Math. Model. Nat. Phenom.
Volume 14, Number 6, 2019
Reviews in mathematical modelling
|Number of page(s)||12|
|Published online||04 December 2019|
Mathematical modeling of thermal explosion with natural convection: a brief survey★
Laboratory of Mathematics and Applications, University Hassan II of Casablanca,
PO Box 146,
2 Complex Systems Engineering and Human Systems, Mohammed VI Polytechnic University, Benguerir, Morocco.
** Corresponding author: firstname.lastname@example.org
Accepted: 30 October 2019
Thermal (or heat) explosion occurs in a reacting medium if the heat production due to an exothermic chemical reaction exceeds the heat loss through the boundary. In the mathematical approximation heat explosion is characterized by an unbounded temperature growth. If the reaction occurs in a liquid or gaseous medium, then a nonuniform temperature distribution can lead to natural convection. The interaction of heat explosion with natural convection can result in various regimes with a bounded temperature distribution (stationary, periodic, chaotic) and to a transition to heat explosion. The latter can be accompanied by a monotonic temperature growth or by temperature oscillations (oscillating heat explosion). This paper presents a review on mathematical modelling of heat explosion with natural convection in a homogeneous fluid and in a porous medium.
Mathematics Subject Classification: 35K57 / 76R10
Key words: natural convection / porous medium / Navier Stokes equations / thermal explosion
© EDP Sciences, 2019
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