Effect of heating a semi-transparent medium by radiant energy on ignition characteristics in thermal explosion theory

Abstract

Abstract In ignition theory, there are no volume heat sources in a substance which is being heated through the surface. In most actual cases, ignition occurs under more complex heating conditions. One of these heating conditions is the ignition of a semi-transparent body by the flow of radiant energy. This case is investigated, showing the effect of the presence of volume heat sources of a non-chemical nature on critical and ignition conditions. The Arrhenius heat reaction law and the Frank-Kamenetskii exponential approximation for this law are also used. The ignition characteristics and transition conditions are demonstrated. The transition conditions can be obtained from the condition d θ d θ a = 0 , as well as from d 2 ψ d θ 2 = 0 . The results show that the critical point in the temperature-time plane can be obtained by setting d θ d τ = 0 , d 2 θ d τ 2 = 0 , and d 3 θ d τ 3 = 0 . The non-stationary solutions are also presented.