The Critical Conditions in a Reactive Slab with Slowly Varying Surface Temperature

Liouville's non-linear partial differential equation is consideredfor an infinite rectangular strip domain with a slowly varyingboundary condition. The equation describes a layer of chemicallyreactive material under conditions where the resistance to surfaceheat transfer is negligible and the ambient temperature variesslowly along the surface. Symmetrical heating by a zero orderexothermic reaction is assumed. If is a small dimensionlesstemperature difference between regions where the surface temperatureis effectively constant, a perturbation series solution in may be determined provided the Frank-Kamenetskii parameter satisfies _c(). It is shown that a plausible value for thecritical parameter is _c() = _c(0) e^–e,where _c(0) = 0.878.The corresponding critical temperature distribution is shownto have a dependence on different from that for subcriticalcases.