The Stability of Thermal Oscillations in a Reactive Slab: Reduction to Hill's Equation

J. Adler, D. M. Herbert
1982 Proceedings of the Royal Society A  
The therm al stability of an exothermic chemically reacting slab with timeperiodic surface tem perature variation is examined. I t is shown, on the basis of a good approximation due to Boddington, Gray and Walker, th a t the behaviour depends on the solutions of an ordinary differential equation of first order. The equation contains a modified amplitude, for small values of which it can be reduced to a particular form of Hill's equation. Critical values of the Frank-Kamenetskii param eter, as a
more » ... ii param eter, as a function of the amplitude e and frequency o) of the surface tem perature oscillations, are derived from the latter equation. For to = 2n and 0 < < 2 the values ar m ent with previously calculated ones. [ 455 ]
doi:10.1098/rspa.1982.0167 fatcat:efzfwitnxfc53fgjrdpjln5yky