Mathematical modeling of thermal explosion with natural convection: a brief survey

2019 ◽  
Vol 14 (6) ◽  
pp. 602
Author(s):  
Karam Allali ◽  
Youssef Joundy ◽  
Ahmed Taik
Keyword(s):  
Mathematical Modeling ◽  
Natural Convection ◽  
Temperature Distribution ◽  
Gaseous Medium ◽  
Nonuniform Temperature ◽  
Homogeneous Fluid ◽  
Temperature Growth ◽  
Temperature Oscillations ◽  
Exothermic Chemical Reaction ◽  
Mathematical Approximation

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.

scholarly journals Simulation of Diffusion Processes in Chemical and Thermal Processing of Machine Parts

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 698
Author(s):  
Kateryna Kostyk ◽  
Michal Hatala ◽  
Viktoriia Kostyk ◽  
Vitalii Ivanov ◽  
Ivan Pavlenko ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Temperature Distribution ◽  
Thermal Treatment ◽  
Diffusion Processes ◽  
Nitrogen Concentration ◽  
The Body ◽  
Functional Dependencies ◽  
Technological Parameters ◽  
Gas Nitriding ◽  
Temperature State

To solve a number of technological issues, it is advisable to use mathematical modeling, which will allow us to obtain the dependences of the influence of the technological parameters of chemical and thermal treatment processes on forming the depth of the diffusion layers of steels and alloys. The paper presents mathematical modeling of diffusion processes based on the existing chemical and thermal treatment of steel parts. Mathematical modeling is considered on the example of 38Cr2MoAl steel after gas nitriding. The gas nitriding technology was carried out at different temperatures for a duration of 20, 50, and 80 h in the SSHAM-12.12/7 electric furnace. When modeling the diffusion processes of surface hardening of parts in general, providing a specifically given distribution of nitrogen concentration over the diffusion layer’s depth from the product’s surface was solved. The model of the diffusion stage is used under the following assumptions: The diffusion coefficient of the saturating element primarily depends on temperature changes; the metal surface is instantly saturated to equilibrium concentrations with the saturating atmosphere; the surface layer and the entire product are heated unevenly, that is, the product temperature is a function of time and coordinates. Having satisfied the limit, initial, and boundary conditions, the temperature distribution equations over the diffusion layer’s depth were obtained. The final determination of the temperature was solved by an iterative method. Mathematical modeling allowed us to get functional dependencies for calculating the temperature distribution over the depth of the layer and studying the influence of various factors on the body’s temperature state of the body.

DIMENSIONLESS PHYSICAL-MATHEMATICAL MODELING OF TURBULENT NATURAL CONVECTION

2021 ◽  
Vol 20 (3) ◽  
pp. 37
Author(s):  
S. A. Verdério Júnior ◽  
V. L. Scalon ◽  
S. R. Oliveira ◽  
P. C. Mioralli ◽  
E. Avellone
Keyword(s):  
Mathematical Modeling ◽  
Natural Convection ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Thermal Engineering ◽  
Physical Parameters ◽  
Problem Situation ◽  
Dimensionless Numbers ◽  
Turbulent Natural Convection ◽  
Cooling Coils

Natural convection heat transfer is present in the most diverse applications of Thermal Engineering, such as in electronic equipment, transmission lines, cooling coils, biological systems, etc. The correct physical-mathematical modeling of this phenomenon is crucial in the applied understanding of its fundamentals and the design of thermal systems and related technologies. Dimensionless analyses can be applied in the study of flows to reduce geometric and experimental dependence and facilitate the modeling process and understanding of the main influence physical parameters; besides being used in creating models and prototypes. This work presents a methodology for dimensionless physical-mathematical modeling of natural convection turbulent flows over isothermal plates, located in an “infinite” open environment. A consolidated dimensionless physical-mathematical model was defined for the studied problem situation. The physical influence of the dimensionless numbers of Grashof, Prandtl, and Turbulent Prandtl was demonstrated. The use of the Theory of Dimensional Analysis and Similarity and its application as a tool and numerical device in the process of building and simplifying CFD simulations were discussed.

Temperature distribution in a rod with temperature oscillations on its surface

1966 ◽  
Vol 10 (6) ◽  
pp. 470-472
Author(s):  
M. A. Bagirov ◽  
V. P. Malin ◽  
B. P. Nikolaev
Keyword(s):  
Temperature Distribution ◽  
Temperature Oscillations

Airflow Simulation of the Huge Telescope Assemble

2010 ◽  
Vol 439-440 ◽  
pp. 880-883
Author(s):  
Fu Zhao ◽  
Ping Wang ◽  
Yan Jue Gong ◽  
Yu De Liu ◽  
Hong Bin Xin
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Natural Convection ◽  
Temperature Distribution ◽  
Velocity Field ◽  
Three Dimensional ◽  
Horizontal Line ◽  
Air Velocity ◽  
Turbulent Airflow ◽  
Dynamics Method

With the three-dimensional computational fluid dynamics method, the airflow effects over the huge telescope assemble is investigated in this article. The distributing of velocity field and natural convection are studied by modeling and simulating the turbulent airflow of the huge telescope. Numerical simulations show the best observation direction is the 90o angle between the main optics axis and the horizontal line in which the air velocity distribution is the least. And the air temperature distribution and uniformity around the telescope are also provided by simulation.

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