Investigating Thermal Stability in a Two-Step Convective Radiating Cylindrical Pipe

2021 ◽  
Vol 408 ◽  
pp. 99-107
Author(s):  
Ramoshweu Solomon Lebelo ◽  
Radley Kebarapetse Mahlobo ◽  
Samuel Olumide Adesanya
Keyword(s):  
Differential Equation ◽  
Thermal Stability ◽  
Kinetic Parameters ◽  
Numerical Solutions ◽  
Combustion Process ◽  
Numerical Approach ◽  
Cylindrical Pipe ◽  
Surrounding Environment ◽  
Exothermic Chemical Reaction ◽  
Governing Differential Equation

Thermal stability in a stockpile of reactive materials is analyzed in this article. The combustion process is modelled in a long cylindrical pipe that is assumed to lose heat to the surrounding environment by convection and radiation. The study of effects of different kinetic parameters embedded on the governing differential equation, makes it easier to investigate the complicated combustion process. The combustion process results with nonlinear molecular interactions and as a result it is not easy to solve the differential equation exactly, and therefore the numerical approach by using the Finite Difference Method (FDM) is applied. The numerical solutions are depicted graphically for each parameter’s effect on the temperature of the system. In general, the results indicate that kinetic parameters like the reaction rate promote the exothermic chemical reaction process by increasing the temperature profiles, whilst kinetic parameters such as the order of the reaction show the tendency to retard the combustion process by lowering the temperature of the system.

Transient Heat and Reactant Consumption Investigation in a Cylindrical Pipe of Variable Thermal Conductivity

2019 ◽  
Vol 392 ◽  
pp. 178-188
Author(s):  
Ramoshweu Solomon Lebelo
Keyword(s):  
Thermal Conductivity ◽  
Combustion Process ◽  
Reaction System ◽  
Variable Thermal Conductivity ◽  
Heat Generation Rate ◽  
Cylindrical Pipe ◽  
Reactive Material ◽  
Surrounding Environment ◽  
Exothermic Chemical Reaction ◽  
Rate Of Heat Release

This article investigates the transfer of heat with reactant (oxygen) consumption in a stockpile of reactive material. A reactive material is any carbon or hydrocarbon containing component in a stockpile that readily reacts with the oxygen due to exothermic chemical reaction, where self-ignition may take place if heat generation rate during the combustion process within the stockpile, may exceed the rate of heat release to the surrounding environment. The study is modeled in a long cylindrical pipe whose material thermal conductivity varies with the temperature at a given time. The heat and mass transfer partial differential equations governing the problem were solved numerically using the finite difference method (FDM). Kinetic parameters embedded within the reaction system were analyzed to understand their effects on the temperature and the reactant consumption process. The results shew that the parameters that influence the increase in temperature, increase also the consumption rate of the reactant.

On Thermal Stability Analysis of a Convective and Radiative Slab of Variable Thermal Conductivity with Reactant Consumption

2018 ◽  
Vol 389 ◽  
pp. 195-204
Author(s):  
Ramoshweu Solomon Lebelo ◽  
K.C. Moloi ◽  
C.C. Chitumwa ◽  
M.W.R. Sadiki ◽  
P. Baloyi ◽  
...  
Keyword(s):  
Thermal Stability ◽  
Kinetic Parameters ◽  
Nonlinear Differential Equations ◽  
Combustion Process ◽  
Variable Thermal Conductivity ◽  
Nonlinear Interactions ◽  
O2 Consumption ◽  
Shooting Technique ◽  
Surrounding Environment ◽  
Rectangular Slab

Thermal stability in a stockpile of reactive materials that are assumed to lose heat to the surrounding environment by convection and radiation is studied in this article. The reactant (O2) consumption is also considered and the investigation is modeled in a rectangular slab. The complicated combustion process results with nonlinear interactions and therefore, the nonlinear differential equations governing the problem are solved numerically with the Runge-Kutta Fehlberg Method (RKF45) that is coupled with the Shooting Technique. The behaviors of the temperature and the reactant, due to effects of some embedded kinetic parameters, are depicted graphically and discussed accordingly. The results show that kinetic parameters that increase the temperature of the system, correspondingly increase the reactant consumption.

Transient Heat Analysis in a Two-Step Radiative Combustible Slab

2021 ◽  
Vol 872 ◽  
pp. 15-19
Author(s):  
Ramoshweu Solomon Lebelo ◽  
Kholeka Constance Moloi
Keyword(s):  
Heat Transfer ◽  
Kinetic Parameters ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Heat Transfer Analysis ◽  
Shooting Technique ◽  
Surrounding Environment ◽  
Article Analysis ◽  
Exothermic Chemical Reaction ◽  
Rectangular Slab

In this article, analysis of heat transfer in a stockpile of reactive materials modelled in a rectangular slab is carried out. A two-step exothermic chemical reaction is assumed and the heat loss to the surrounding environment is by radiation. The ordinary differential equation (ODE) governing the problem is tackled numerically by Runge-Kutta Fehlberg (RKF45) method coupled with Shooting technique. The heat transfer analysis is simplified by investigation some kinetic parameters’ effects on the temperature of the combusting system. It was found out that some kinetic parameters raise the levels of the temperature by encouraging the exothermic chemical reaction, whereas some, reduce the levels of the temperature to slow down the heat transfer rate. The results are depicted graphically and discussed accordingly.

scholarly journals Heat loss analysis in a radiating slab of variable thermal conductivity

2018 ◽  
Vol 7 (2.23) ◽  
pp. 228 ◽  
Author(s):  
Ramoshweu S. Lebelo ◽  
Kholeka C. Moloi
Keyword(s):  
Differential Equation ◽  
Thermal Conductivity ◽  
Chemical Reaction ◽  
Combustion Process ◽  
Variable Thermal Conductivity ◽  
Temperature Profiles ◽  
Reactive Material ◽  
Loss Analysis ◽  
Exothermic Chemical Reaction ◽  
Rectangular Slab

This article investigates the transfer of heat in a stockpile of reactive materials, that is assumed to lose heat to the environment by radiation. The study is modeled in a rectangular slab whose materials are of variable thermal conductivity. The stockpile’s reactive material in this context is one that readily reacts with the oxygen trapped within the stockpile due to exothermic chemical reaction. The study of the combustion process in this case is conducted theoretically by using the Mathematical approach. The differential equation governing the problem is tackled numerically by applying the Runge-Kutta Fehlberg (RKF45) method coupled with the Shooting technique. To investigate the heat transfer phenomena, some kinetic parameters embedded in the governing differential equation, are varied to observe the behavior of the temperature profiles during the combustion process. The results obtained from the temperature profiles, are depicted graphically and discussed accordingly. It was discovered that kinetic phenomena such as the reaction rate parameter, accelerates the exothermic chemical reaction. However, the radiation parameter decelerates the exothermic chemical reaction by lowering the temperature profiles.  

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.

A Numerical Approach for Fractional Order Riccati Differential Equation Using B-Spline Operational Matrix

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Hossein Jafari ◽  
Haleh Tajadodi ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equation ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Algebraic Equations ◽  
Riccati Differential Equation ◽  
Suggested Approach ◽  
B Spline ◽  
Riccati Differential Equations ◽  
The Given

AbstractIn this article, we develop an effective numerical method to achieve the numerical solutions of nonlinear fractional Riccati differential equations. We found the operational matrix within the linear B-spline functions. By this technique, the given problem converts to a system of algebraic equations. This technique is used to solve fractional Riccati differential equation. The obtained results are illustrated both applicability and validity of the suggested approach.

On linear wave motions in magnetic-velocity shears

1977 ◽  
Vol 285 (1328) ◽  
pp. 607-636 ◽  
Keyword(s):  
Differential Equation ◽  
Critical Level ◽  
Velocity Shear ◽  
Linear Wave ◽  
Wave Amplification ◽  
Isothermal Fluid ◽  
Governing Differential Equation ◽  
Boussinesq Fluid ◽  
Propagation Properties ◽  
Background State

The propagation properties of linear wave motions in magnetic and/or velocity shears which vary in one coordinate z (say) are usually governed by a second order linear ordinary differential equation in the independent variable z. It is proved that associated with any such differential equation there always exists a quantity A which is independent of z. By employing A a measure of the intensity of the wave, this result is used to investigate the general propagation properties of hydromagnetic-gravity waves (e.g. critical level absorption, valve effects and wave amplification) in magnetic and/or velocity shears, using a full wave treatment. When variations in the basic state are included, the governing differential equation usually has more singularities than it has in the W.K.B.J. approximation, which neglects all variations in the background state. The study of a wide variety of models shows that critical level behaviour occurs only at the singularities predicted by the W.K.B.J. approximation. Although the solutions of the differential equation are necessarily singular at the irregularities whose presence is solely due to the inclusion of variations in the basic state, the intensity of the wave (as measured by A) is continuous there. Also the valve effect is found to persist whatever the relation between the wavelength of the wave and the scale of variations of the background state. In addition, it is shown that a hydromagnetic-gravity wave incident upon a finite magnetic and/or velocity shear can be amplified (or over-reflected) in the absence of any critical levels within the shear layer. In a Boussinesq fluid rotating uniformly about the vertical, wave amplification can occur if the horizontal vertically sheared flow and magnetic field are perpendicular. In a compressible isothermal fluid, on the other hand, wave amplification not only occurs in both magnetic-velocity and velocity shears but also in a magnetic shear acting alone.

scholarly journals An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed Al-Smadi ◽  
Nadir Djeddi ◽  
Shaher Momani ◽  
Shrideh Al-Omari ◽  
Serkan Araci
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Reproducing Kernel ◽  
Numerical Approach ◽  
Accurate Solution ◽  
Stability And Convergence ◽  
Type Model ◽  
Schmidt Orthogonalization ◽  
And Performance ◽  
Abel Differential Equation

AbstractOur aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create an orthonormal set of bases that leads to an appropriate solution in the Hilbert space $\mathcal{H}^{2}[a,b]$ H 2 [ a , b ] . We investigate and discuss stability and convergence of the proposed method. The n-term series solution converges uniformly to the analytic solution. We present several numerical examples of potential interests to illustrate the reliability, efficacy, and performance of the method under the influence of the Caputo–Fabrizio derivative. The gained results have shown superiority of the reproducing kernel algorithm and its infinite accuracy with a least time and efforts in solving the fractional Abel-type model. Therefore, in this direction, the proposed algorithm is an alternative and systematic tool for analyzing the behavior of many nonlinear temporal fractional differential equations emerging in the fields of engineering, physics, and sciences.

scholarly journals New Bi-modular Material Approach to Buckling Problem of Reinforced Concrete Columns

2016 ◽  
Vol 6 (1) ◽  
pp. 19 ◽  
Author(s):  
Ahmad Salah Edeen Nassef ◽  
Mohammed A. Dahim
Keyword(s):  
Differential Equation ◽  
Reinforced Concrete ◽  
Differential Equations ◽  
Concrete Columns ◽  
Neutral Axis ◽  
Reinforced Concrete Columns ◽  
New Approach ◽  
Codes Of Practice ◽  
Governing Differential Equation ◽  
Transverse Deflection

<p class="1Body">This paper was investigating the buckling problem of reinforced concrete columns considering the reinforced concrete as bi – modular material. Governing differential equations was driven. The relation between the non-dimensional transverse deflection and non-dimensional distance between centroid axis and the neutral axis "eccentricity" was drawn to enable the solution of the governing differential equation. The new approach was verified with different experimental results and different codes of practice.<strong></strong></p>

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