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

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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 tign//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 (ψcr/ψ0)–=Δcrθ–2/3 ad(1 –H)–1/3., Values for Δcr and H are again readily calculated.

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