Repository logo

Doctoral Degrees (Applied Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7094

Browse

Browsing Doctoral Degrees (Applied Mathematics) by Subject "Boundary layer flow."

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    A numerical study of heat and mass transfer in non-Newtonian nanofluid models.
    (2019) Mthethwa, Hloniphile Mildred Sithole.; Sibanda, Precious.; Motsa, Sandile Sydney.
    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.
  • Thumbnail Image
    Item
    On paired decoupled quasi-linearization methods for solving nonlinear systems of differential equations that model boundary layer fluid flow problems.
    (2018) Otegbeye, Olumuyiwa.; Motsa, Sandile Sydney.
    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.