on oxygen consumption. Fire and Materials , 8 ( 2 ): 81 – 95 .
  • Babrauskas , V. and Parker , W.J. ( 1986 ). Ignitability measurements with the cone calorimeter. , National Bureau of Standards, Gathersburg MD . NBSIR 86–3445.
  • Babrauskas , V. and Parker , W.J. ( 1987 ). Ignilability Measurements with the Cone Calorimeter. Fire and Materials , 11 : 31 – 43 .
  • Balakrishnan , E. , Nelson , M.I. , and Wake , G.C. ( 1999 ). Radiative ignition of combustible materials I. Polymeric materials undergoing non-flaming thermal degradation - The critical storage problem. Mathematical and Computer Modelling , 30 : 177 – 195 ,
  • Búcsi , A. and Rychlý , J. ( 1992 ). A theoretical approach to understanding the connection between ignitability and the flammability parameters of organic polymers. Polymer Degradation and Stability , 38 : 33 – 40 .
  • Coppersthwaite , D.P. , Griffiths , J.F. and Gray , B.F. ( 1991 ) Oscillations in the H2 + C12 Reaction: Experimental Measurements and Numerical Simulation. Journal of Chemical Physics , 95 ( 18 ): 6961 – 6967 .
  • Doedel , E. , Wang , X. and Fairgrieve , T. ( 1994 ) AUTO 94 Software for continuation and bifurcation problems in ordinary differential equations. , Applied Mathematics Report, California Institute of Technology, Pasadena , California 91125.
  • Drysdale , D. ( 1987 ). An Introduction to Fire Dynamics. , John Wiley and Sons. Forbes , L .K. ( 1990 ). Limit-cycle behaviour in a model chemical reaction: The Sal'nikov thermokinetic oscillator. Proceedings of the Royal Society of London A, 430 : 641 – 651 .
  • Forbes , L.K. and Gray , B.F. ( 1998 ). Burning down the house: the time to ignition of an irradiated solid. Proceedings of the Royal Society A , 454 : 2667 – 2688 .
  • Forbes , L.K. , Myerscough , M.R. , and Gray , B.F. ( 1991 ) On the presence of limit-cycles in a model exothermic chemical reaction: Sal'nikov's oscillator with two temperature-dependent reaction rates. Proceedings of the Royal Society A , 435 : 591 – 604 .
  • Gray , B.F. and Merkin , J.H. ( 1993 ) Thermal explosion: escape times in the uniform temperature approximation. Part 2. Perturbations of critical initial conditions. MathematicalEngineering in Industry, 4 ( 1 ): 13 – 26 .
  • Gray , B.F. , Merkin , J.H. and Wake , G.C. ( 1991 ) Disjoint bifurcation diagrams in combustion systems. Mathematical and Computer Modelling , 15 ( 11 ): 25 – 33 .
  • Gray , B.F. and Roberts , M.J. ( 1988 a). A method for the complete qualitative analysis of two coupled ordinary differential equations dependent on three parameters. Proceedings of the Royal Society A , 416 : 361 – 389 .
  • Gray , B.F. and Roberts , M.J. ( 1988 b). Analysis of chemical kinetic systems over the entire parameter space I. The Sal'nikov thermokinetic oscillator. Proceedings of the Royal Society A , 416 : 391 – 402 , 1988.
  • Gray , B.F. and Roberts , M.J. ( 1988 c) Analysis of chemical kinetic systems over the entire parameter space II. Isothermal oscillators. Proceedings of the Royal Society A , 416 : 403 – 424 , 1988 .
  • Gray , P. and Scott , S.K. ( 1990 ). Chemical Oscillations and Instabilities: Non-linear Chemical Kinetics. , Oxford University Press, 1 st edition.
  • Hatakeyama , T. and Quinn , F.X. ( 1994 ). Thermal analysis: Fundamentals and applications to polymer science. , John Wiley & Sons Ltd.
  • Kay , S.R. and Scott , S.K. ( 1988 ) Oscillations of simple exothermic reactions in a closed system. II Exact Arrhenius kinetics. Proceedings of the Royal Society A , 416 : 343 – 359 .
  • Kuznetsov , Y.A. ( 1995 ) Elements of Applied Bifurcation Theory. Applied Mathematical Sciences 112. , Springer-Verlag, 1st edition.
  • McIntosh , A.C. ( 1998 ). Lagging ignition of combustible fluids in porous media - effect of fuel supply rate. Combustion Theory and Modelling , 2 : 179 – 192 .
  • McIntosh , A.C. , Gray , B.F. and Wake , G.C. ( 1997 ). Analysis of the bifurcational behaviour of a simple model of vapour ignition in porous material. Proceedings of the Royal Society A , 453 : 281 – 301 .
  • Nayfeh , A.H. and Balachandran , B. ( 1995 ). Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. , Wiley Series in Nonlinear Science. Wiley Interscience, 1st edition.
  • Nelson , M.I. ( 1997 ). A dynamical systems model of autoignition in the cone calorimeter. In Fire Safety Science: Proceedings of the Fifth International Symposium , pages 547 – 558 . International Association for Fire Safety Science. ISBN 4–9900625-5–5.
  • Nelson , M.I. ( 1998 ). Ignition mechanisms of thermally thin thermoplastics in the cone calorimeter. Proceedings of the Royal Society of London A , 454 : 789 – 814 .
  • Nelson , M.I. and Brindley , J. ( 1999 ). Polymer combustion: Effects of flame emissivity. Philosophical Transactions of the Royal Society of London Series A , 357 : 3655 – 3673 .
  • Nelson , M.I. , Brindley , J. and Mcintosh , AC. ( 1995 ). A mathematical model of ignition in the cone calorimeter. Combustion Science and Technology , 104 : 35 – 54 .
  • Perko , L. ( 1996 ) Differential Equations and Dynamical Systems. , Texts in Applied Mathematics 7. Springer, 2nd edition.
  • Russo , L.P. and Bequette , B.W. ( 1995 ) Impact of process design on the multiplicity behaviour of a jacketed exothermic cstr. AIChe Journal , 41 ( 1 ): 135 – 147 .
  • Rychlý , J. and Costa , L. ( 1995 ). Modelling of polymer ignition and burning adopted for cone calorimeter measurements: The correlation between the rate of heat release and oxygen index. Fire and Materials , 19 : 215 – 220 .
  • Rychlý , J. and Rychlá , L. ( 1986 ) Effect of flame retardants on polyolefines. Fire and Materials , 10 : 7 – 10 .
  • Rychlý , J. and Rychlá , L. ( 1996 ). Modelling of heat-release rate-time curves from cone calorimeter for burning ofpolymers with intumescence additives. Polymer Degradation and Stability, 54 : 249 – 254 .
  • Sexton , M.J. and Forbes , L.K. ( 1996 ). An exothermic chemical reaction with linear feedback control. Dynamics and Stability of Systems , 11 ( 3 ): 219 – 238 .

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