Group theoretical and compatibility approaches to some nonlinear PDEs arising in the study of non-Newtonian fluid mechanics

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015.This thesis is primarily concerned with the analysis of some nonlinear problems arising in the study of non-Newtonian fluid mechanics by employing group theoretic and compatibility approaches. It is well known now that many manufacturing processes in industry involve non-Newtonian fluids. Examples of such fluids include polymer solutions and melts, paints, blood, ketchup, pharmaceuticals and many others. The mathematical and physical behaviour of non-Newtonian fluids is intermediate between that of purely viscous fluid and that of a perfectly elastic solid. These fluids cannot be described by the classical Navier–Stokes theory. Striking manifestations of non-Newtonian fluids have been observed experimentally such as the Weissenberg or rod-climbing effect, extrudate swell or vortex growth in a contraction flow. Due to diverse physical structure of non-Newtonian fluids, many constitutive equations have been developed mainly under the classification of differential type, rate type and integral type. Amongst the many non-Newtonian fluid models, the fluids of differential type have received much attention in order to explain features such as normal stress effects, rod climbing, shear thinning and shear thickening. Most physical phenomena dealing with the study of non-Newtonian fluids are modelled in the form of nonlinear partial differential equations (PDEs). It is easier to solve a linear problem due to its extensive study as well due t

Comparison of Selected Agro-Based Filter Media for Stormwater Quality Improvement

Polluted stormwater has become a severe problem in the environment as the runoff collecting various contaminants before discharged into water bodies, degrading the water quality and risking aquatic life. This study aims to evaluate selected agro-based filter media to treat stormwater through environmental laboratory works. These include kernel shell, coconut husk, coconut shell, durian shell, sugarcane bagasse, and pineapple leaves. The stormwater samples used were collected from a pond in Universiti Malaysia Sabah, whereas the filter column is configured through a combination of 80% of agro-based media and 20% of aggregate. Filter performance is evaluated for turbidity, pH, dissolved oxygen, biochemical oxygen demand, and ammoniacal nitrogen. Overall, the findings show the potential in utilizing agro-based media, particularly the shell-based media of CS300, KS300, and DS200. Further investigations are recommended to further study the application of agro-based media in improving the quality of stormwate

Comparison between polyvinyl alcohol (PVA) nanofiber and polyvinyl alcohol (PVA) nanofiber/hydroxyapatite (HA) for removal of Zn2+ ions from wastewater

AbstractNanocomposites in the form of continuous and aligned polyvinyl alcohol (PVA) nanofibers have been obtained by the electrospinning process. These fibers were used as matrix for hydroxyapatite (HA). PVA and PVA/HA nanofibers were fabricated and crosslinked with glutaraldehyde (GA). The hybrid of polymer with ceramics (HA) shows good properties of large surface area and good porosity that were demonstrated by different characterization techniques such as FTIR, SEM, XRD and EDX which illustrate the ratio of HA. The prepared nanofibrous membranes are used for removal of Zn2+ from simulated water. The potential of these synthesized sorbents to remove Zn2+ ions from aqueous solutions was investigated in batch experiments, where several parameters such as the sorbate/sorbent’s contact time, initial Zn2+ ions concentration and sorbent dosage were investigated. The equilibrium concentration of Zn2+ ions was identified by the atomic absorption spectrophotometry and the adsorption process was studied by the isotherm models such as Langmuir, Freundlich and Temkin. The Zn2+ adsorption process for PVA and PVA/HA nanofibrous membranes was fitted to Langmuir and Freundlich isotherm models respectively

Closed-Form Solutions for a Nonlinear Partial Differential Equation Arising in the Study of a Fourth Grade Fluid Model

The unsteady unidirectional flow of an incompressible fourth grade fluid bounded by a suddenly moved rigid plate is studied. The governing nonlinear higher order partial differential equation for this flow in a semiinfinite domain is modelled. Translational symmetries in variables and are employed to construct two different classes of closed-form travelling wave solutions of the model equation. A conditional symmetry solution of the model equation is also obtained. The physical behavior and the properties of various interesting flow parameters on the structure of the velocity are presented and discussed. In particular, the significance of the rheological effects are mentioned

The dynamism of the red berries sector and its implication on water resources in the Loukkos region of Morocco

La filière marocaine des fruits rouges a connu un essor consistant durant la dernière décennie, soutenue par la stratégie nationale agricole et tractée par l’expansion de la demande sur les marchés internationaux. Cependant, l’évolution qu’a enregistrée la production marocaine interpelle sur la pérennité et la bonne gestion des ressources hydriques. Cette étude vise à évaluer les implications du système de production des fruits rouges en matière d’utilisation et de valorisation de l’eau d’irrigation. Pour y répondre, nous avons calculé la valorisation financière et agronomique de l’eau, correspondant respectivement au rapport de la marge bénéficiaire nette et de la production totale sur le volume d’eau apportée. Les données ont été collectées sur le terrain moyennant un échantillonnage aléatoire et simple dans le périmètre du Loukkos sur 93 exploitations de fruits rouges. Au niveau de la valorisation financière, la myrtille affiche une rentabilité de 67,3 DH/m³ d’eau, expliquée principalement par son prix élevé, suivie de la framboise avec 54,2 DH/m³ puis de la fraise avec 12,4 DH/m³ d’eau. A l’inverse, la valorisation agronomique est plus importante chez la fraise avec 7,12 Kg/m³, suivie de la framboise avec 3,35 Kg/m³ puis de la myrtille à 1,96 Kg/m³. Cet article met l’accent sur les points cruciaux de la filière tels que la durabilité de l’apport hydrique, la disponibilité de la main d’œuvre qualifiée et le foncier. Il préconise également la conquête d’autres marchés d’export et la mise aux normes nationales des produits destinés à aux marchés internationaux. Mots-clés: Fruits rouges, valorisation de l’eau, productivité de l’eau, Loukkos, Irrigation.The Moroccan red fruits sector has grown steadily over the last decade, supported by the national agricultural strategy and pulled by the expansion of demand in the international markets. However, the evolution recorded by Moroccan production calls into question the sustainability and good management of water resources. This study aims to evaluate the implications of the red fruits production system for the use and valorization of irrigation water. For this purpose, we calculate the financial and agronomic valorization of water, corresponding respectively to the ratio of the net profit margin and the total production on the volume of water supplied. Data were collected in the field through random and simple sampling in the region of Loukkos on 93 farms producing the red berries. In terms of financial valorization, the blueberry has a profitability of 67.3 DH/m³ of water, explained mainly by its high price, followed by raspberry with 54.2 DH/m³ and strawberry with 12.4 DH/m³ of water. Conversely, the agronomic valorization is higher for strawberries with 7.12 Kg / m³, followed by raspberry with 3.35 Kg/m³ and blueberry with 1.96 Kg/m³. This article discusses the crucial points of the sector such as the sustainability of water supply, the availability of qualified labor and land issues. It also advocates the search of other international markets and setting up national standards for products for export. Key words: Red berries, water valorization, water productivity, Loukkos, irrigation

Study on adsorption behavior and separation efficiency of naturally occurring clay for some elements by batch experiments

This paper describes the versatile nature of clay that was obtained from Suez Gulf, Suez city, Egypt, as a new low cost natural resource which is non toxic to ecosystem and highly effective adsorbent material. The properties of the natural clay and its significance in removing Th(IV) and Ce(IV) as a representative of tetravalent actinides and lanthanides, respectively, La(III) as a representative of trivalent lanthanides as well as homologues of americium and Sr(II) as one of the fission products, in aqueous solutions have been studied, in order to consider its application for nuclear waste treatment. Batch experiments have been carried out to determine the effect of various factors such as initial metal ion concentration, clay dose, pH, contact time, and temperature on the adsorption process. The results have dictated that, the adsorption efficiency of the natural clay was significantly high at pH = 4. Maximum metal ion uptake capacity of clay has been obtained from batch studies was 99.24, 98.21, 77.76 and 57.94% for Th(IV), Ce(IV), La(III) and Sr(II), respectively. The thermodynamic parameters (ΔHo, ΔSo and ΔGo) have been calculated from the temperature dependent adsorption isotherms. Furthermore, separation factors (α) have been calculated in order to separate these elements from each other at pH = 4

Influence of social networking on Malaysian female secondary students: a qualitative study across three schools

Social networking (SN) allows individuals to make connections with each other for both social and business purposes. The purpose of this research study is to find out the influence of SN on students from three Malaysian secondary schools by comparing their attitudes and behaviour towards SN besides finding out whether they are aware of the risks and danger involved, and how they handle them. These schools are all normal day schools and are located in three different types of school environments in Selangor and Kuala Lumpur namely: urban, suburban and rural. Focus groups interviews were conducted on these students who were asked to give their response to seven scenarios depicting negative situations involving SN such as texting, cyberbullying, and hacking and identity theft. The findings revealed that these students were not very different from those in the west in that they are aware of risks involving in SN and will stay clear of risky behaviours. However, students in these three schools handled the problems related to SN in a more direct manner compared to the elite students in Thang et al.’s (2016) study. In particular, students in School C which is a rural school seemed to be less perturbed over the negative consequences of SN compared to students in the other schools

Sequencing of Rhinoviruses in Egyptian children with respiratory tract infections

Background: Human rhinoviruses (HRV) are one of the most common causes of upper respiratory tract infections among young children.  Human rhinoviruses have  a wide genetic diversity. They include three different species A, B and-C. Acute Respiratory Infection (ARI) is considered to be  an important  cause of morbidity and mortality in neonates and children. Aim of the study:  To  detect  the common  subtypes of circulating HRV among Egyptian children with respiratory infections for  further epidemiological characterization. Methods: We enrolled 161 children admitted to Ain Shams Pediatric University Hospital complaining of respiratory tract infections.  Human rhinoviruses  were detected by RT-PCR. Sequencing of HRV was done based on viral proteins (VP4-VP2) genomic region analyses by RT-PCR. Results: HRV were detected in 54 cases (33.5%)with respiratory tract infections.Sixty-five (65) % of detected HRV was in children aged 5-10 years. Molecular sequencing  showed high prevalence of HRV-C (67%) followed by HRV-A (33%). Conclusion:  This study is from the first few studies that revealed diversity of HRV in Egypt. Different phylogenetic studies are needed to evaluate their diversity and to trace their spread and epidemiological origin

Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest