Thermal explosion theory for a slab with partial insulation

Abstract

Liouville's nonlinear partial differential equation is considered for an infinite rectangular strip domain with mixed boundary conditions. It arises in the determination of the two-dimensional temperature distribution within an exothermically reacting slab having parts of its surface insulated and the remainder offering no resistance to heat transfer. For symmetrical heating, with insulating strips on upper and lower surfaces, the critical Frank-Kamenetskii parameter is found to be δ c(∈)=δ c(0)(1— ∈—0.555 ∈ 3 2 +⋯), where δ c (0) = 0.878 and ϵ, assumed small, is the ratio of the insulation width to the slab thickness.