scholarly journals Thermal Stability Investigation in a Reactive Sphere of Combustible Material

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
R. S. Lebelo
Keyword(s):  
Differential Equation ◽  
Thermal Stability ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Energy Equation ◽  
Combustible Material ◽  
One Dimensional ◽  
Complicated Process ◽  
Exothermic Chemical Reaction ◽  
Implicit Finite Difference

An investigation of thermal stability in a stockpile of combustible material is considered. The combustible material is any carbon containing material that can react with oxygen trapped in a stockpile due to exothermic chemical reaction. The complicated process is modelled in a sphere and one-dimensional energy equation is used to solve the problem. The semi-implicit finite difference method (FDM) is applied to tackle the nonlinear differential equation governing the problem. Graphical solutions are displayed to describe effects of embedded kinetic parameters on the temperature of the system.

scholarly journals Thermal decomposition analysis in a sphere of combustible materials

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769251 ◽  
Author(s):  
Ramoshweu Solomon Lebelo ◽  
Oluwole Daniel Makinde ◽  
T Chinyoka
Keyword(s):  
Thermal Decomposition ◽  
Chemical Reaction ◽  
Spontaneous Combustion ◽  
Decomposition Analysis ◽  
Combustible Material ◽  
Balance Equations ◽  
One Dimensional ◽  
Spherical Domain ◽  
Exothermic Chemical Reaction ◽  
Implicit Finite Difference

In this article, we look at spontaneous combustion due to exothermic chemical reaction taking place within a stockpile of combustible material. The model includes mass and energy balance equations in a spherical domain. The complicated chemical reaction is simplified by considering a one-dimensional process. The differential equations governing the problem are solved using semi-implicit finite difference method. The effects of kinetic parameters embedded within the system are analyzed and the results are expressed graphically and discussed accordingly.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

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