Search results for: Water dew point

Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: Maher J. Tadros, Naji K. Al-Mefleh

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The evaluation of non-conventional water resources on seed germination and seedling growth performance at early growth stages is still in progress especially in forage crops. This study was designed to test the effect of four types of water qualities (treated wastewater (TWW), industrial water (IW), grey water (GW), and Distilled water (DW)) on germination and early seedling vigor of Leucaena leucocephala. The results showed that the germination was not significantly affected by the different water qualities. Seed germination reached maximum after 17, 14, 14, and 21 days under GW, IW, TWW, and DW treatments, respectively. The highest mean of shoot length was scored under the GW treatment. And, the highest mean of root length was scored under DW which was not significant from GW treatment. The means of shoot fresh was the highest under the TWW. The means of root fresh weight was not significantly different from each other's under different treatments. The growth performance was in progress with no mortality during 21 days of growth. Thus, the best non-conventional water qualities alternatives based on the cleanness, nutrients, and toxicity are the GW, TWW and IW, respectively.

Keywords: Seed germination, Growth performance, Leucaena, Multipurpose forest trees, Waste water, Grey water

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Authors: V. G. Cappellesso, D. M. G. da Silva, J. A. Arndt, N. dos Santos Petry, A. B. Masuero, D. C. C. Dal Molin

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Concrete elements are subject to cracking, which can be an access point for deleterious agents that can trigger pathological manifestations reducing the service life of these structures. Finding ways to minimize or eliminate the effects of this aggressive agents’ penetration, such as the sealing of these cracks, is a manner of contributing to the durability of these structures. The cementitious self-healing phenomenon can be classified in two different processes. The autogenous self-healing that can be defined as a natural process in which the sealing of this cracks occurs without the stimulation of external agents, meaning, without different materials being added to the mixture, while on the other hand, the autonomous seal-healing phenomenon depends on the insertion of a specific engineered material added to the cement matrix in order to promote its recovery. This work aims to evaluate the autogenous self-healing of concretes produced with different water/cement ratios and exposed to wet/dry cycles, considering two ages of crack openings, 3 days and 28 days. The self-healing phenomenon was evaluated using two techniques: crack healing measurement using ultrasonic waves and image analysis performed with an optical microscope. It is possible to observe that by both methods, it possible to observe the self-healing phenomenon of the cracks. For young ages of crack openings and lower water/cement ratios, the self-healing capacity is higher when compared to advanced ages of crack openings and higher water/cement ratios. Regardless of the crack opening age, these concretes were found to stabilize the self-healing processes after 80 days or 90 days.

Keywords: Self-healing, autogenous, water/cement ratio, curing cycles, test methods.

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Authors: Erica T. R. Mendonça, Caroline M. B. de Araujo, Filho, Osvaldo Chiavone, Sobrinho, Maurício A. da Motta

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Oil and gas exploration is an essential activity for modern society, although the supply of its global demand has caused enough damage to the environment, mainly due to produced water generation, which is an effluent associated with the oil and gas produced during oil extraction. It is the aim of this study to evaluate the treatment of produced water, in order to reduce its oils and greases content (OG), by using flotation as a pre-treatment, combined with oxidation for the remaining organic load degradation. Thus, there has been tested Advanced Oxidation Process (AOP) using both Fenton and photo-Fenton reactions, as well as a chemical oxidation treatment using sodium ferrate(VI), Na₂[FeO₄], as a strong oxidant. All the studies were carried out using real samples of produced water from petroleum industry. The oxidation process using ferrate(VI) ion was studied based on factorial experimental designs. The factorial design was used in order to study how the variables pH, temperature and concentration of Na₂[FeO₄] influences the O&G levels. For the treatment using ferrate(VI) ion, the results showed that the best operating point is obtained when the temperature is 28 °C, pH 3, and a 2000 mg.L^-1 solution of Na₂[FeO₄] is used. This experiment has achieved a final O&G level of 4.7 mg.L^-1, which means 94% percentage removal efficiency of oils and greases. Comparing Fenton and photo-Fenton processes, it was observed that the Fenton reaction did not provide good reduction of O&G (around 20% only). On the other hand, a degradation of approximately 80.5% of oil and grease was obtained after a period of seven hours of treatment using photo-Fenton process, which indicates that the best process combination has occurred between the flotation and the photo-Fenton reaction using solar radiation, with an overall removal efficiency of O&G of approximately 89%.

Keywords: Advanced oxidation process, ferrate(VI) ion, oils and greases removal, produced water treatment.

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Authors: Cigdem Safak Saglam

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Most thermal power plants use steam as working fluid in their power cycle. Therefore, in addition to fuel, water is the other main input for thermal plants. Water and steam must be highly pure in order to protect the systems from corrosion, scaling and biofouling. Pure process water is produced in water treatment plants having many several treatment methods. Treatment plant design is selected depending on raw water source and required water quality. Although working principle of fossil-fuel fired thermal power plants are same, there is no standard design and equipment arrangement valid for all thermal power plant utility systems. Besides that, there are many other technology evaluation and selection criteria for designing the most optimal water systems meeting the requirements such as local conditions, environmental restrictions, electricity and other consumables availability and transport, process water sources and scarcity, land use constraints etc. Aim of this study is explaining the adopted methodology for technology selection for process water preparation and industrial waste water treatment plant in a thermal power plant project located in Tufanbeyli, Adana Province in Turkey. Thermal power plant is fired with indigenous lignite coal extracted from adjacent lignite reserves. This paper addresses all above-mentioned factors affecting the thermal power plant water treatment facilities (demineralization + waste water treatment) design and describes the ultimate design of Tufanbeyli Thermal Power Plant Water Treatment Plant.

Keywords: Thermal power plant, lignite coal, pre-treatment, demineralization, electrodialysis, recycling, waste water, process water.

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Authors: Abdulfatah Faraj Aboufayed

Abstract:

Water erosion is the most important problems of the soil in the Jabel Nefusa area located in northwest of Libya; therefore, erosion station had been established in the Faculty of Veterinary and dryfarming research Station, University of the Al-japel Al-gharbi in Zentan. The length of the station is 72.6 feet, 6 feet width and the percentage of its slope is 3%. The station were established to measure the amount of soil eroded and amount of surface water produced during the seasons 95/96 and 96/97 from each rain storms. The monitoring shows that there was a difference between the two seasons in the number of rainstorms which made differences in the amount of surface runoff water and the amount of soil eroded between the two seasons. Although the slope is low (3%), the soil texture is sandy and the land ploughed twice during each season surface runoff and soil eroded were occurred. The average amount of eroded soil was 3792 grams (gr) per season and the average amount of surface runoff water was 410 liter (L) per season. The amount of surface runoff water would be much greater from Jebel Nefusa upland with steep slopes and collecting of them will save a valuable amount of water which lost as a runoff while this area is in desperate of this water. The regression analysis of variance show strong correlation between rainfall depth and the other two depended variable (the amount of surface runoff water and the amount of eroded soil. It shows also strong correlation between amount of surface runoff water and amount of eroded soil.

Keywords: Rain, Surface runoff water, Soil, Water erosion, Soil erosion.

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Authors: P. Murugesan, G. Venkateswaran, V. A. Shanmuga Selvan

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Water used for brewing tea plays a major role in the quality of tea. Water with higher hardness gives very dark coloured brew. This study was conducted to determine the effect of water hardness and free residual chlorine on the quality of black tea liquor. Theaflavin (TF) and Thearubigin (TR) levels are lower in comparison with the tea brewed in distilled water. At the same time, there is an increase in High Polymerized Substance (HPS) and Total Liquor Colour (TLC). While water with higher hardness has a negative impact on tea brew, water with high concentration of free residual chlorine did not affect the quality of tea brew.

Keywords: Theaflavin, Thearubigin, high polymerized substance, total liquor colour, hardness, residual chlorine.

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Authors: Olayinka Gafar Okeola, Akinola Muyiwa Moore

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Urban population is rapidly increasing in Ilorin, (the capital of Kwara State of Nigeria) along with related increased water demand. The inadequacies of water supply services have forced the populace to depend on dug wells, boreholes, water tankers, street vendors etc. for their water needs. People spend hours daily carrying jerry can all around to collect and queue for water at the public water tap with high opportunity cost both in time and economic wastage. This situation motivated this study to assess the sustainability of an urban water supply services to unravel the factors undermining the effective delivery of services. Contingent Valuation Method was used to place value on water supply services using the Double Bounded Dichotomous Choice format for willingness to pay elicitation. A database was created with Microsoft Excel and Stata 12 Software to model and evaluate the variables that affect household willingness to pay. The results of the study reveal that about 92% of the total households surveyed were connected to the Government water supply out of which 87% reported that they were not satisfied with the existing services. The results furthered revealed that respondents are willing to pay ₦2500 monthly to enjoy sustainable water supply service delivery.

Keywords: Willingness-to-pay, contingent valuation method, Nigeria, service, delivery.

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Authors: Hamed Rafiei, Masoud Rabbani

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This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Hironori Kakuta, Kajiro Watanabe, Yosuke Kurihara

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Water leakage is a serious problem in the maintenance of a waterworks facility. Monitoring the water flow rate is one way to locate leakage. However, conventional flowmeters such as the wet-type flowmeter and the clamp-on type ultrasonic flowmeter require additional construction for their installation and are therefore quite expensive. This paper proposes a novel estimation system for the flow rate in a water pipeline, which employs a vibration sensor. This assembly can be attached to any water pipeline without the need for additional high-cost construction. The vibration sensor is designed based on a condenser microphone. This sensor detects vibration caused by water flowing through a pipeline. It is possible to estimate the water flow rate by measuring the amplitude of the output signal from the vibration sensor. We confirmed the validity of the proposed sensing system experimentally.

Keywords: Condenser microphone, Flow rate estimation, Piping vibration, Water pipe.

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Authors: Henning Bjornlund, Alec Zuo, Sarah Wheeler, Rob de Loë

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There is currently intensive debate in Alberta, Canada, regarding rural to urban water reallocation. This paper explores the demographic and attitudinal influences that are associated with the acceptance of water reallocation policies and whether such acceptance differs between urban and rural residents. We investigate three policy orientations in regards to water policies: i) government intervention; ii) environmental protection; and iii) protecting irrigators- water rights. We find that urban dwellers are more likely to favour government intervention while rural dwellers are more likely to support policies that aim at protecting irrigators- water rights. While urban dwellers are also more likely to favour environmental protection, the difference is not statistically significant. We also find that other factors have a significant impact on policy choice irrespective of residence such as demographic and socioeconomic factors as well as the values people hold toward water and the environment.

Keywords: Canada, rural, urban, water transfers.

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Authors: Chengming Li, Yong Yin, Peipei Guo, Xiaoli Liu

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Without taking account of the attribute richness of POI (point of interest) data and spatial distribution limited by roads, a POI generalization method considering both attribute information and spatial distribution has been proposed against the existing point generalization algorithm merely focusing on overall information of point groups. Hierarchical characteristic of urban POI information expression has been firstly analyzed to point out the measurement feature of the corresponding hierarchy. On this basis, an urban POI generalizing strategy has been put forward: POIs urban road network have been divided into three distribution pattern; corresponding generalization methods have been proposed according to the characteristic of POI data in different distribution patterns. Experimental results showed that the method taking into account both attribute information and spatial distribution characteristics of POI can better implement urban POI generalization in the mapping presentation.

Keywords: POI, Road network, spatial information expression, selection method, distribution pattern.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

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Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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Authors: Y. Chaiko

Abstract:

It is important to provide possibility of so called “handover" for the mobile subscriber from GSM network to Wi-Fi network and back. To solve specified problem it is necessary to estimate connection time between base station and wireless access point. Difficulty to estimate this parameter is that it doesn-t described in specifications of the standard and, hence, no recommended value is given. In this paper, the analytical model is presented that allows the estimating connection time between base station and IEEE 802.11 access point.

Keywords: Access point, connection procedure, Wi-Fi network.

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Authors: Guclu Insel, Efe Gumuslu, Gulten Yuksek, Nilay Sayi Ucar, Emine Ubay Cokgor, Tugba Olmez Hanci, Didem Okutman Tas, Fatos Germirli Babuna, Derya Firat Ertem, Okmen Yildirim, Ozge Erturan, Betul Kirci

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In order to eliminate water scarcity problems, effective precautions must be taken. Growing competition for water is increasingly forcing facilities to tackle their own water scarcity problems. At this point, application of wastewater reclamation and reuse results in considerable economic advantageous. In this study, an enamel coating facility, which is one of the high water consumed facilities, is evaluated in terms of its wastewater reuse potential. Wastewater reclamation and reuse can be defined as one of the best available techniques for this sector. Hence, process and pollution profiles together with detailed characterization of segregated wastewater sources are appraised in a way to find out the recoverable effluent streams arising from enamel coating operations. Daily, 170 m³ of process water is required and 160 m³ of wastewater is generated. The segregated streams generated by two enamel coating processes are characterized in terms of conventional parameters. Relatively clean segregated wastewater streams (reusable wastewaters) are separately collected and experimental treatability studies are conducted on it. The results reflected that the reusable wastewater fraction has an approximate amount of 110 m³/day that accounts for 68% of the total wastewaters. The need for treatment applicable on reusable wastewaters is determined by considering water quality requirements of various operations and characterization of reusable wastewater streams. Ultra-filtration (UF), Nano-filtration (NF) and Reverse Osmosis (RO) membranes are subsequently applied on reusable effluent fraction. Adequate organic matter removal is not obtained with the mentioned treatment sequence.

Keywords: enamel coating, membrane, reuse, wastewater

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Authors: Sobir T. Navruzov

Abstract:

The problem of complex use of water resources in Central Asia by taking into consideration the sovereignty of the states and increasing demand on use of water for economic aspects are considered. Complex program with appropriate mathematical software intended for calculation of possible variants of using the Amudarya up-stream water resources according to satisfaction of incompatible requirements of the national economics in irrigation and energy generation is proposed.

Keywords: water resources, national economics, irrigation, transboundry, energy generation, optimal solution, program complex, up-stream, down-stream, compensating services.

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Authors: Menglong Su, Shaoyun Shi, Qing Xu

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In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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Authors: Ali Emad

Abstract:

Enhancement of the performance of a reverse osmosis (RO) unit through periodic control is studied. The periodic control manipulates the feed pressure and flow rate of the RO unit. To ensure the periodic behavior of the inputs, the manipulated variables (MV) are transformed into the form of sinusoidal functions. In this case, the amplitude and period of the sinusoidal functions become the surrogate MV and are thus regulated via nonlinear model predictive control algorithm. The simulation results indicated that the control system can generate cyclic inputs necessary to enhance the closedloop performance in the sense of increasing the permeate production and lowering the salt concentration. The proposed control system can attain its objective with arbitrary set point for the controlled outputs. Successful results were also obtained in the presence of modeling errors.

Keywords: Reverse osmosis, water desalination, periodic control, model predictive control.

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Authors: Haodong Wu, Ping Huang, Junsan Wang

Abstract:

In China, with the rapid urbanization and industrialization, and highly accelerated economic development have resulted in degradation of water resource. The water quality deterioration usual result from eutrophication in most cases, so how to dispose this type pollution water higher efficiently is an urgent task. Hower, different with traditional technology, constructed wetlands are effective treatment systems that can be very useful because they are simple technology and low operational cost. A pilot-scale treatment including constructed wetlands was constructed at XingYun Lake, Yuxi, China, and operated as primary treatment measure before eutrophic-lake water draining to riverine landscape. Water quality indices were determined during the experiment, the results indicated that treatment removal efficiencies were high for Nitrate nitrogen, Chlorophyll–a and Algae, the final removal efficiency reached to 95.20%, 93.33% and 99.87% respectively, but the removal efficiency of Total phosphorous and Total nitrogen only reach to 68.83% and 50.00% respectively.

Keywords: Constructed wetland, Eutrophic-lake water, Nutrientremoval, Removal efficiency

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Authors: Mojibul Sajjad, Mohammad G. Rasul, Md. Sharif Imam Ibne Amir

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The rate of natural gas dissociation from the Coal Matrix depends on depressurization of reservoir through removing of the cleat water from the coal seam. These waters are similar to brine and aged of very long years. For improving the connectivity through fracking /fracturing, high pressure liquids are pumped off inside the coal body. A significant quantity of accumulated water, a combined mixture of cleat water and fracking fluids (back flow water) is pumped out through gas well. In Queensland, Australia Coal Seam Gas (CSG) industry is in booming state and estimated of 30,000 wells would be active for CSG production forecasting life span of 30 years. Integrated water management along with water softening programs is practiced for subsequent treatment and later on discharge to nearby surface water catchment. Water treatment is an important part of the CSG industry. A case study on a CSG site and review on the test results are discussed for assessing the Standards & Practices for management of CSG by-product water and their subsequent disposal activities. This study was directed toward (i) water management and softening process in Spring Gully CSG field, (ii) Comparative analysis on experimental study and standards and (iii) Disposal of the treated water. This study also aimed for alternative usages and their impact on vegetation, living species as well as long term effects.

Keywords: Coal Seam Gas (CSG), Cleat Water, Hydro-Fracking, Desalination, Reverse Osmosis.

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Authors: Rou-Han Lee, Jie, Chung Lou, Huang-Ming Fang

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This study uses natural water and the surface properties of powdered activated carbon to acclimatize organics, forming biofilms on the surface of powdered activated carbon. To investigate the influence of different hydraulic retention times on the removal efficacy of trace organics in raw water, and to determine the optimal hydraulic retention time of a biological powdered activated carbon system, this study selects ozone-treated water processed by Feng-shan Advanced Water Purification Plant in southern Taiwan for the experiment. The evaluation indicators include assimilable organic carbon, dissolved organic carbon, and total organic carbon. The results of this study can improve the quality of drinking water treated using advanced water purification procedures.

Keywords: Water Purification Procedures, Biological Powdered Activated Carbon System, Assimilable Organic Carbon

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Authors: Amir Shafeeq, Ayyaz Muhammad, Noman Hassan, Rofice Dickson

Abstract:

Different vegetable oil based biodiesel (FAMES) were prepared by alkaline transesterification using refined oils as well as waste frying oil (WFO). Methanol and sodium hydroxide are used as catalyst under similar reaction conditions. To ensure the quality of biodiesel produced, a series of different ASTM Standard tests were carried out. In this context, various testwere done including viscosity, carbon residue, specific gravity, corrosion test, flash point, cloud point and pour point. Results revealed that characteristics of biodiesel depend on the feedstock and it is far better than petroleum diesel.

Keywords: Biodiesel, Edible oils, Separation.

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Authors: Dnyandip K. Bhamare, Manish K Rathod, Jyotirmay Banerjee

Abstract:

This paper aims to study performance of a thermosiphon solar water heating system with the help of the proposed analytical model. This proposed model predicts the temperature and mass flow rate in a thermosiphon solar water heating system depending on radiation intensity and ambient temperature. The performance of the thermosiphon solar water heating system is evaluated in the Indian context. For this, eight cities in India are selected considering radiation intensity and geographical positions. Predicted performance at various cities reveals the potential for thermosiphon solar water in India.

Keywords: Collector outlet temperature, India, solar water heater, thermosiphon.

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Authors: Peter G. Youssef, Saad M. Mahmoud, Raya K. Al-Dadah

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Many water desalination technologies have been developed but in general they are energy intensive and have high cost and adverse environmental impact. Recently, adsorption technology for water desalination has been investigated showing the potential of using low temperature waste heat (50-85oC) thus reducing energy consumption and CO2 emissions. This work mathematically compares the performance of an adsorption cycle that produces two useful effects namely, fresh water and cooling using two different adsorbents, silica-gel and an advanced zeolite material AQSOA-ZO2, produced by Mitsubishi plastics. It was found that at low chilled water temperatures, typically below 20oC, the AQSOA-Z02 is more efficient than silica-gel as the cycle can produce 5.8 m3 of fresh water per day and 50.1 Rton of cooling per tonne of AQSOA-ZO2. Above 20oC silica-gel is still better as the cycle production reaches 8.4 m3 per day and 62.4 Rton per tonne of silica-gel. These results show the potential of using the AQSOA-Z02 at low chilled water temperature for water desalination and cooling applications.

Keywords: Adsorption, desalination, refrigeration, seawater.

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Authors: Carrie Ho, Darshana J. Kumar

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Urbanization has been found to impact stormwater runoff quantity and quality. A study catchment with mixed land use, residential and industrial were investigated and the water quality discharged from the catchment were sampled and tested for four basic water quality parameters; BOD5, NH3-N, NO3-N and P. One dry weather flow and several stormwater runoff were sampled. Results were compared to the USEPA stormwater quality benchmark values and the Interim National Water Quality Standards for Malaysia (INWQS). The concentration of the parameters was found to vary significantly between storms and the pollutant of concern was found to be NO3-N.

Keywords: Mixed land-use, urban runoff, water quality.

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Authors: R.Balamurugan, S.Subramanian

Abstract:

This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.

Keywords: Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.

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Authors: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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Authors: Li Feng

Abstract:

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.

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