The Influence of Reactant Consumption on the Critical Conditions for Homogeneous Thermal Explosions

Kassoy, D. R.; Liñán, A.

doi:10.1093/qjmam/31.1.99

Cited by 72 publications

(39 citation statements)

References 4 publications

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“…When reactant consumption is accounted for, the approach of Thomas (1961) and Kassoy and Linan (1978) may be used to show that an excellent approximation of the runaway locus for B > 10 is given by:…”

Section: Aiche Journalmentioning

confidence: 99%

Explicit runaway criterion for catalytic reactors with transport limitations

Balakotaiah

Luss

1991

AIChE Journal

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Section: Aiche Journalmentioning

confidence: 99%

Explicit runaway criterion for catalytic reactors with transport limitations

Balakotaiah

Luss

1991

AIChE Journal

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“…It is assumed further a gas-phase frozen WO_rme-und Stoffiibertragung 19 (1985) flow. The quasi-steady governing equations for the gasphase are the following [ (12) It is convenient to introduce the following gas-phase coordinates, (13) …”

Section: Discussionmentioning

confidence: 99%

“…(64) reduces to dq~0 = 6 exp ~0 -450, dr where ~0 is the leading term of ~. This equation is the well known governing equation obtained in thermal explosion problems [13]. The ignition time in this zeroth order approximation is given by 7 dq~0…”

Section: Transient Analysismentioning

confidence: 98%

Catalytic combustion in stagnation-point flow

Treviño

Sen

1985

Wärme- und Stoffübertragung

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Abstract. Catalytic ignition and extinction processes are analyzed in this paper. The premixed fuel flows towards a catalytic plate of finite thermal conductivity and thickness. The effect of the external heating or cooling on these critical phenomena is also evaluated. Depending on the ratio of the thermal resistance of the plate to the gas, the transition to the weakly reactive to the strong reactive flow can be single or multivalued, for a high activation energy of the catalytic reaction. Analytical expressions for the critical Damk6hler numbers for ignition and extinction are obtained. Also, transient processes leading to catalytic ignition are studied and ignition times for a catalytic adiabatic plate are obtained. Katalytische Verbrennung in StaupunktstriJmungenZusammenfassung. Es werden die Vorg[inge bei katalytischer Entztindung und Erl6schung untersucht. Dabei str6mt der vorgemischte Brermstoff gegen eine katalytische Platte endlicher W~irmeleitf~ihigkeit und Dicke, Der EinfluB yon externer Heizung oder Kiihlung auf diese kritischen Ph~inomene wird ebenfalls berechnet. AbNingig vom Verh~iltnis des thermischen Widerstandes der Platte zu dem des Gases kann der Ubergang yon einer schwach reagierenden zur stark reagierenden Str6mung bei hoher Aktivierungsenergie der katalytischen Reaktion einfach oder mehrwertig sein. Es werden analytische Ausdrficke ftir die kritische Damk6hlerzahl fiir Entziindung und Erl6schung erzielt. Zudem werden transiente Prozesser, die zur katalytischen Entztindung ftthren, untersucht und die Ziindzeiten bei einer adiabaten katalytischen Platte angegeben.

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“…1;2017 way of the modeling of thermal explosion processes is to present the model in singularly perturbed system (SPS) of differential equations. The most common and successful way to study such systems is to apply a different asymptotic methods (for example, Kassoy & Liñan, 1978;Kotovich & Nesenenko, 2000).…”

Section: Application Of Mim To Thermal Explosion Fast and Slow Invarmentioning

confidence: 99%

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

Nave¹,

Ajadi²,

Gol’dshtein³

2016

APR

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In the present paper we applied two well-known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter ℏ. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions. γ (conventional parameter of Semenov's theory of thermal explosion), the final dimensionless adiabatic temperature of the thermally insulated system after explosion. This parameter is small compared with unity for most gaseous mixture due to the high exothermicity and activation energy of the chemical reactionwhere ϵ d is the emissivity of the droplet surface ϵ 1,2 dimensionless parameters, introduced for the first time (Gol'dshtein, Goldfarb, Shreiber, & Zinoviev, 1996) and describe the relations between the thermo physical properties of the gas and liquid phases

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The Influence of Reactant Consumption on the Critical Conditions for Homogeneous Thermal Explosions

Cited by 72 publications

References 4 publications

Explicit runaway criterion for catalytic reactors with transport limitations

Explicit runaway criterion for catalytic reactors with transport limitations

Catalytic combustion in stagnation-point flow

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

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