Thermal explosion of a reactive mixture under conditions of oscillating ambient temperature

Thermal explosion in oscillating ambient conditions

“…Similar problem was considered in the papers 23 24 but only in “zero-dimensional” formulation, that is neglecting temperature variations across reacting media. This formulation is not physically realistic.…”

“…This formulation is not physically realistic. In relevant practical applications temperature variations across the medium during self-ignition are significant 25 and therefore the model of the papers 23 24 is not physically relevant. It does not allow the influence of parameters controlling heat exchange with surroundings, such as Biot number Bi , on critical conditions to be investigated.…”

“…Mathematically, derivation of the “zero-dimensional” model in 23 24 is inconsistent as it is being obtained by spatially averaging the heat transfer equation with the boundary condition of the first kind at the outer boundary. In the present problem, such a condition implies Bi ≥ 1 (intensive heat exchange with surroundings), which is emphasized in 23 .…”

“…Besides, no estimation of parameters of practical systems are presented in 23 24 to judge whether thermal explosion regimes with oscillating boundary conditions are relevant for practical applications. Since the model is oversimplified and estimations of parameters relevant for practical systems are not provided, papers 23 24 do not prove, in fact, that predictions made in these papers may occur in reality.…”