1,721,004 research outputs found
Double-diffusive convection flow in a porous medium saturated with a nanofluid.
Get PDFIn this work, we studied heat and mass transfer in a nanofluid flow over a stretching sheet.
Fluid flow in different flow geometries was studied and a co-ordinate transformation was
used to transform the governing equations into non-dimensional non-similar boundary layer
equations. These equations were then solved numerically using both established and recent
techniques such as the spectral relaxation and spectral quasi-linearization methods. Numerical
solutions for the heat transfer, mass transfer and skin friction coefficients have been presented
for different system parameters, such as heat generation, Soret and Dufour effects, chemical
reaction, thermal radiation influence, the local Grashof number, Prandtl number, Eckert number,
Hartmann number and the Schmidt number. The dependency of the skin friction, heat
and mass transfer coefficients on these parameters has been quantified and discussed. The
accuracy, and validity of the spectral relaxation and spectral quasi-linearization methods has
been established
Numerical study of convective fluid flow in porous and non-porous media.
Get PDFPh. D. University of KwaZulu-Natal, Pietermaritzburg 2015.Abstract available in PDF file
On the numerical solution of fractional partial differential equations : an investigation of spectral methods.
Get PDFMaster of Science in Mathematics. University of KwaZulu-Natal, Pietermaritzburg 2017.Abstract available in PDF file
A numerical study of heat transfer and entropy generation in Powell-Eyring nanofluid flows.
Get PDFDoctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The heat transfer in non-Newtonian nanofluid flow through different geometries is an important
research area due to the wide application of these fluids in biomedical, chemical and thermal engineering
processes. The continuous generation of entropy leads to exergy loss which reduces the
performance and efficiency of any physical system, therefore, the minimization of entropy generation
becomes necessary. In this thesis, we present a numerical study of heat transfer and entropy
generation in non-Newtonian nanofluid flows. We study the flow of a Powell-Eyring nanofluid,
using models developed from experimental data. The equations that model the flow are, in each
case, reduced to systems of nonlinear differential equations using Lie group theory scaling transformations.
Accurate, efficient and rapidly converging spectral numerical techniques including
the spectral quasilinearizzation, spectral local linearization and bivariate spectral quasilinearization
methods are used to find the numerical solutions. The results show, among other findings,
that increasing either the nanoparticle volume fraction or thermal radiation parameter enhances the
nanofluid temperature, entropy generation and the Bejan number. In addition, we find that the Nusselt
number increases with the temperature ratio parameter and thermal radiation. The results from
this study may find use in the design of cooling devices to enhance and optimize the performance
of thermal systems
On convection and flow in porous media with cross-diffusion.
No full textThesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.In this thesis we studied convection and cross-diffusion effects in porous media.
Fluid flow in different flow geometries was investigated and the equations for momentum, heat and mass transfer transformed into a system of ordinary differential
equations using suitable dimensionless variables. The equations were solved using a
recent successive linearization method. The accuracy, validity and convergence of the
solutions obtained using this method were tested by comparing the calculated results
with those in the published literature, and results obtained using other numerical
methods such as the Runge-Kutta and shooting methods, the inbuilt Matlab bvp4c
numerical routine and a local non-similarity method.
We investigated the effects of different fluid and physical parameters. These
include the Soret, Dufour, magnetic field, viscous dissipation and thermal radiation
parameters on the fluid properties and heat and mass transfer characteristics.
The study sought to (i) investigate cross-diffusion effects on momentum, heat and
mass transport from a vertical flat plate immersed in a non-Darcy porous medium
saturated with a non-Newtonian power-law fluid with viscous dissipation and thermal
radiation effects, (ii) study cross-diffusion effects on vertical an exponentially stretching surface in porous medium and (iii) apply a recent hybrid linearization-spectral
technique to solve the highly nonlinear and coupled governing equations. We further
sought to show that this method is accurate, efficient and robust by comparing it with established methods in the literature.
In this study the non-Newtonian behaviour of the fluid is characterized using the
Ostwald-de Waele power-law model. Cross-diffusion effects arise in a broad range
of fluid flow situations in many areas of science and engineering. We showed that
cross-diffusion has a significant effect on heat and mass-transfer processes and cannot
be neglected
Multi-parameter perturbation analysis of a second grade fluid flow past an oscillating infinite plate.
No full textThesis (M.Sc.) - University of KwaZulu-Natal, Pietermaritzburg, 2009.In this dissertation we consider the two dimensional flow of an incompressible and electrically conducting second grade fluid past a vertical porous plate with constant suction. The flow is permeated by a uniform transverse magnetic field. The aim of this study is to use the multi-parameter perturbation technique to study the effects of Eckert numbers on the flow of a pulsatile second grade fluid along a vertical plate. We further aim to investigate the effects of other fluid and physical parameters such as the Prandtl numbers, Hartmann numbers, viscoelastic parameter, angular frequency and suction velocity on boundary layer velocity, temperature, skin friction and the rate of heat transfer. Similarity transformations are used to reduce the governing partial differential equations to ordinary differential equations. We used perturbation methods to solve the coupled ordinary differential equations for zero Eckert number and the multiparameter perturbation technique to solve the coupled ordinary differential equations for small viscoelastic parameters and Eckert numbers. It is found that increasing the Eckert number or the viscoelastic parameter enhances the boundary layer velocity while reducing the temperature, the rate of heat transfer and the skin-friction. The results for the boundary layer velocity and the temperature are presented graphically and discussed. The results for the rate of heat transfer in terms of the Nusselt number and the skin friction are tabulated and discussed. A good agreement is found between these results and other published research. The comparison between the results for zero Eckert numbers and small Eckert numbers is also presented graphically and discussed
A numerical study of entropy generation, heat and mass transfer in boundary layer flows.
Get PDFDoctoral 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
Double-diffusive convection flow in porous media with cross-diffusion.
No full textThesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.In this thesis we study double-diffusive convection and cross-diffusion effects in flow
through porous media. Fluid flows in various flow geometries are investigated and
the governing equations are solved analytically and numerically using established
and recent techniques such as the Keller-box method, the spectral-homotopy analysis
method and the successive linearisation method. The effects of the governing parameters
such as the Soret, Dufour, Lewis, Rayleigh and the Peclet numbers and the
buoyancy ratio on the fluid properties, and heat and mass transfer at the surface are
determined. The accuracy, computational efficiency and validity of the new methods
is established.
This study consists of five published and one submitted paper whose central theme is
the study of double-diffusive convection in porous media. A secondary theme is the
application of recent numerical semi-numerical methods in the solution of nonlinear
boundary value problems, particularly those that arise in the study of fluid flow
problems.
Paper 1. An investigation of the quiescent state in a Maxwell fluid with double-diffusive
convection in porous media using linear stability analysis is presented. The
fluid motion is modeled using the modified Darcy-Brinkman law. The critical Darcy-
Rayleigh numbers for the onset of convection are obtained and numerical simulations
carried out to show the effects of the Soret and Dufour parameters on the critical
Darcy-Rayleigh numbers. For some limiting cases, known results in the literature are
recovered.
Paper 2. We present an investigation of heat and mass transfer in a micropolar fluid
with cross-diffusion effects. Approximate series solutions of the governing non-linear
differential equations are obtained using the homotopy analysis method (HAM). A
comparison is made between the results obtained using the HAM and the numerical
results obtained using the Matlab bvp4c numerical routine.
Paper 3. The spectral homotopy analysis method (SHAM) as a new improved version
of the homotopy analysis method is introduced. The new technique is used to solve
the MHD Jeffery-Hamel problem for a convergent or divergent channel. We show
that the SHAM improves the applicability of the HAM by removing the restrictions
associated with the HAM as well as accelerating the convergence rate.
Paper 4. We present a study of free and forced convection from an inverted cone
in porous media with diffusion-thermo and thermo-diffusion effects. The highly nonlinear
governing equations are solved using a novel successive linearisation method
(SLM). This method combines a non-perturbation technique with the Chebyshev
spectral collection method to produce an algorithm with accelerated and assured
convergence. Comparison of the results obtained using the SLM, the Runge-Kutta
together with a shooting method and the Matlab bvp4c numerical routine show the
accuracy and computational efficiency of the SLM.
Paper 5. Here we study cross-diffusion effects and convection from inverted smooth
and wavy cones. In the case of a smooth cone, the highly non-linear governing
equations are solved using the successive linearisation method (SLM), a shooting
method together with a Runge-Kutta of order four and the Matlab bvp4c numerical
routine. In the case of the wavy cone the governing equations are solved using the
Keller-box method.
Paper 6. We examine the problem of mixed convection, heat and mass transfer along
a semi-infinite plate in a fluid saturated porous medium subject to cross-diffusion and
radiative heat transfer. The governing equations for the conservation of momentum,
heat and solute concentration transfer are solved using the successive linearisation
method, the Keller-box technique and the Matlab bvp4c numerical routine
A numerical study of entropy generation in nanofluid flow in different flow geometries.
Get PDFThis 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
On free convection and heat transfer in a micropolar fluid flow past a moving semi-infinite plate.
No full textThesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.In this dissertation we investigate free convective heat and mass transfer in micropolar fluid flow past a moving semi-infinite vertical porous plate in the presence of a magnetic field. The aim of this study was to use recent semi-numerical methods such as the successive linearisation method and the spectral-homotopy analysis method to study the effects of viscous heating and the effects of different fluid parameters. The governing boundary layer equations for linear momentum, angular momentum (microrotation), temperature and concentration profiles are transformed to a system of ordinary differential equations and solved using the successive linearisation method and the spectral-homotopy analysis method. The accuracy of the solutions was determined by comparison with numerical approximations obtained using the Matlab bvp4c solver. The influences of the micropolar parameter, Darcy number, Prandtl number, Schmidt number, magnetic parameter, heat absorption parameter, Soret and Dufour numbers, local Reynolds number and Grashof number on velocity, microrotation, temperature and concentration profiles were determined. The results obtained are presented graphically and in tabular form
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