ABSTRACT Determining the criticality and disappearance of optically thin droplets (gas phase) by thermal explosions is crucial for maintaining thermal stability in various industrial and nonindustrial applications. The governing nonlinear ordinary differential equations of this problem make use of two distinct approximation models for thermal radiation loss, which were completed by Cogley et al. and Sohrab et al. Two methods of solving the problem – the Semenov method and the inflection point method – are used to identify the circumstances of criticality and disappearance of criticality (transition conditions). The governing equations utilize the use of the temperature-dependent Arrhenius frequency factor of the reaction and the thermal conductivity of the gas. The analytical solution of the equations yields the transitional values of the distinctive parameters at various initial conditions. Numerical methods are used to determine the equation’s exact solution. At specific initial conditions, the impact of θo, θa, γSh,F, and αSh,F on the temperature-time histories of ignition (supercritical region), non-ignition (subcritical region), and the critical boundary between them is derived. Notable effects on the ignition, non-ignition, and critical temperatures and times include the changing frequency of the reaction, the gas thermal conductivity, and two approximation models of radiation heat loss. The two radiation heat loss approximation models of the analytical and numerical findings are compared.
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