Thermal explosion, times to ignition and near-critical behaviour in uniform-temperature systems. Part 3.—Effects of variable heat-transfer coefficients

Abstract

Although it is common in thermal-explosion theory to neglect the temperature dependence of thermophysical properties, there are circumstances in which this is not justifiable. This paper examines how (i) times-to-ignition and (ii) the Semenov criterion for criticality are affected when the heat-transfer coefficient χ is not constant but depends on temperature, χ/χ₀=h(θ). A systematic approach is used that can cope with generalized forms of temperature dependence and concentration dependence of reaction rate.

When reactant consumption is unimportant the time-to-ignition depends on the degree of supercriticality according to t_ign//_tad=L//_{(ψ/ψcr–1)^½}∝1//_{(degree of supercriticality)^1/2}.

Values for L are readily calculated; L is commonly of order unity but grows without limit as transition (from criticality to continuous behaviour) is approached.

When reactant consumption is considered, the shift of the Semenov criterion ψ from its standard value at criticality ψ₀ is given by (ψ_cr/ψ₀)–=Δ_crθ^–2/3_ad(1 –H)^–1/3., Values for Δ_cr and H are again readily calculated.