Abstract
The thermal runaway and eventual ignition of flammable fluids in lagging materials has occurred with sufficient frequency for there to be considerable awareness of this problem in the process engineering industry. Earlier (mainly spatially invariant) models are here modified to include the important effect of diffusion. The aim is to identify boundaries in parameter space where ignition will or will not occur. In this paper, a model of the three main contributing quantities (temperature, fuel and oxygen concentration) is considered which includes exothermic oxidation and endothermic evaporation/desorption processes and primarily centres on the energy balance equation. The shape of the ignition boundary is found to depend crucially on a key value of the ratio of thermal diffusion to mass diffusion of oxidant (inverse Lewis number). The critical value of this ratio is in fact size-dependent and beyond a certain value, ignition will be suppressed.
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