A numerical study of entropy generation, heat and mass transfer in boundary layer flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.This study lies at the interface between mathematical modelling of fluid flows and numerical methods for differential equations. It is an investigation, through modelling techniques, of entropy generation in Newtonian and non-Newtonian fluid flows with special focus on nanofluids. We seek to enhance our current understanding of entropy generation mechanisms in fluid flows by investigating the impact of a range of physical and chemical parameters on entropy generation in fluid flows under different geometrical settings and various boundary conditions. We therefore seek to analyse and quantify the contribution of each source of irreversibilities on the total entropy generation. Nanofluids have gained increasing academic and practical importance with uses in many industrial and engineering applications. Entropy generation is also a key factor responsible for energy losses in thermal and engineering systems. Thus minimizing entropy generation is important in optimizing the thermodynamic performance of engineering systems. The entropy generation is analysed through modelling the flow of the fluids of interest using systems of differential equations with high nonlinearity. These equations provide an accurate mathematical description of the fluid flows with various boundary conditions and in different geometries. Due to the complexity of the systems, closed form solutions are not available, and so recent spectral schemes are used to solve the equations. The methods of interest are the spectral relaxation method, spectral quasilinearization method, spectral local linearization method and the bivariate spectral quasilinearization method. In using these methods, we also check and confirm various aspects such as the accuracy, convergence, computational burden and the ease of deployment of the method. The numerical solutions provide useful insights about the physical and chemical characteristics of nanofluids. Additionally, the numerical solutions give insights into the sources of irreversibilities that increases entropy generation and the disorder of the systems leading to energy loss and thermodynamic imperfection. In Chapters 2 and 3 we investigate entropy generation in unsteady fluid flows described by partial differential equations. The partial differential equations are reduced to ordinary differential equations and solved numerically using the spectral quasilinearization method and the bivariate spectral quasilinearization method. In the subsequent chapters we study entropy generation in steady fluid flows that are described using ordinary differential equations. The differential equations are solved numerically using the spectral quasilinearization and the spectral local linearization methods

A numerical study of entropy generation in nanofluid flow in different flow geometries.

This thesis is concerned with the mathematical modelling and numerical solution of equations for boundary layer flows in different geometries with convective and slip boundary conditions. We investigate entropy generation, heat and mass transport mechanisms in non-Newtonian fluids by determining the influence of important physical and chemical parameters on nanofluid flows in various flow geometries, namely, an Oldroyd-B nanofluid flow past a Riga plate; the combined thermal radiation and magnetic field effects on entropy generation in unsteady fluid flow in an inclined cylinder; the impact of irreversibility ratio and entropy generation on a three-dimensional Oldroyd-B fluid flow along a bidirectional stretching surface; entropy generation in a double-diffusive convective nanofluid flow in the stagnation region of a spinning sphere with viscous dissipation and a study of the fluid velocity, heat and mass transfer in an unsteady nanofluid flow past parallel porous plates. We assumed that the nanofluids are electrically conducting and that the velocity slip and shear stress at the boundary have a linear relationship. We also consider different boundary conditions for all the flow models. The study further analyzes and quantifies the influence of each source of irreversibility on the overall entropy generation. The transport equations are solved using two recent numerical methods, the overlapping grid spectral collocation method and the bivariate spectral quasilinearization method, first to determine which of these methods is the most accurate, and secondly to authenticate the numerical accuracy of the results. Further, we determine the skin friction coefficient and the changes in the heat and mass transfer coefficients with various system parameters. The results show, inter alia that reducing the heat transfer coefficient, the particle Brownian motion parameter, chemical reaction parameter, Brinkman number, thermophoresis parameter and the Hartman number all lead individually to a reduction in entropy generation. The overlapping grid spectral collocation method gives better computational accuracy and converge faster than the bivariate spectral quasilinearization method. The fluid flow problems have engineering and industrial applications, particularly in the design of cooling systems and in aerodynamics

Dynamics of MHD Convection of Walters B Viscoelastic Fluid through an Accelerating Permeable Surface Using the Soret–Dufour Mechanism

The MHD convective Walters-B memory liquid flow past a permeable accelerating surface with the mechanism of Soret-Dufour is considered. The flow equation constitutes a set of partial differential equations (PDEs) to elucidate the real flow of a non-Newtonian liquid. The radiation thermo-physical parameters were employed based on the use of Roseland approximation. This implies the fluid employed in this exploration is optically thick. Utilizing suitable similarity terms, the flow equation PDEs were simplified to become total differential equations. The spectral homotopy analysis method (SHAM) was utilized to provide outcomes to the model. The SHAM involves the addition of the Chebyshev pseudospectral approach (CPM) alongside the homotopy analysis approach (HAM). The outcomes were depicted utilizing graphs and tables for the quantities of engineering concern. The mechanisms of Soret and Dufour were separately examined. The imposed magnetism was found to lessen the velocity plot while the thermal radiation term elevates the temperature plot because of the warm particles of the fluid.This research was funded by a grant of the Romanian Ministry of Research, Innovation and Digitalization, project number PFE 26/30.12.2021, PERFORM-CDI@UPT100—The increasing of the performance of the Polytechnic University of Timis, oara by strengthening the research, development and technological transfer capacity in the field of “Energy, Environment and Climate Change” at the beginning of the second century of its existence, within Program 1—Development of the national system of Research and Development, Subprogram 1.2—Institutional Performance—Institutional Development Projects—Excellence Funding Projects in RDI, PNCDI III.info:eu-repo/semantics/publishedVersio

Free Convection Fluid Flow from a Spinning Sphere with Temperature-Dependent Physical Properties

Conference ProceedingsNatural convection from a spinning sphere with temperature dependent viscosity, thermal conductivity and viscous dissipation was studied. A unique system of non-similar partial differential equations was solved using the bivariate local-linearization method (BLLM). This method use Chebyshev spectral collocation method applied in both the η and ξ directions. Similar equations in the literature are normally solved by inaccurate time-consuming finite difference methods. This work introduces a robust method for solving partial differential equations arising in heat and mass transfer. The numerical method was validated by comparison to the results previously published in the literature. The method is fully described in this article and can be used as an alternative method in solving boundary value problems. This work also presents rarely reported results of the effect of selected parameters on spin-velocity profiles g(η)

A mathematical study of boundary layer nanofluid flow using spectral quasilinearization methods.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.Heat and mass transfer enhancement in industrial processes is critical in improving the efficiency of these systems. Several studies have been conducted in the past to investigate different strategies for improving heat and mass transfer enhancement. There are however some aspects that warrant further investigations. These emanate from different constitutive relationships for different non-Newtonian fluids and numerical instability of some numerical schemes. To investigate the convective transport phenomena in nanofluid flows, we formulate models for flows with convective boundary conditions and solve them numerically using the spectral quasilinearisation methods. The numerical methods are shown to be stable, accurate and have fast convergence rates. The convective transport phenomena are studied via parameters such as the Biot number and buoyancy parameter. These are shown to enhance convective transport. Nanoparticles and microorganisms’ effects are studied via parameters such as the Brownian motion, thermophoresis, bioconvective Peclet number, bioconvective Schmidt number and bioconvective Rayleigh number. These are also shown to aid convective transport

A numerical study of heat and mass transfer in non-Newtonian nanofluid models.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.A theoretical study of boundary layer flow, heat and mass transport in non-Newtonian nanofluids is presented. Because of the diversity in the physical structure and properties of non-Newtonian fluids, it is not possible to describe their behaviour using a single constitutive model. In the literature, several constitutive models have been proposed to predict the behaviour and rheological properties of non-Newtonian fluids. The question of interest is how the fluid physical parameters affect the boundary layer flow, and heat and mass transfer in various nanofluids. In this thesis, nanofluid models in various geometries and subject to different boundary conditions are constructed and analyzed. A range of fluid models from simple to complex are studied, leading to highly nonlinear and coupled differential equations, which require advanced numerical methods for their solution. This thesis is a conjoin between mathematical modeling of non-Newtonian nanofluid flows and numerical methods for solving differential equations. Some recent spectral techniques for finding numerical solutions of nonlinear systems of differential equations that model fluid flow problems are used. The numerical methods of primary interest are spectral quasilinearization, local linearization and bivariate local linearization methods. Consequently, one of the objectives of this thesis is to test the accuracy, robustness and general validity of these methods. The dependency of heat and mass transfer, and skin friction coefficients on the physical parameters is quantified and discussed. Results show that nanofluids and physical parameters have an important and significant impact on boundary layer flows, and on heat and mass transfer processes.The year on the title page reflects as 2019 on the thesis and differs from that on pages ii to iv which indicates the year 2020

Application of bivariate spectral quasilinearization method to second grade fluid flow equations.

Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.In this study, the steady flow of a second grade magnetohydrodynamic fluid in a porous channel is investigated. We further investigate the hydromagnetic flow of a second grade fluid over a stretching sheet. The partial differential equations that describe the flows are solved numerically using the bivariate spectral quasilinearization method. The method is extended to a system of non-similar partial differential equations that model the steady two dimensional flow of Falkner-Skan flow of an incompressible second grade nano fluid. The work is also concerned with heat and the mass transfer from the electrically conducting second grade magnetohydrodynamic fluid over a stretching sheet. The sensitivity of the flow characteristics with respect to the second grade fluid parameter, magnetic field parameter, thermal radiation parameter, and the chemical reaction parameter are investigated. The accuracy of the numerical method is determined using the residual error analysis

Numerical studies of nanofluid boundary layer flows using spectral methods.

Doctoral Degree. University of KwaZulu-Natal, PietermaritzburgThis thesis is focused on numerical studies of heat and mass transport processes that occur in nanofluid boundary layer flows. We investigate heat and mass transfer mechanisms in the flow of a micropolar nanofluid above a stretching sheet, the squeezed nanofluid flow between two parallel plates and the impact of activation energy and binary chemical reaction on nanofluid flow past a rotating disk. We present an analysis of entropy generation in nanofluid flow past a rotating disk and nanofluid flow past a stretching surface under the influence of an inclined magnetic field. This study aims to numerically determine to a high degree of accuracy, how nanoparticles can be utilized to alter heat and transport properties of base fluids in order to enhance or achieve desirable properties for thermal systems. The heat and mass transfer processes that feature in nanofluid boundary layer flow are described by complex nonlinear transport equations which are difficult to solve. Because of the complex nature of the constitutive equations describing the flow of nanofluids, finding analytic solutions has often proved intractable. In this study, the model equations are solved using the spectral quasilinearization method. This method is relatively recent and has not been adequately utilized by researchers in solving related problems. The accuracy and reliability of the method are tested through convergence error and residual error analyses. The accuracy is further tested through a comparison of results for limiting cases with those in the literature. The results confirm the spectral quasilinearization method as being accurate, efficient, rapidly convergent and suited for solving boundary value problems. In addition, among other findings, we show that nanofluid concentration enhances heat and mass transfer rates while the magnetic field reduces the velocity distribution. The fluid flows considered in this study have significant applications in science, engineering and technology. The findings will contribute to expanding the existing knowledge on nanofluid flow

On paired decoupled quasi-linearization methods for solving nonlinear systems of differential equations that model boundary layer fluid flow problems.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.Two numerical methods, namely the spectral quasilinearization method (SQLM) and the spectral local linearization method (SLLM), have been found to be highly efficient methods for solving boundary layer flow problems that are modeled using systems of differential equations. Conclusions have been drawn that the SLLM gives highly accurate results but requires more iterations than the SQLM to converge to a consistent solution. This leads to the problem of figuring out how to improve on the rate of convergence of the SLLM while maintaining its high accuracy. The objective of this thesis is to introduce a method that makes use of quasilinearization in pairs of equations to decouple large systems of differential equations. This numerical method, hereinafter called the paired quasilinearization method (PQLM) seeks to break down a large coupled nonlinear system of differential equations into smaller linearized pairs of equations. We describe the numerical algorithm for general systems of both ordinary and partial differential equations. We also describe the implementation of spectral methods to our respective numerical algorithms. We use MATHEMATICA to carry out the numerical analysis of the PQLM throughout the thesis and MATLAB for investigating the influence of various parameters on the flow profiles in Chapters 4, 5 and 6. We begin the thesis by defining the various terminologies, processes and methods that are applied throughout the course of the study. We apply the proposed paired methods to systems of ordinary and partial differential equations that model boundary layer flow problems. A comparative study is carried out on the different possible combinations made for each example in order to determine the most suitable pairing needed to generate the most accurate solutions. We test convergence speed using the infinity norm of solution error. We also test their accuracies by using the infinity norm of the residual errors. We also compare our method to the SLLM to investigate if we have successfully improved the convergence of the SLLM while maintaining its accuracy level. Influence of various parameters on fluid flow is also investigated and the results obtained show that the paired quasilinearization method (PQLM) is an efficient and accurate method for solving boundary layer flow problems. It is also observed that a small number of grid-points are needed to produce convergent numerical solutions using the PQLM when compared to methods like the finite difference method, finite element method and finite volume method, among others. The key finding is that the PQLM improves on the rate of convergence of the SLLM in general. It is also discovered that the pairings with the most nonlinearities give the best rate of convergence and accuracy

Unsteady Squeezing Flow Of Cu-Al2O3/Water Hybrid Nanofluid In A Horizontal Channel With Magnetic Field

The proficiency of hybrid nanofluid from Cu-Al2O3/water formation as the heat transfer coolant is numerically analyzed using the powerful and user-friendly interface bvp4c in the Matlab software. For that purpose, the Cu-Al2O3/water nanofluid flow between two parallel plates is examined where the lower plate can be deformed while the upper plate moves towards/away from the lower plate. Other considerable factors are the wall mass suction/injection and the magnetic field that applied on the lower plate. The reduced ordinary (similarity) differential equations are solved using the bvp4c application. The validation of this novel model is conducted by comparing a few of numerical values for the reduced case of viscous fluid. The results imply the potency of this heat transfer fluid which can enhance the heat transfer performance for both upper and lower plates approximately by 7.10% and 4.11%, respectively. An increase of squeezing parameter deteriorates the heat transfer coefficient by 4.28% (upper) and 5.35% (lower), accordingly. The rise of suction strength inflates the heat transfer at the lower plate while the presence of the magnetic field shows a reverse resul