Numerical studies of nanofluid boundary layer flows using spectral methods.

Doctoral Degree. University of KwaZulu-Natal, PietermaritzburgThis thesis is focused on numerical studies of heat and mass transport processes that occur in nanofluid boundary layer flows. We investigate heat and mass transfer mechanisms in the flow of a micropolar nanofluid above a stretching sheet, the squeezed nanofluid flow between two parallel plates and the impact of activation energy and binary chemical reaction on nanofluid flow past a rotating disk. We present an analysis of entropy generation in nanofluid flow past a rotating disk and nanofluid flow past a stretching surface under the influence of an inclined magnetic field. This study aims to numerically determine to a high degree of accuracy, how nanoparticles can be utilized to alter heat and transport properties of base fluids in order to enhance or achieve desirable properties for thermal systems. The heat and mass transfer processes that feature in nanofluid boundary layer flow are described by complex nonlinear transport equations which are difficult to solve. Because of the complex nature of the constitutive equations describing the flow of nanofluids, finding analytic solutions has often proved intractable. In this study, the model equations are solved using the spectral quasilinearization method. This method is relatively recent and has not been adequately utilized by researchers in solving related problems. The accuracy and reliability of the method are tested through convergence error and residual error analyses. The accuracy is further tested through a comparison of results for limiting cases with those in the literature. The results confirm the spectral quasilinearization method as being accurate, efficient, rapidly convergent and suited for solving boundary value problems. In addition, among other findings, we show that nanofluid concentration enhances heat and mass transfer rates while the magnetic field reduces the velocity distribution. The fluid flows considered in this study have significant applications in science, engineering and technology. The findings will contribute to expanding the existing knowledge on nanofluid flow

Overlapping grid spectral collocation methods for nonlinear differential equations modelling fluid flow problems.

Doctoral Degree. University of KwaZulu-Natal, Durban.The focus of this thesis is on computational grid-manipulation to enhance the accuracy, convergence and computational efficiency of spectral collocation methods for the solution of differential equations in fluid mechanics. The need to develop highly accurate, convergent and computationally efficient numerical techniques for solving nonlinear problems is an ever-recurring theme in numerical mathematics. Spectral methods have been shown in the literature to be more accurate and efficient than some common numerical methods, such as finite difference methods. However, their accuracy deteriorates as the computational domain increases and when the number of grid points reaches a certain critical value. The spectral collocation algorithm produces dense matrix equations, for which there is no known efficient solution method. These deficiencies necessitate the development of spectral techniques that produce less dense matrix equations using fewer grid points. This thesis presents a new improvement in spectral collocation methods with particular application to nonlinear differential equations that model problems arising in fluid mechanics. The improvement described in this thesis requires the use of overlapping grids when descritizing the solution domain for Chebyshev spectral collocation method. The thesis is presented in two related subdivisions. In Part A, the overlapping grid approach is used only in space variable when solving nonlinear ordinary and partial differential equations. Subsequently, the overlapping grid approach is used in both the space and time variables in the solution of partial differential equations. This thesis is also devoted to analysing solutions of fluid flow models through various practical geometries with particular interest in non-Newtonian fluid flows. The physics of these fluid flows is studied through parametric studies on the effects of diverse thermophysical parameters on the fluid properties, changes in shear stresses, and heat and mass transport. Key findings, are inter alia, that the overlapping multi-domain spectral techniques are computationally efficient, produce stable and accurate results using a small number of grid points in each subinterval and in the entire computational domain. Using the overlapping grids yields less dense coefficient matrices that invert easily. Changes in thermophysical parameters has significant consequences for the fluid properties, and heat and mass transfer processes

Book of abstracts of the 10th International Chemical and Biological Engineering Conference: CHEMPOR 2008

This book contains the extended abstracts presented at the 10th International Chemical and Biological Engineering Conference - CHEMPOR 2008, held in Braga, Portugal, over 3 days, from the 4th to the 6th of September, 2008. Previous editions took place in Lisboa (1975, 1889, 1998), Braga (1978), Póvoa de Varzim (1981), Coimbra (1985, 2005), Porto (1993), and Aveiro (2001). The conference was jointly organized by the University of Minho, “Ordem dos Engenheiros”, and the IBB - Institute for Biotechnology and Bioengineering with the usual support of the “Sociedade Portuguesa de Química” and, by the first time, of the “Sociedade Portuguesa de Biotecnologia”. Thirty years elapsed since CHEMPOR was held at the University of Minho, organized by T.R. Bott, D. Allen, A. Bridgwater, J.J.B. Romero, L.J.S. Soares and J.D.R.S. Pinheiro. We are fortunate to have Profs. Bott, Soares and Pinheiro in the Honor Committee of this 10th edition, under the high Patronage of his Excellency the President of the Portuguese Republic, Prof. Aníbal Cavaco Silva. The opening ceremony will confer Prof. Bott with a “Long Term Achievement” award acknowledging the important contribution Prof. Bott brought along more than 30 years to the development of the Chemical Engineering science, to the launch of CHEMPOR series and specially to the University of Minho. Prof. Bott’s inaugural lecture will address the importance of effective energy management in processing operations, particularly in the effectiveness of heat recovery and the associated reduction in greenhouse gas emission from combustion processes. The CHEMPOR series traditionally brings together both young and established researchers and end users to discuss recent developments in different areas of Chemical Engineering. The scope of this edition is broadening out by including the Biological Engineering research. One of the major core areas of the conference program is life quality, due to the importance that Chemical and Biological Engineering plays in this area. “Integration of Life Sciences & Engineering” and “Sustainable Process-Product Development through Green Chemistry” are two of the leading themes with papers addressing such important issues. This is complemented with additional leading themes including “Advancing the Chemical and Biological Engineering Fundamentals”, “Multi-Scale and/or Multi-Disciplinary Approach to Process-Product Innovation”, “Systematic Methods and Tools for Managing the Complexity”, and “Educating Chemical and Biological Engineers for Coming Challenges” which define the extended abstracts arrangements along this book. A total of 516 extended abstracts are included in the book, consisting of 7 invited lecturers, 15 keynote, 105 short oral presentations given in 5 parallel sessions, along with 6 slots for viewing 389 poster presentations. Full papers are jointly included in the companion Proceedings in CD-ROM. All papers have been reviewed and we are grateful to the members of scientific and organizing committees for their evaluations. It was an intensive task since 610 submitted abstracts from 45 countries were received. It has been an honor for us to contribute to setting up CHEMPOR 2008 during almost two years. We wish to thank the authors who have contributed to yield a high scientific standard to the program. We are thankful to the sponsors who have contributed decisively to this event. We also extend our gratefulness to all those who, through their dedicated efforts, have assisted us in this task. On behalf of the Scientific and Organizing Committees we wish you that together with an interesting reading, the scientific program and the social moments organized will be memorable for all.Fundação para a Ciência e a Tecnologia (FCT