Abstract
The spatial structure and temporal evolution of a nondiffusive hot spot are examined in a confined, planar enclosure. The situation is modelled by the reactive Euler equations and single-step Arrhenius kinetics with a large (scaled) activation temperature 1/ε The initial state of the medium is taken to be one of uniform pressure but with a prescribed thermal gradient of order ε across the domain. The induction equations, which govern order ε disturbances to the initial state, are analyzed in the limit of small α, where α measures the width of the domain relative to the acoustic length based on a characteristic reaction time at the initial state. The solution displays a sequence of finite-time singularities as the hot spot grows in strength and shrinks in size in a spatially homogeneous pressure environment. Ultimately, in a region of exponentially small size, significant pressure gradients appear as acoustic and reaction times become comparable and the hot-spot structure is found to obey the full, but previously analyzed, Clarke equations.
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Kapila, A., Short, M. Nondiffusive hot spot in a confined, narrow domain. Journal of Engineering Mathematics 45, 335–366 (2003). https://doi.org/10.1023/A:1022610730167
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DOI: https://doi.org/10.1023/A:1022610730167