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

Computer modelling of contaminants mobility in subsurface regions

One of the keys to realistic mathematical modelling of any transport phenomenon is to understand the fluid mechanics of the process correctly. However, this is a daunting task for the subsurface flow systems: the geometry of the domain is irregular, the physical/structural characteristics are not known with certainty and, to make the problem further complicated, the processes often involve combined free and porous flow regions. Modelling for combined free and porous flow under the ground is of significant practical importance in many areas of water resources engineering. These include, for example, water seepage and contaminant mobility through preferential flow channel boundaries, groundwater rise and fall and flow circulation in the subsurface, permeable reactive barrier technology and many other important transport processes. The presence of impermeable or multiple number of permeable interfaces in the physical domains of the combined free and porous flow sections and the aspect ratios between the sub-domains may also significantly influence the fluid dynamics in such coupled systems. [Continues.

Analysis of Inertia Effect on Axisymmetric Squeeze Flow of Slightly Viscoelastic Fluid Film between Two Disks by Recursive Approach

In this study, we analyzed the inertia effect on the axisymmetric squeeze flow of slightly viscoelastic fluid film between two disks. A system of nonlinear partial differential equations (PDEs) in cylindrical coordinates, along with nonhomogenous boundary conditions, illustrates the phenomenon of fluid flow caused by squeezing with the inertia effect. The Langlois recursive approach was applied to obtain the analytical solution of the system having a stream function, axial and radial velocities, pressure distribution, normal and tangential stresses and normal squeeze force. These flow variables are also portrayed graphically to describe the effects of the Reynolds number and slightly viscoelastic parameter. The results show that by increasing the Reynolds number, the velocity profile decreases, and both the pressure distribution and shear stresses increase. Moreover, there is a small increase in normal squeeze force. When the slightly viscoelastic parameter approaches zero, the obtained solution of flow variables matches with the classical results. This study can be applied to understand the mechanism of load-bearing features in thrust bearings and in arthrodial human joint (knee and hip) diseases.Basque Government Grants IT1555-22 and KK-2022/00090; and MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

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

Heat Transfer

Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer

Second All-Union Seminar on Hydromechanics and Heat and Mass Exchange in Weightlessness, summaries of reports

Abstracts of reports are given which were presented at the Second All Union Seminar on Hydromechanics and Heat-Mass Transfer in Weightlessness. Topics include: (1) features of crystallization of semiconductor materials under conditions of microacceleration; (2) experimental results of crystallization of solid solutions of CDTE-HGTE under conditions of weightlessness; (3) impurities in crystals cultivated under conditions of weightlessness; and (4) a numerical investigation of the distribution of impurities during guided crystallization of a melt

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffusothermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values