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- W2022339977 abstract "An approximate simple analytic theory of critically for thermal hot spots is given which leads to estimates of the critical explosion parameter δc, a dimensionless rate of heat production, within 10% of the values computed by the sphere, by Merzhanov, Barzykin and Gontkovskaya, and the slab. The result may be expressed as follows. If an inert symmetrical hot spot of unit dimensions and unit diffusivity is initially at unit dimensionless temperature above its surroundings, the temperature of its centre falls with time, and if this drop in temperature is denoted by ψ0(λ) at dimensionless time λ (Fourier number), where ψ0(λ) can be evaluated by conventional thermal conduction theory, then for a hot spot generating heat according to the Arrhenius law with high activation energy and having an initial dimensionless temperature. , where E is the activation energy, R is the universal gas constant, T0 is the initial temperature of the hot spot, and T1 is that of the surroundings, the relation between δc and θ0 is approximately and it links δc and θ0 directly through the cooling characteristic of the equivalent inert hot spot. The effects of shape, initial distribution of temperature, and boundary conditions are embodied in this one term ψ. For a sphere this result gives A low and a high value of δc can give the same value of θ0 but only the higher value is relevant here. The treatment is expected to apply to shapes where the position of the maximum temperature can be assumed and to initial temperature differences high enough for the reactivity of the material outside the hot spot to be neglected. The critical condition has been used for evaluating δc as a function of surface heat transfer for pieces or piles of self-heating materials placed in cooling surroundings. There value of δc are relevant to the definition of safe conditions for the industrial processing and storage of such materials when the finally-processed material is hot. The form of the relation between δc and θ0 appears to be significantly dependent on the “initial” temperature distribution, i.e. on the processes involved in the formation of the hot spot." @default.
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- W2022339977 date "1968-06-01" @default.
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- W2022339977 title "On critical hot spot size" @default.
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- W2022339977 doi "https://doi.org/10.1016/0010-2180(68)90030-8" @default.
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