On the explosion of chain-thermal reactions

Abstract

A chain reaction of oxygen (reactant) and hydrogen (active intermediary) with nitrosyl chloride (sensitizer) as a catalyst may be modelled mathematically as a non-isothermal reaction. In this paper we present an asymptotic analysis of a spatially homogeneous model of a non-isothermal branched-chain reaction. Of particular interest is the so-called explosion time and we provide an upper bound for it as a function of the activation energy which can vary over all positive values. We also establish a bound on the temperature when the activation energy is finite.

On Thermal Explosion of Sensitized Reaction with Variable Heat Loss

“…Previous study on thermal explosion involving perturbation and numerical analysis were presented in references stated in Okoya [10] . It is worth noting that equations (3.2) and (3.3) with the heat loss term βθ has not considered by the earlier authors but we employ the "sensitized" form of reaction in Ayeni [7] , Okoya [10] and Ajadi and Okoya [11] . We consider the special case of 2 − = r corresponding to the" Sensitized" reaction for which heat exchange between the combustible material and the walls of the slab (i.e.…”

“…Since that time more and more complicated models have been suggested (Zeldovich et al [4] , Kuo [5] , Boddington et al [6] and related references therein). The problems of exothermic chemically reactive material in a slab obeying an Arrhenius law and accounting for temperature dependence of pre-exponential factor ( ) A T are based on the assumptions that the reacting material is motionless, that the heat losses are purely determined by the thermal conductivity of the reacting material and that the chemical reaction proceeds non-uniformly over the vessel volume (Ayeni [7] , Okoya [9,10] , Ajadi [11] and related references therein). The analyses of these problems have been performed based on close-form, approximation and phase-plane methods and numerical techniques using computational fluid dynamics (CFD) packages.…”

Numerical Solution For Frank-Kamenetskii And Activation Energy Parameters in Reactive-Diffusive Equation with Variable One-Exponential Factor

“…Neglecting the bar symbol for clarity, the dimensionless governing equations are obtained as: is the Frank-Kamenetskii parameter, = RT o /E is the activation energy parameter. Bowes [3] , Dainton [4] reported that it has been shown experimentally that this model is able to predict the critical ignition temperature for a variety of combustible materials while Ayeni [2] studied an asymptotic analysis of a spatially homogeneous model of a non-isothermal branched-chain reaction ,in particular he showed the explosion time and provide an upper bound for it as a function of the activation energy which can vary over all positive value.…”

Unsteady/Steady Natural Convection Flow of Reactive Viscous Fluid in a Vertical Annulus

“…Makinde (2005;2006;2008) examined exothermic explosions in a heated cylindrical pipe under Biomolecular Arrhenus and sensitized reaction rates neglecting the consumption of the material. Similarly, Ayeni (1982) and Dainton (1960) studied a realistic mathematical desription of thermal expolosion which include the effects of Arrhenius temperature dependence with variable pre-exponential factor. Most recently, Jha et al (2011) investigated a transient natural convection flow of a reactive viscous flow in a vertical channel formed by two infinite vertical parallel plates.…”