Complexity Reduction Approach for Solving Second Kind of Fredholm Integral Equations

Initially, the concept of the complexity reduction approach was applied to solve symmetry algebraic systems that were generated from the discretization of the partial differential equations. Consequently, in this paper, the effectiveness of a complexity reduction approach based on half- and quarter-sweep iteration concepts for solving linear Fredholm integral equations of the second kind is investigated. Half- and quarter-sweep iterative methods are applied to solve dense linear systems generated from the discretization of the second kind of linear Fredholm integral equations using a repeated modified trapezoidal (RMT) scheme. The formulation and implementation of the proposed methods are presented. In addition, computational complexity analysis and numerical results of test examples are also included to verify the performance of the proposed methods

Analysis of greenhouse gas emission from reactive materials and its thermodynamics

Thesis (DTech(Mechanical Engineering))--Cape Peninsula University of Technology, 2013The environment is polluted by many gases of which carbon dioxide is one of them and unfortunately during the emission of carbon dioxide, oxygen, which is very important for keeping all species alive, is depleted. Increased industrial activities led to more emission of carbon dioxide and ultimately global warming arose as a result of the greenhouse effect. Global warming has resulted with high temperatures and carbon dioxide production in the atmosphere and it was necessary to come up with mathematical modelling to investigate processes that may try to reduce temperature rise, carbon dioxide emission and oxygen depletion in a stockpile of combustible material. The work done in this thesis considered three differential equations, first for temperature behaviour, second for oxygen depletion and third for carbon dioxide emission. The three equations were solved simultaneously for a reactive slab of combustible material. An exothermic reaction in a stockpile of combustible material results due to the reaction of oxygen with reactive hydrocarbon material and the products are usually heat and carbon dioxide. A detailed discussion on this part is given in chapter 1, and also some definitions of terms applied in this work, together with literature review, statement of problem, aim of the study, objectives of the study and methodology are part of the chapter. In chapter 2, the nonlinear partial differential equations governing the process are derived

Numerical investigation of CO emission and thermal stability of a convective and radiative stockpile of reactive material in a cylindrical pipe

In this article, we investigate the combined effects of emission of CO 2 and O 2 depletion on thermal stability in a long cylindrical pipe of combustible reactive material. The cylindrical pipe loses heat by convection and radiation at the surface, and the nonlinear differential equations governing the heat and mass transfer problem are tackled numerically using Runge–Kutta–Fehlberg method coupled with shooting technique. The effects of various thermo-physical parameters on the temperature, CO 2 and O 2 fields, and thermal stability are presented graphically and discussed quantitatively

Thermal decomposition analysis in a sphere of combustible materials

CITATION: Lebelo, R. S., Makinde, O. D. & Chinyoka, T. 2017. Thermal decomposition analysis in a sphere of combustible materials. Advances in Mechanical Engineering, 9(2):1–14, doi:10.1177/1687814017692515.The original publication is available at https://journals.sagepub.com/home/adeIn 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.https://journals.sagepub.com/doi/full/10.1177/1687814017692515Publisher's versio

Nonlinear Mixed Convection in a Reactive Third-Grade Fluid Flow with Convective Wall Cooling and Variable Properties

Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the working environment becomes hazardous is presented in the present investigation together with the entropy generation analysis that guarantees the efficient management of expensive energy resources. In this regard, the nonlinear mixed convective flow behavior of a combustible third-grade fluid through a vertical channel with wall cooling by convection is investigated. The mathematical formulation captures the nonlinearities arising from second-order Boussinesq approximation and exponential dependence of internal heat generation, viscosity, and thermal conductivity on temperature. The resulting nonlinear boundary value problems were solved based on the spectral Chebyshev collocation method (SCCM) and validated with the shooting-Runge–Kutta method (RK4). The nonlinear effects on the flow velocity, temperature distribution, entropy generation, and Bejan heat irreversibility ratio are significant. Further analyses include the thermal stability of the fluid. Findings from the study revealed that flow, temperature, and entropy generation are enhanced byincreasing values of the Grashof number, the quadratic component of buoyancy, and the Frank-Kameneskii parameter, but are reducedbyincreasing the third-grade material parameter. Moreover, it was shown that increasing values of the third-grade parameter encourages the thermal stability of the flow, while increasing values of the linear and nonlinear buoyancy parameter destabilizes the flow. The present result is applicable to thick combustible polymers with increased molecular weight

Nonlinear Mixed Convection in a Reactive Third-Grade Fluid Flow with Convective Wall Cooling and Variable Properties

Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the working environment becomes hazardous is presented in the present investigation together with the entropy generation analysis that guarantees the efficient management of expensive energy resources. In this regard, the nonlinear mixed convective flow behavior of a combustible third-grade fluid through a vertical channel with wall cooling by convection is investigated. The mathematical formulation captures the nonlinearities arising from second-order Boussinesq approximation and exponential dependence of internal heat generation, viscosity, and thermal conductivity on temperature. The resulting nonlinear boundary value problems were solved based on the spectral Chebyshev collocation method (SCCM) and validated with the shooting-Runge–Kutta method (RK4). The nonlinear effects on the flow velocity, temperature distribution, entropy generation, and Bejan heat irreversibility ratio are significant. Further analyses include the thermal stability of the fluid. Findings from the study revealed that flow, temperature, and entropy generation are enhanced byincreasing values of the Grashof number, the quadratic component of buoyancy, and the Frank-Kameneskii parameter, but are reducedbyincreasing the third-grade material parameter. Moreover, it was shown that increasing values of the third-grade parameter encourages the thermal stability of the flow, while increasing values of the linear and nonlinear buoyancy parameter destabilizes the flow. The present result is applicable to thick combustible polymers with increased molecular weight

Numerical Investigation of a Combustible Polymer in a Rectangular Stockpile: A Spectral Approach

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values

Exergy Analysis for Combustible Third-Grade Fluid Flow through a Medium with Variable Electrical Conductivity and Porous Permeability

A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In this regard, a numerical investigation of the flow and heat transfer of hydromagnetic third-grade liquid through a porous medium. The permeability of the medium and electrical conductivity of the fluid are assumed to be temperature functions. The appropriate mathematical formulations for momentum, energy, and entropy equations are presented in both dimensional and dimensionless forms. We obtained the numerical solutions using the spectral version of the Chebyshev collocation method and compared the result with the shooting Runge–Kutta method. Numerical results for velocity, temperature, entropy, and Bejan profiles are communicated through tables and graphs with adequate physical interpretation. The thermal stability of the thermo-fluid system that guarantees the prevention of spontaneous fluid heating that fuels climate change is also included in the analysis

Numerical Investigation of the Magnetized Reactive Viscous Couple Stress Fluid Flow Down an Inclined Riga Plate with Variable Viscosity

Accurate determination of optimum flow and heat transfer condition is one of the major challenges faced in the application of magnetic fluid in the field of medicine and engineering, especially when applied as ferrofluids for targeted drug deliveries, treatment of hyperthermia, sealants in computer hard drives, lubricants in car shafts. In view of these important applications, a mathematical investigation of the flow and heat transfer behavior of reactive magnetic fluids containing nanostructures is presented based on a couple of stress constitutive models. The reactive fluid is assumed to flow through inclined magnetized solid boundaries for energy conversion. The formulation leads to nonlinear coupled equations. The dimensionless equations are numerically solved using the spectral Chebyshev assumed solution for the weighted residual technique, and the correctness of the solution is confirmed using the shooting Runge–Kutta method. The effects of various fluid parameters on velocity, temperature, skin friction, and heat transfer rates are described in tabular and graphical form, along with suitable physical explanations. Thermal analysis computations are also presented. According to the findings, an enhanced couple of stress fluid and variable viscosity parameters reduced the skin drag and heat transfer rate at the bottom wall. Furthermore, the thermal stability of the flow can be achieved with increasing values modified Hartman number while increasing couple stress parameter encourages thermal instability in the flow domain