A second-order, single-point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity-pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar-pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

Biodiesel has the potential to contribute significantly to the elimination of the present global energy and climate change logjam, but its production and commercialization have been hindered by the diverse nature of the feedstocks used for production. This paper reviews the effectiveness of applying various types of crop and animal waste-derived catalysts together with innovative feedstock hybridization as an economically viable technique for biodiesel production. Feedstock challenges, availability, and sustainability for large-scale applications are addressed with a view to bridging the existing gaps. Challenges in the use of edible oils and algae oil sources and development remain, but the technique of feedstock hybridization appears to be very promising, innovative, and cost-effective for biodiesel production. The present state of biodiesel production could be improved by the application of simple and cost-effective technologies in the feedstock system. High free fatty acid (FFA) content is the major hurdle to the use of most oils, especially low-grade/advanced oil feedstocks, in biodiesel production. This could be addressed through technological application of feedstock hybrids and biogenic waste-derived heterogenous catalysts, and their biochemical modifications. Conventional technology for the large-scale application of inorganically derived catalysts in biodiesel production with various characteristic differences is presented. Heterogenous catalysts derived from biogenic wastes and their modification could be used to overcome associated problems with the use of inorganic catalysts in biodiesel production. Biogenic waste-derived heterogenous catalysts are renewable, available, eco-friendly, and cost-effective. Technological applications of heterogeneous catalysts derived from biogenic waste are outlined and reviewed, considering various materials and different modification techniques to identify appropriate options for scaling up development. This review also discusses fundamental considerations for the Review

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The sugar industry contributes significantly to the economic growth of South Africa by creating jobs in the agricultural and industrial sectors. However, this industry discharges large amounts of effluent containing a high level of suspended and dissolved solids, which impart colour to the wastewater stream and add treatment cost. Chitosan, a natural polymer, has been used in the coagulation of impurities from the sugar refinery using the one-factor-at-a-time (OFAT) method. The results indicated the removal of total suspended solids (TSS) and colour of 87% and 76% respectively at the pH of 9. Response surface methodology (RSM) was used to maximize the efficiency of this coagulant according to the BoxBehnken design (BBD). The use of RSM was found to have several advantages in comparison to the OFAT, such as the identification of interaction, the use of statistical analysis that produce model equations for optimization and prediction of the behavior of a particular system. Furthermore, at the pH of 9, the BBD yielded TSS and colour removals of 99% and 90% respectively. This should be a motivation for an industrial researcher to deviate from the traditional OFAT especially in process optimization studies.

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The response surface methodology was used to investigate the removal of Pb (II) from an aqueous solution using banana peel with varying operating parameters in a batch mode. The central composite design was used to study the interactive effects of the operating parameters (initial concentration, pH of the solution, adsorbent dosage and the particle size). The banana peel was characterized by FTIR which showed the functional groups, while SEM and EDS were used to study morphology and elemental composition. The optimum removal of Pb(II) was 98.146 % at initial concentration 100 mg/L, pH 5, adsorbent dosage 0.55 g and particle size 75 µm. The deviation between the experimental and the model predicted percentage removal was 5.17 %. The analysis of variance showed that the regression model was significant with a low probability and the correlation coefficient R 2 value of 0.9153. The results showed that the biosorption of Pb(II) was highly influenced by the pH and the adsorbent dosage, while the particle size had little effect on the biosorption process.