Papers by Ramoshweu S Lebelo
Symmetry
Initially, the concept of the complexity reduction approach was applied to solve symmetry algebra... more 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.
Defect and Diffusion Forum, Apr 1, 2019
This article investigates the transfer of heat with reactant (oxygen) consumption in a stockpile ... more 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.
Mathematics, Apr 15, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Advances in Mechanical Engineering, Jun 1, 2018
The special collection 'Mathematical Application and Computing in Mechanical Engineering' for Adv... more The special collection 'Mathematical Application and Computing in Mechanical Engineering' for Advances in Mechanical Engineering presents noble computational modelling of different nonlinear systems. The articles in this special collection cover application of mathematical equations to heat transfer in solids and fluids, error tracing based on Monte Carlo theory, error calibration for Ant Colony theory, mass spring damper systems, energy saving pumping systems, computational fluid dynamics simulations, flight dynamics simulations, numerical methods and eigenvalue problems, velocity estimations for electronic stability control systems, aerodynamic shape optimization and hydraulic pumping systems. This special collection will hopefully inspire readers in the academic sphere, including researchers and engineers.
International journal of pure and applied mathematics, May 23, 2017
In this paper, entropy generation rate in the flow of couple stress fluid undergoing exothermic c... more In this paper, entropy generation rate in the flow of couple stress fluid undergoing exothermic chemical reaction through a porous vertical channel is studied by applying the second law of thermodynamics. A semi-analytical solution for the governing equations is obtained using Adomian decomposition method (ADM). The effects of couple stress parameter, internal heat generation parameter, Dufour number on the velocity, temperature distribution, entropy generation rate and Bejan number are investigated and the results were presented graphically. The results show that solutal diffusivity has significant effect on the entropy generation rate and irreversibility of heat in a couple stress fluid flow.
WSEAS transactions on fluid mechanics, Jul 27, 2023
The current study is designed to model the hydrothermal feature of a hybrid nano liquid slip flow... more The current study is designed to model the hydrothermal feature of a hybrid nano liquid slip flows over a permeable expanding/contracting surface with entropy generation. The model incorporates Cu-Al2O3 nanoparticles with water as the host liquid to simulate the flow. Additional impacts incorporated into the novelty of the model are viscous dissipation and Joule heating. The model is transformed appropriately to its dimensionless form using similarity quantities and the solution is numerically obtained using the spectral quasi-linearization method (SQLM). The impact of pertinent factors on the flow characteristics is communicated through graphs for the hybrid nanosuspension to discuss the hydrothermal variations. The friction factor and the rate of heat transport are also discussed with sensible judgment through tables. To ensure the code validity, a comparison with earlier studies is conducted and excellent consensus is accomplished. The result explored that diminution in the irreversibility ratio is witnessed for rising magnetic field strength along the free stream, distance away from the permeable surface as the heat dissipation to the surrounding decelerates. Also, the augmented nonlinearity parameter intensified the heat transfer rate for about 2.79% of the hybrid nano-suspension.
Defect and Diffusion Forum, Oct 1, 2018
In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel ... more In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel is investigated. Due to channel porosity, the asymmetrical slip conditions are imposed on both walls. The coupled dimensionless partial differential equations are reduced to a system of second-order boundary-value problems based on some flow assumptions and solved by Adomian decomposition method (ADM). Variations in velocity and temperature profiles are presented and discussed in detail. The result of the analysis revealed that increasing Hartmann number decreases the flow velocity while the slip parameters enhance the flow.
Mathematics, Dec 12, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Mathematics
Energy management and heat control whenever a reactive viscous fluid is the working medium has be... more 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 valid...
International Review of Mechanical Engineering (IREME), 2017
In this article, we consider thermal stability and oxygen consumption rate in a reactive stockpil... more In this article, we consider thermal stability and oxygen consumption rate in a reactive stockpile material and at the same time spontaneously combusts. Spontaneous combustion usually takes place when a material containing carbon or hydrocarbon reacts with oxygen that is trapped within the stockpile due to low-temperature oxidation. Heat is one of the products of combustion in any exothermic chemical reaction, and in this case, complete combustion is assumed with the reactant oxygen consumption. The study is done theoretically with the application of energy and mass transfer equations, to give an understanding of the complicated process of combustion. The nonlinear differential equations governing the problem are solved numerically using semi-implicit finite difference method (FDM). The reactant and the temperature behaviors are depicted graphically, and results are discussed accordingly.
Entropy, 2017
This paper addresses entropy generation in the flow of an electrically-conducting couple stress n... more This paper addresses entropy generation in the flow of an electrically-conducting couple stress nanofluid through a vertical porous channel subjected to constant heat flux. By using the Buongiorno model, equations for momentum, energy, and nanofluid concentration are modelled, solved using homotopy analysis and furthermore, solved numerically. The variations of significant fluid parameters with respect to fluid velocity, temperature, nanofluid concentration, entropy generation, and irreversibility ratio are investigated, presented graphically, and discussed based on physical laws.
International Journal of Heat and Technology, 2017
The present work examines the effect of temperature-dependent fluid density on the reactive coupl... more The present work examines the effect of temperature-dependent fluid density on the reactive couple stress fluid flowing steadily in a vertical channel saturated with porous materials. The thermal effect gave rise to a linked differential system of equations. In the dimensionless form, the boundary-valued problems (BVP) are uncoupled and solved by using Adomian decomposition method (ADM). The solutions are used to obtain expressions for entropy generation and Bejan heat irreversibility number in the porous medium. The relevant fluid parameters are varied and discussed physically. The present result shows good agreement with the previously obtained result when buoyancy force is neglected. The present study is relevantal in the thermal treatment of combustible fluids in chemical and petrochemical engineering.
Defect and Diffusion Forum, 2019
The significance of this paper is to analyse thermal decomposition and reactant consumption in a ... more The significance of this paper is to analyse thermal decomposition and reactant consumption in a stockpile of reactive materials, such as that of coal, hay or wood, for example. The study is modelled in a rectangular slab and a two-step combustion process like the one taking place in fuel combustion of an automobile is assumed. The coupling of Runge-Kutta-Fehlberg (RKF) method and Shooting technique is applied to solve the differential equations governing the problem. The combustion process that is so complicated is investigated by consideration of effects of some embedded kinetic parameters, such as the activation energy, on the temperature and the reactant (O2) consumption. It was discovered that parameters such as the activation energy, tend to lower the temperature of the system and correspondingly reduce the O2 consumption rate, whereas parameters like the rate of reaction, increase the temperature during the combustion process, to reduce the O2 concentration of the system. The...
Physica A: Statistical Mechanics and its Applications, 2019
In this article, a computational approach to monitor entropy production in a fully developed grav... more In this article, a computational approach to monitor entropy production in a fully developed gravity-driven couple stress film flow on an inclined heated surface subjected to convective cooling is examined. The free end of the thin film is maintained in a manner that follows the Newtonian law of cooling. Exact solutions of the dimensionless boundary-value problems (BVP) are obtained and utilized for the entropy expression and the heat irreversibility ratio along the heated plate. The effects of pertinent parameters on the flow and thermal build up are shown graphically and explained based on physical laws. Most importantly, the rate of heat transfer is shown to be a decreasing function of the couple stress inverse while the skin friction remains constant along the heated wall. The present computation is relevant in coating and drying processes and several metallurgical engineering.
Mathematical Methods in the Applied Sciences, 2018
The present work examines the combined influence of variable thermal conductivity and viscosity o... more The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity ...
Journal of Physics: Conference Series, 2018
The main aim of this paper is to study the performance of two-stage Gauss-Seidel (TSGS) iterative... more The main aim of this paper is to study the performance of two-stage Gauss-Seidel (TSGS) iterative method in solving glioma growth model with treatment. In this paper, the implicit scheme is used to discretize the governing model. The derivation and implementation of the proposed method are discussed. Also, some numerical results are also presented.
Journal of Physics: Conference Series, 2018
The study of heat transfer in a stockpile of reactive materials, modeled in a cylindrical domain,... more The study of heat transfer in a stockpile of reactive materials, modeled in a cylindrical domain, is carried out in this article. The reactive cylinder is assumed to lose heat to the surrounding environment by convection and radiation. The complicated combustion process results with nonlinear interactions, and therefore, the ordinary differential equation (ODE) governing the problem cannot be solved exactly, but numerically. The Runge-Kutta-Fehlberg (RKF45) numerical method is applied to solve the ODE. The solutions are expressed graphically and discussed accordingly. The results generally show that the reaction rate parameter increases the temperature of the system, whereas the radiation parameter reduces the temperature profiles thereof.
Defect and Diffusion Forum, 2018
Thermal stability in a stockpile of reactive materials that are assumed to lose heat to the surro... more 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.
IOP Conference Series: Materials Science and Engineering, 2017
Heat transfer analysis of compound multilayer insulation for cryogenic tank under different servi... more Heat transfer analysis of compound multilayer insulation for cryogenic tank under different service conditions H L Zhu, C Yao, Y Li et al.-Steady heat transfer analysis of 2D plates using the numerical manifold method
Heliyon, 2018
The present article investigates the entropy generation rate in the nonlinear convective flow of ... more The present article investigates the entropy generation rate in the nonlinear convective flow of a reactive couple stress liquid through a channel filled with saturated materials and subjected to convective cooling. Analytical solutions of the coupled nonlinear boundary-value problems arising from the mathematical formulation are obtained by using the Homotopy Analysis Method (HAM). The analytical solutions are further validated numerically with the fourth order Runge-Kutta (RK4) to establish the accuracy of the method. Velocity, temperature, entropy generation, and heat irreversibility ratio profiles are presented and discussed extensively. The result of the computation shows that entropy generation increases significantly with increasing buoyancy parameter.
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Papers by Ramoshweu S Lebelo