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

The problem of the thermal explosion of a finite volume of a reactive material in a medium with harmonically oscillating temperature is solved in the classical formulation. A kind of resonance is shown to arise when the oscillation period is commensurate with the adiabatic induction period of thermal explosion at the mean ambient temperature. At both high and very low oscillation frequencies, the critical condition parameter and induction period are only slightly affected by ambient temperature oscillations. By contrast, at moderately low frequencies, even small-amplitude oscillations of ambient temperature can strongly influence the critical condition and, especially, induction period of thermal explosion.