Ignition times for a branched-chain thermal explosion chemistry with heat loss

Abstract

The ignition times for a branched-chain thermal explosion involving simplified initiation, branching, and termination of chains, as well as heat exchange with the surroundings, but assuming that consumption of fuel is negligible for the combustion of acetylene oxidation chemistry that covers nth Arrhenius kinetics for the chain-branching step, is studied. An approximate solution is presented in the form of temperature as a function of time in terms of the physical parameters in the special case when the order of branching reaction is zero. The effect of heat loss on the problem studied is addressed numerically and we showed different qualitative effects of varying the dimensionless parameters.

Keywords:

• acetylene – oxygen ignition time
• nonadiabatic situation
• high temperature ignition
• nth Arrhenius kinetics
• stiff nonlinear equation
• physical coordinates