106 research outputs found
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
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Pore-scale modeling of viscoelastic flow and the effect of polymer elasticity on residual oil saturation
textPolymers used in enhanced oil recovery (EOR) help to control the mobility ratio between oil and aqueous phases and as a result, polymer flooding improves sweep efficiency in reservoirs. However, the conventional wisdom is that polymer flooding does not have considerable effect on pore-level displacement because pressure forces would not be enough to overcome trapping caused by capillary forces. Recently, both coreflood experiments and field data suggest that injecting viscoelastic polymers, such as hydrolyzed polyacrylamide (HPAM), can result in lower residual oil saturation. The hypothesis is that the polymer elasticity provides several pore-level mechanisms for oil mobilization that are generally not significant for purely-viscous fluids. Both experiments and modeling need to be performed to investigate the effect of polymer elasticity on residual oil saturation. Pore-scale modeling and micro-fluidic experiments can be used to investigate pore-level physics, and then used to upscale to the macro-scale. The objective of this work is to understand the effect of polymer elasticity on apparent viscosity and residual oil saturation in porous media. Single- and multi-phase pore-level computational fluid dynamics (CFD) modeling for viscoelastic polymer flow is performed to investigate the dominant mechanisms at the pore level to mobilize trapped oil. Several interesting results are found from the CFD results. First, the elasticity of the polymer results in an increase in normal stress at the pore-level; therefore, the normal stresses exerted on a static oil droplet are significant and not negligible as for a purely-viscous fluid. The CFD results show that viscoelastic fluid exerts additional forces on the oil-phase which may help mobilize trapped oil out of the porous medium. Second, due to the elasticity of polymer, the viscoelastic polymer has some level of pulling effect; while passing above a dead-end pore it can pull out the trapped oil phase and then mobilize it. However, both CFD modeling and micro-fluidic experiments show the pulling-effect is not likely the main mechanism to reduce oil saturation at pore-level. Third, dynamic CFD simulations show less deformation of the oil phase while viscoelastic polymer is displacing fluid compared to purely viscous fluid. It may justify the hypothesis that polymer elasticity resists against snap-off mechanism. As a result, when viscoelastic polymer displaces the oil ganglia, the oil phase does not snap off, and the oil phase remains connected, and therefore easier to move in porous media compared to disconnected oil. For single phase flow, a closed-form flow equation has been developed based on CFD modeling in converging/diverging ducts representative of pore throats. The pore-level equations were substituted into a pore-network model and validated against experimental data. Good agreement is observed. This study reveals important findings about the effect of polymer elasticity to reduce the residual oil saturation; however, more experiments and simulations are recommended to fully-understand the mobilization mechanisms and take advantage of them to optimize the polymer-flooding process in the field.Petroleum and Geosystems Engineerin
Transient Stage Comparison of Couette Flow under Step Shear Stress and Step Velocity Boundary Conditions
Couette flow has been widely used in many industrial and research processes, such as viscosity measurement. For the study on thixotropic viscosity, step-loading, which includes (1) step shear stress and (2) step velocity conditions, is widely used. Transient stages of Couette flow under both step wall shear stress and step wall velocity conditions were investigated. The relative coefficient of viscosity was proposed to reflect the transient process. Relative coefficients of viscosity, dimensionless velocities and dimensionless development times were derived and calculated numerically. This article quantifies the relative coefficients of viscosity as functions of dimensionless time and step ratios when the boundary is subjected to step changes. As expected, in the absence of step changes, the expressions reduce to being functions of dimensionless time. When step wall shear stresses are imposed, the relative coefficients of viscosity changes from the values of the step ratios to their steady-state value of 1. but With step-increasing wall velocities, the relative coefficients of viscosity decrease from positive infinity to 1. The relative coefficients of viscosity increase from negative infinity to 1 under the step-decreasing wall velocity condition. During the very initial stage, the relative coefficients of viscosity under step wall velocity conditions is further from 1 than the one under step wall shear stress conditions but the former reaches 1 faster. Dimensionless development times grow with the step ratio under the step-rising conditions and approaches the constant value of 1.785 under the step wall shear stress condition, and 0.537 under the step wall velocity condition respectively. The development times under the imposed step wall shear stress conditions are always larger than the same under the imposed step wall velocity conditions
Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel : mathematical model
A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic nonNewtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption and lubrication theory approximations. Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV) is also considered. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design
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
Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate : a thermodynamic analysis
The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The non-dimensional conservation equations for mass, momentum, and energy are solved using a Crank-Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems
Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects
In recent years, significant progress has been made in modern micro- and nanotechnologies related to
applications in micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluent
media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological
micro-organisms. Motivated by bio-nanofluid rotating disk oxygenators in medical engineering, in the current
work, a mathematical model is developed for steady convective Von Karman swirling flow from an
impermeable power-law radially stretched disk rotating in a Darcy porous medium saturated with nanofluid
doped with gyrotactic micro-organisms. Anisotropic slip at the wall and blowing effects due to concentration
are incorporated. The nano-bio transport model is formulated using non-linear partial differential equations
(NPDEs), which are transformed to a set of similarity ordinary differential equations (SODEs) by appropriate
transformations. The transformed boundary value problem is solved by a Chebyshev collocation method. The
impact of key parameters on dimensionless velocity components, concentration, temperature and motile
microorganism density distributions are computed and visualized graphically. Validation with previous studies
is included. It is found that that the effects of suction provide a better enhancement of the heat, mass and
microorganisms transfer in comparison to blowing. Moreover, physical quantities decrease with higher slip
parameters irrespective of the existence of blowing. Temperature is suppressed with increasing thermal
slip whereas nanoparticle concentration is suppressed with increasing wall mass slip. Micro-organism
density number increases with the greater microorganism slip. Radial skin friction is boosted with
positive values of the power law stretching parameter whereas it is decreased with negative values.
The converse response is computed for circumferential skin friction, nanoparticle mass transfer rate
and motile micro-organism density number gradient. Results from this study are relevant to novel
bioreactors, membrane oxygenators, food processing and bio-chromatography
RHEOLOGICAL CHARACTERIZATION OF SUSPENSIONS
The aim of this research is to obtain a meaningful rheological
characterization of deflocculated china clay suspensions. It is
generally true that in the study of suspensions relatively little
successful work has been carried out on the flow properties of highly
concentrated suspensions as compared with dilute suspensions; it was
decided therefore that the work, presented in this thesis, should be
confined to the study of higher concentration suspensions. A survey
is given of previous work on the rheological characterization of
suspensions and the reasons for choosing the clay suspensions in
particular, are discussed. Since a knowledge of the microscopic nature
of the particles in suspension is important for the understanding of
the macroscopic behaviour of the suspensions, a detailed account of
the relevant aspects of clay and its rheological behaviour is presented.
The investigation consists of a theoretical and experimental study
of the suspensions. The experimental results are obtained by using a
commercial rheometer, the Weissenberg Rheogoniometer. Experiments are
performed which include steady shear studies, oscillatory shear studies
and studies of a combined steady and low-amplitude oscillatory shear
flow. A theory is developed for this latter flow situation and
expressions for the percentage increase in couple are obtained based
on different rheological equations of state.
Concentration effects are examined and it is shown that, with
increasing concentration, an initial shear thinning region is followed
by a shear thickening one. It is also found that marked elastic
properties are exhibited by these highly concentrated clay suspensions.
Qualitative agreement is obtained between theory and experiment for
all suspensions considered and at the highest concentrations it is
shown (for the first time) that it is possible to characterize shear
thinning and shear thickening properties of a fluid using one equation
of state.
The experimental results indicate that this programme of work may
have important implications for certain industrial nearly viscometric
flow situations as well as the whole approach being applicable to other
concentrated suspension systems
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