Advanced search
Publication Cover
Combustion Science and Technology Volume 3, 1971 - Issue 2
Submit an article Journal homepage
74
Views
94
CrossRef citations to date
0
Altmetric
Original Articles

Theory of Ignition of a Reactive Solid by Constant Energy Flux

A. LIÑÁN Escuela de Ingenieros Aeronauticos, Ciudad Uniuersitaria, Madrid, and Institute National de Tecnica Aeroespacial, “Esteban Terradas”, Madrid
&
F. A. WILLIAMS Department of Aerospace and Mechanical Engineering Sciences, University of California, San Diego, La Jolla, California
Pages 91-98 | Received 16 Feb 1971, Published online: 10 May 2007

Citations (94)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (14)

G. Kats & J.B. Greenberg. (2018) Forced thermal ignition of a polydisperse fuel spray. Combustion Science and Technology 190:5, pages 849-877.
Read now
K.-P. Liao & C. Pantano. (2009) A numerical study of reignition induced by a diffusion flame. Combustion Theory and Modelling 13:6, pages 1025-1052.
Read now
A Shah, A Mcintosh, J Brindley, J Griffiths & M Pourkashanian. (2003) The effect of oxygen starvation on ignition phenomena in a reactive solid containing a hot-spot. Combustion Theory and Modelling 7:3, pages 509-523.
Read now
AlexanderM. Telengator, StephenB. Margolis & FormanA. Williams. (1999) Ignition analysis of a porous energetic material: II. Ignition at a closed heated end. Combustion Theory and Modelling 3:3, pages 433-445.
Read now
Alexander M Telengator, Stephen B Margolis & Forman A Williams. (1999) Analysis of ignition of a porous energetic material. Combustion Theory and Modelling 3:1, pages 33-49.
Read now
C. VÁZQUEZ-ESPÍ. (1998) The Ignition of Solids: An Asymptotic Analysis. Combustion Science and Technology 133:4-6, pages 191-225.
Read now
D. Glenn Lasseigne. (1988) Critical Conditions for the Ignition of a Combustible Solid: Application to Combustion Synthesis. Combustion Science and Technology 60:4-6, pages 335-344.
Read now
P. H. THOMAS. (1984) On the Surface Ignition of Self-Heating Materials. Combustion Science and Technology 36:5-6, pages 263-283.
Read now
J. POLAND, I.O. HINDASH & D. R. KASSOY. (1982) Ignition Processes in Confined Thermal Explosions. Combustion Science and Technology 27:5-6, pages 215-227.
Read now
T. NIIOKA. (1978) Heterogeneous Ignition of a Solid Fuel in a Hot Stagnation-Point Flow. Combustion Science and Technology 18:5-6, pages 207-215.
Read now
M. KINDELAN & F. A. WILLIAMS. (1977) Gas-Phase Ignition of a Solid with In-Depth Absorption of Radiation. Combustion Science and Technology 16:1-2, pages 47-58.
Read now
CHOONG SE KIM & PAUL M. CHUNG. (1977) Ignition of a Porous Solid Fuel by Convective Heat and Mass Transfer at the Fuel Surface. Combustion Science and Technology 15:1-2, pages 75-82.
Read now
M. KINDELAN & F. A. WILLIAMS. (1975) Theory for Endothermic Gasification of a Solid by a Constant Energy Flux. Combustion Science and Technology 10:1-2, pages 1-19.
Read now
AMABLE LIN¯ÁN & ANTONIO CRESPO. (1972) An Asymptotic Analysis of Radiant and Hypergolic Heterogeneous Ignition of Solid Propellants. Combustion Science and Technology 6:4, pages 223-232.
Read now

Articles from other publishers (80)

Ali S. Rangwala & Vasudevan RaghavanAli S. Rangwala & Vasudevan Raghavan. 2022. Mechanism of Fires. Mechanism of Fires 115 152 .
Robert Timms & Richard Purvis. (2019) A boundary layer analysis for the initiation of reactive shear bands. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475:2226, pages 20180899.
Crossref
Ning Tian & Aixi Zhou. (2016) Sensitivity and uncertainty analyses for ignition of fiber-reinforced polymer panels. Fire and Materials 40:3, pages 396-415.
Crossref
Jerrold B. Greenberg & Gershon Kats. (2016) Analysis of the Ignition of a Combustible Fuel Spray-Oxidant Mixture. Analysis of the Ignition of a Combustible Fuel Spray-Oxidant Mixture.
Peter V. Gordon, Daniel J. Gotti, Uday G. Hegde, Michael C. Hicks, Michael J. Kulis & Gregory I. Sivashinsky. (2015) An elementary model for autoignition of laminar jets. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471:2179, pages 20150059.
Crossref
Ning Tian & Aixi Zhou. (2015) An ignition criterion for combustible solids integrating surface temperature and heating rate. Fire and Materials 39:2, pages 139-152.
Crossref
Ning Tian & Aixi Zhou. (2014) A simplified model for predicting the ignition of FRP composites with validation using intermediate-scale fire experiment data. Fire and Materials 38:3, pages 356-380.
Crossref
M.A. Delichatsios, M. Gummala & D.G. Vlachos. (2013) Extinction of surface stabilized gaseous diffusion flames: Part I Simplified numerical model and implications for solid fuels in fires. Fire Safety Journal 55, pages 152-159.
Crossref
A.A. Shah, J. Brindley, A.C. McIntosh & J. Rademacher. (2008) The effects of heat exchange and fluid production on the ignition of a porous solid. Nonlinear Analysis: Real World Applications 9:2, pages 562-584.
Crossref
Merrill W. Beckstead, Karthik Puduppakkam, Piyush Thakre & Vigor Yang. (2007) Modeling of combustion and ignition of solid-propellant ingredients. Progress in Energy and Combustion Science 33:6, pages 497-551.
Crossref
A.A Shah, J Brindley, A.C McIntosh & J Griffiths. (2007) Ignition and combustion of low-exothermicity porous materials by a local hotspot. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463:2081, pages 1287-1305.
Crossref
A. A. Shah, J. Brindley, A. C. McIntosh & J. Griffiths. (2006) Gas-phase and heat-exchange effects on the ignition of high- and low-exothermicity porous solids subject to constant heating. Journal of Engineering Mathematics 56:2, pages 161-177.
Crossref
Jeremy Cain & M. Quinn Brewster. (2006) Radiative Ignition of Fine‐Ammonium Perchlorate Composite Propellants. Propellants, Explosives, Pyrotechnics 31:4, pages 278-284.
Crossref
J.K. Dienes, Q.H. Zuo & J.D. Kershner. (2006) Impact initiation of explosives and propellants via statistical crack mechanics. Journal of the Mechanics and Physics of Solids 54:6, pages 1237-1275.
Crossref
M. Q. Brewster. (2006) Surface-Absorption Assumption for Radiant Heating and Ignition of Energetic Solids. Journal of Thermophysics and Heat Transfer 20:2, pages 348-351.
Crossref
A.A Shah & G.C Wake. (2004) The existence of steady states to a combustion model with internal heating. Nonlinear Analysis: Real World Applications 5:3, pages 421-439.
Crossref
A. Shah, J. Brindley, J. Griffiths, A. Mcintosh & M. Pourkashanian. (2004) The Ignition of Low-Exothermicity Solids by Local Heating. Process Safety and Environmental Protection 82:2, pages 156-169.
Crossref
Guanyu Zheng, Indrek S. Wichman & André Bénard. (2003) Energy balance analysis of ignition over a melting polymer subjected to a high radiation heat flux in a channel cross flow. Fire Safety Journal 38:3, pages 229-256.
Crossref
L. R. Ritter, V. A. Volpert & W. E. Olmstead. (2003) Initiation of Free-Radical Polymerization Waves. SIAM Journal on Applied Mathematics 63:5, pages 1831-1848.
Crossref
Eun. S. Kim, Rongjie Yang & Vigor Yang. 2003. Energetic Materials - Part 2. Detonation, Combustion. Energetic Materials - Part 2. Detonation, Combustion 295 350 .
Y.-C. Liau, E.S. Kim & V. Yang. (2001) A comprehensive analysis of laser-induced ignition of RDX monopropellant. Combustion and Flame 126:3, pages 1680-1698.
Crossref
A. Makino. (2001) Fundamental aspects of the heterogeneous flame in the self-propagating high-temperature synthesis (SHS) process. Progress in Energy and Combustion Science 27:1, pages 1-74.
Crossref
Mohammad K. Alkam & P. Barry Butler. (2000) Impingement Heating and Ignition of Condensed-Phase Energetic Materials. Journal of Propulsion and Power 16:6, pages 1075-1082.
Crossref
Atsushi Makino & C.K. Law. (2000) Transient radiative initiation of the heterogeneous flame in self-propagating high-temperature materials synthesis: Theory and experimental comparisons. Proceedings of the Combustion Institute 28:1, pages 1439-1446.
Crossref
Yuji Nakamura, Hiroshi Yamashita, Tadao Takeno & Genichiro Kushida. (2000) Effects of gravity and ambient oxygen on a gas-phase ignition over a heated solid fuel. Combustion and Flame 120:1-2, pages 34-48.
Crossref
Alexander Telengator, Forman Williams & Stephen Margolis. (1999) Ignition analyses of porous energetic materials. Ignition analyses of porous energetic materials.
Catherine A. Roberts. (1998) Analysis of explosion for nonlinear Volterra equations. Journal of Computational and Applied Mathematics 97:1-2, pages 153-166.
Crossref
K.G. Shkadinsky, G.V. Shkadinskaya & B.J. Matkowsky. (1998) Ignition of Heterogeneous Mixtures in Gravitational Fields. Combustion and Flame 113:3, pages 388-405.
Crossref
J. A. DiLellio & W. E. Olmstead. (1997) Shear Band Formation due to a Thermal Flux Inhomogeneity. SIAM Journal on Applied Mathematics 57:4, pages 959-971.
Crossref
M. Delichatsios & M. Delichatsios. (1997) Critical Mass Pyrolysis Rates For Extinction Of Fires Over Solid Materials. Fire Safety Science 5, pages 153-164.
Crossref
Carlos Vázquez-Espí & Amable LiÑán. (1994) Ignition of a Rectangular Solid by an External Heat Flux. SIAM Journal on Applied Mathematics 54:5, pages 1181-1202.
Crossref
C.A. Roberts, D.G. Lasseigne & W.E. Olmstead. (1993) Volterra Equations which Model Explosion in a Diffusive Medium. Journal of Integral Equations and Applications 5:4.
Crossref
H. G. Im, J. K. Bechtold & C. K. Law. (2006) Analysis of thermal ignition in supersonic flat-plate boundary layers. Journal of Fluid Mechanics 249:-1, pages 99.
Crossref
F.A. Williams. (1992) The role of theory in combustion science. Symposium (International) on Combustion 24:1, pages 1-17.
Crossref
Peter J. Tonellato. (1991) Critical behavior of an ignition model in chemical combustion. Quarterly of Applied Mathematics 49:4, pages 795-812.
Crossref
D. Glenn Lasseigne & W. E. Olmstead. (1991) Ignition or nonignition of a combustible solid with marginal heating. Quarterly of Applied Mathematics 49:2, pages 303-312.
Crossref
S.W. Baek, M. Sichel & C.W. Kauffman. (1990) Asymptotic analysis of the shock wave ignition of dust particles. Combustion and Flame 81:3-4, pages 219-228.
Crossref
C. Treviño, W. Stüttgen & N. Peters. (1990) Pressure gradients due to gas expansion in the boundary layer combustion of a condensed fuelDruckgradienten aufgrund von Expansion bei der Grenzschichtverbrennung eines festen Brennstoffes. Wärme- und Stoffübertragung 25:5, pages 309-319.
Crossref
Avner Friedman & Miguel A. Herrero. (1990) A nonlinear nonlocal wave equation arising in combustion theory. Nonlinear Analysis: Theory, Methods & Applications 14:2, pages 93-106.
Crossref
G. N. Isakov & R. A. Dekhtyar'. (1990) Relaxation analysis of mechanisms for heterogeneous ignition of polymers with radiation-convective heat exchange. Combustion, Explosion, and Shock Waves 25:4, pages 383-388.
Crossref
F. Méndez, C. Treviño & A. Liñán. (1989) Transient analysis of carbon combustion in stagnation flow. Combustion and Flame 75:3-4, pages 281-295.
Crossref
Lolke G. Vorsteveld & C. E. Hermance. (1989) Effect of geometry on ignition of a reactive solid - Acute angles. Journal of Propulsion and Power 5:1, pages 26-31.
Crossref
D.Glenn Lasseigne & W.E. Olmstead. (1989) The effect of perturbed heating on the ignition of a combustible solid. International Journal of Engineering Science 27:12, pages 1581-1587.
Crossref
Indrek S. Wichman & Arvind Atreya. (1987) A simplified model for the pyrolysis of charring materials. Combustion and Flame 68:3, pages 231-247.
Crossref
Lolke G. Vorsteveld & C. E. Hermance. (1987) Effect of geometry on ignition of a reactive solid - Square corner. AIAA Journal 25:4, pages 592-597.
Crossref
D. Glenn Lasseigne & W. E. Olmstead. (1987) Ignition of a Combustible Solid with Reactant Consumption. SIAM Journal on Applied Mathematics 47:2, pages 332-342.
Crossref
LOLKE VORSTEVELD & C. HERMANCE. (1987) Effect of geometry on ignition of a reactive solid - Acute angles. Effect of geometry on ignition of a reactive solid - Acute angles.
F.A. Williams. (1986) Lectures on applied mathematics in combustion. Physica D: Nonlinear Phenomena 20:1, pages 21-34.
Crossref
T. L. Jackson & A. K. Kapila. (1985) Shock-Induced Thermal Runaway. SIAM Journal on Applied Mathematics 45:1, pages 130-137.
Crossref
V. V. Matveev & A. N. Grechanyi. (1985) Heterogeneous ignition of a solid fuel particle by a hot gas. Combustion, Explosion, and Shock Waves 20:5, pages 531-534.
Crossref
Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich & G. M. MakhviladzeYa. B. Zeldovich, G. I. Barenblatt, V. B. Librovich & G. M. Makhviladze. 1985. The Mathematical Theory of Combustion and Explosions. The Mathematical Theory of Combustion and Explosions 186 234 .
M. E. Egorov & V. V. Matveev. (1984) Thermal theory of heterogeneous ignition of gasifying condensed substances. Combustion, Explosion, and Shock Waves 20:3, pages 277-281.
Crossref
. 1984. Fundamentals of Solid-Propellant Combustion. Fundamentals of Solid-Propellant Combustion 239 304 .
W.E. Olmstead. 1984. Mathematical Modelling in Science and Technology. Mathematical Modelling in Science and Technology 473 476 .
. (1997) Thermal explosion and the theory of its initiation by steady intense light. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 390:1799, pages 265-281.
Crossref
A. K. Kapila, B. J. Matkowsky & A. van Harten. (1983) An Asymptotic Theory of Deflagrations and Detonations I. The Steady Solutions. SIAM Journal on Applied Mathematics 43:3, pages 491-519.
Crossref
W. E. Olmstead. (1983) Ignition of a Combustible Half Space. SIAM Journal on Applied Mathematics 43:1, pages 1-15.
Crossref
D. Glenn Lasseigne & W. E. Olmstead. (1983) Ignition of a combustible solid by convection heating. ZAMP Zeitschrift f�r angewandte Mathematik und Physik 34:6, pages 886-898.
Crossref
D. D. Do & R. H. Weiland. (2009) Dynamics of rapid extinction in a lumped system with Arrhenius chemistry. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics 23:3, pages 278-290.
Crossref
I. S. Lyubchenko, V. V. Matveev & G. N. Marchenko. (1982) Asymptotic-thermal theory of the ignition of condensed materials with successive reactions. Combustion, Explosion, and Shock Waves 18:2, pages 157-163.
Crossref
A.K. Kapila. (1981) Evolution of deflagration in a cold combustible subjected to a uniform energy flux. International Journal of Engineering Science 19:4, pages 495-509.
Crossref
D. R. Kassoy & Justin Poland. (1980) The Thermal Explosion Confined by a Constant Temperature Boundary:I—The Induction Period Solution. SIAM Journal on Applied Mathematics 39:3, pages 412-430.
Crossref
D. D. Do & R. H. Weiland. (2009) Poisoning-induced exchange of steady states in a catalytic chemical reactor. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics 22:2, pages 237-253.
Crossref
A. K. Kapila. (1980) Reactive-Diffusive System with Arrhenius Kinetics: Dynamics of Ignition. SIAM Journal on Applied Mathematics 39:1, pages 21-36.
Crossref
A. KULKARNIM. KUMARK. KUO. (1980) Review of solid-propellant ignition studies. Review of solid-propellant ignition studies.
M. KINDELÁN & A. LIÑáN. 1980. Gasdynamics of Explosions and Reactive Systems. Gasdynamics of Explosions and Reactive Systems 1199 1211 .
V.S. Berman, Iu.S. Riazantsev & V.M. Shevtsova. (1980) Asymptotic analysis of the process of igniting a combustible gas mixture by thermal inhomogeneity. Journal of Applied Mathematics and Mechanics 44:1, pages 60-64.
Crossref
A. Liñán & F. A. Williams. (1979) Ignition of a Reactive Solid Exposed to a Step in Surface Temperature. SIAM Journal on Applied Mathematics 36:3, pages 587-603.
Crossref
Noriyuki Mutoh, Toshisuke Hirano & Kazuo Akita. (1979) Experimental study on radiative ignition of polymethylmethacrylate. Symposium (International) on Combustion 17:1, pages 1183-1190.
Crossref
T. Niioka & F.A. Williams. (1979) Relationship between theory and experiment for radiant ignition of solids. Symposium (International) on Combustion 17:1, pages 1163-1171.
Crossref
V.S Berman, Iu.S. Riazantsev & V.M. Shevtsova. (1979) On igniting a reacting gas by a heat source of finite heat capacity. Journal of Applied Mathematics and Mechanics 43:1, pages 79-87.
Crossref
M. Kindelán & A. Liñán. (1978) Gasification effects in the heterogeneous ignition of a condensed fuel by a hot gas. Acta Astronautica 5:11-12, pages 1199-1211.
Crossref
T. Niioka & F.A. Williams. (1977) Ignition of a reactive solid in a hot stagnation-point flow. Combustion and Flame 29, pages 43-54.
Crossref
W.B. Bush & F.A. Williams. (1976) Influence of strong conductive gas-phase cooling on radiant ignition of a reactive solid. Combustion and Flame 27, pages 321-329.
Crossref
M. KINDELAN & A. LINAN. (1976) Gasification of a condensed material in a hot gas. Gasification of a condensed material in a hot gas.
J. Buckmaster. (1975) Combustion of a fuel drop immersed in a hot atmosphere. International Journal of Engineering Science 13:11, pages 915-921.
Crossref
W.B. Bush & F.A. Williams. (1975) Radiant ignition of a surface-cooled reactive solid. Acta Astronautica 2:5-6, pages 445-462.
Crossref
Gerald Rosen. (1974) Fundamental theoretical considerations for an air-suspension vortex flow incinerator system. Chemical Engineering Science 29:1, pages 97-104.
Crossref
A. Broido & F.A. Williams. (1973) Use of asymptotic analysis of the large activation- energy limit to compare graphical methods of treating thermogravimetry data. Thermochimica Acta 6:2, pages 245-253.
Crossref
A. Linan & F.A. Williams. (1972) Radiant ignition of a reactive solid with in-depth absorption. Combustion and Flame 18:1, pages 85-97.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.