Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 6, 2019
Reviews in mathematical modelling
|
|
---|---|---|
Article Number | 602 | |
Number of page(s) | 12 | |
DOI | https://doi.org/10.1051/mmnp/2019049 | |
Published online | 04 December 2019 |
Mathematical modeling of thermal explosion with natural convection: a brief survey★
1
Laboratory of Mathematics and Applications, University Hassan II of Casablanca,
PO Box 146,
FST-Mohammadia
20650, Morocco.
2
Complex Systems Engineering and Human Systems, Mohammed VI Polytechnic University,
Benguerir, Morocco.
** Corresponding author: joundy.youssef@yahoo.fr
Received:
22
August
2019
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.