Thermophoretic Deposition of Nanoparticles Due Toa Permeable Rotating Disk: Effects of Partial Slip, Magnetic Field, Thermal Radiation, Thermal-Diffusion, and Diffusion-Thermo

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications

Mixed Convection Heat Transfer of MHD Flow Due to Permeable Sheet: An Analytical Solution

In this paper we investigate the analytical solution for MHD flow and heat transfer of electrically conducting fluid due to vertical starching surface. Here the diffusion thermo (Dufour) and thermal diffusion (Soret) effects are considered. It is shown that the porosity, magnetic, convection, concentrationand buoyancy effects can be combined with a new parameter called porous- magneto-convection-concentration parameters .The effect of physical parameter influencing the flow and heat transfer are studied and results are plotted and discussed. Keywords: Heat Transfer, Porous-Magneto-Convection-Concentration parameter, Buoyancy, Soret,  Dufour,  Lewis

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid

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 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

Finite element simulation of twist forming process to study twist springback pattern

Springback is one of the most common defects found in the metal forming of automotive parts. There are three conditions which can be considered as springback i.e. flange angle change, sidewall curl and twist springback and among them, twist springback is the most complicated problem. This study will focuses on the development of finite element simulation model of the twist forming process. The main aim of this project is to investigate the parameters that may affect the twist springback. Few parameters including twist angle, hardening constant and thickness are explored using finite element (FE) software ANSYS Workbench (16.0). The rectangular mild strips are used to form the twist forming. The standard material properties and stress-strain curve of mild steel had been used to get the springback prediction. The results of springback were measured by the difference of the bending angles before and after unloading process. The results were then be validated with the research made of Dwivedi et al., (2002). The results show that the springback angle reduces as the thickness of strips are increased and also as the angle of twist increases

Steady and unsteady mhd mixed convection flow of casson and casson nanofluid over a nonlinear stretching sheet and moving wedge

Casson fluid is a shear thinning fluid which is one of the non-Newtonian fluids that exhibit yield stress. In this fluid, if a shear stress less than the yield stress is applied, it behaves like a solid, whereas if vice-versa the fluid starts to move. The advantage of Casson fluid is that it can be reduced to Newtonian fluid at very high wall shear stress. Due to these reasons, the steady and unsteady two-dimensional, electrically conducting mixed convection flow of Casson fluid was studied in this thesis. Flow that was generated due to nonlinear stretching sheet and moving wedge filled with and without nanoparticles were given attention. Specific problems were studied with various effects include, porous medium, thermal radiation, chemical reaction, slip and convective boundary conditions. Similarity transformations were used to convert nonlinear governing equations into nonlinear ordinary differential equations. The obtained equations were then solved numerically via the implicit finite difference scheme, known as Keller-box method. Moreover, an algorithm was developed in MATLAB software in order to obtain the numerical solutions. The accuracy of the numerical results was validated through comparison with the results available in the published journal. The effects of pertinent parameters on velocity, temperature and concentration profiles as well as wall shear stress, heat and mass transfer rates were displayed graphically and also presented in tabular form. Findings reveals that, when Casson fluid parameter increases the momentum boundary layer thickness reduces in both cases, nonlinear stretching sheet and moving wedge. It is noticed that in the case of moving wedge, the strength of magnetic parameter reduces the wall shear stress. Whereas, opposite trend is observed in the case of nonlinear stretching sheet. In both geometries, the influence of Brownian motion and thermophoresis parameters on the nanoparticles concentration is notably more pronounced

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value