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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. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

A steady state two-dimensional mixed convection problem in an air filled square unit cavity has been numerically investigated. Two different cases of heating are investigated and compared. In the first case, the bottom wall was uniformly heated, the side walls were linearly heated and the top moving wall was heated sinusoidally. The second case differed from the first in that the side walls were instead uniformly cooled. This investigation is an extension of the work by Basak et al. [6, 7] who investigated mixed convection in a square cavity with similar boundary conditions to the cases listed above with the exception of the top wall which was well insulated. In this dissertation, their work is extended to include a sinusoidally heated top wall. The nonlinear coupled equations are solved using the Penalty Galerkin Finite Element Method. Stream function and isotherm results are found for various values of the Reynolds number and the Grashof number. The strength of the circulation is seen to increase with increasing Grashof number and to decrease with increasing Reynolds number for both cases of heating. A comparison is made between the stream function and isotherm results for the two cases. The results for the rate of heat transfer in terms of the Nusselt number are discussed. Both local and average Nusselt number results are presented and discussed. The average Nusselt number is found using Simpson's 1/3rd rule. The rate of heat transfer is found to be higher at all four walls for the case of cooled side walls than that of linearly heated side walls. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

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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. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

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. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

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