On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium

An analysis of double diffusive convection induced by a uniformly heated and salted horizontal wavy surface in a porous medium is presented. The wavy surface is first transformed into a smooth surface via a suitable coordinate transformation and the transformed nonsimilar coupled nonlinear parabolic equations are solved using the Keller box method. The local and average Nusselt and Sherwood numbers are given as functions of the streamwise coordinate and the effects of various physical parameters are discussed in detail. The effects of the Lewis number, buoyancy ratio, and wavy geometry on the dynamics of the flow are studied. It was found, among other observations, that the combined effect of Dufour and Soret parameters is to reduce both heat and mass transfer

Temperature dependent viscosity on single-phase and two-phase flow of eyring powell fluid over a vertical stretching sheet

Advancement in the study of fluid mechanics has gained worldwide attention owing to its prominence applications in industry and engineering, those related to chemicals industries, thermal oil recovery, food and slurry transportation, polymer and food processing. Keeping views of its rheological features, numerous researchers have concentrated on the flows dealing with these versatile nature fluids. Studies have found that conventional equations such as Navier-Stokes are unable to reliably explain the rheological behavior of some fluids, as investigations on actual applications is expensive and risky at times. Therefore, this study focused on the subfamily undernon-Newtonian fluid models, namely Eyring Powell fluid to overcome these limitations. In line with this, a studyon mathematical model of a convective boundary layer under temperature-dependent viscosity on single-phase and two-phase flow over a vertical stretching sheet with Newtonian heating (NH) boundary conditions for Eyring Powell fluid was carried out. The key contributions of this thesis include filling the research gap on mathematical models of Eyring Powell fluid under single-phase and two-phase flow. Three main analyses were conducted; the first and second analysis focused on the study of forced and mixed convection of single-phase flow, while the third analysis studied the mixed convection under two-phase flow. The governing non-linear equations for each problem converted into ordinary differential equation using suitable set of similarity transformation before numerically solved by using the implicit finite difference scheme known asthe Kellerbox method (KBM). The numerical models were computed usingthe MATLAB software and the results present the behavior of fluid flow characteristics involving non-dimensional velocity and temperature distribution as well as skin friction and heat transfer of fluid for various nondimensional parameters namely, fluid parameters, Prandtl number, mixed convection parameter, fluid-particle interaction, specific heat ratio of mixture, mass concentration of particle phase and viscosity parameter. The numerical solutions obtained were illustrated through graphs and tables. From the obtained results, it was observed that the investigated parameters affect of both fluid and dust fluid characteristics, specifically skin friction, heat transfer and the fluid’s velocity and temperature. Under single-phase and two-phase flow,it clearly indicates that the fluid profiles are asymptotically approached to zero, farther from the plate, which matches the boundary condition appropriately. It is anticipated that the results in this study will lead to a deeper understanding of the characteristics of single-phase and twophase fluid flow as well as the solutions to its flow problems

On paired decoupled quasi-linearization methods for solving nonlinear systems of differential equations that model boundary layer fluid flow problems.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.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