Search results for: surface conditions
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4976

Search results for: surface conditions

2786 Treatment of Recycled Concrete Aggregates by Si-Based Polymers

Authors: V. Spaeth, A. Djerbi-Tegguer

Abstract:

The recycling of concrete, bricks and masonry rubble as concrete aggregates is an important way to contribute to a sustainable material flow. However, there are still various uncertainties limiting the widespread use of Recycled Concrete Aggregates (RCA). The fluctuations in the composition of grade recycled aggregates and their influence on the properties of fresh and hardened concrete are of particular concern regarding the use of RCA. Most of problems occurring while using recycled concrete aggregates as aggregates are due to higher porosity and hence higher water absorption, lower mechanical strengths, residual impurities on the surface of the RCA forming weaker bond between cement paste and aggregate. So, the reuse of RCA is still limited. Efficient polymer based treatment is proposed in order to reuse RCA easier. The silicon-based polymer treatments of RCA were carried out and were compared. This kind of treatment can improve the properties of RCA such as the rate of water absorption on treated RCA is significantly reduced.

Keywords: Recycled concrete aggregates, water absorption, silicon-based agent and polymer.

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2785 Investigation of Mg and Zr Addition on the Mechanical Properties of Commercially Pure Al

Authors: Samiul Kaiser, M. S. Kaiser

Abstract:

The influence of Mg and Zr addition on mechanical properties such as hardness, tensile strength and impact energy of commercially pure Al are investigated. The microstructure and fracture behavior are also studied by using Optical and Scanning Electron Microscopy. It is observed that magnesium addition improves the mechanical properties of commercially pure Al at the expense of ductility due to formation of β (Al3Mg) and β (Al3Mg2) phase into the alloy. Zr addition also plays a positive role through grain refinement effect and the formation of metastable L12 Al3Zr precipitates. In addition, it is observed that the fractured surface of Mg added alloy is brittle and higher numbers of dimples are observed in case of Zr added alloy.

Keywords: Al-alloys, hardness, tensile strength, impact energy, microstructure.

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2784 Stability Analysis of Fractional Order Systems with Time Delay

Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li

Abstract:

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords: Fractional order systems, Time delay, Characteristic equation.

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2783 Cd2+ Ions Removal from Aqueous Solutions Using Alginite

Authors: Vladimír Frišták, Martin Pipíška, Juraj Lesný

Abstract:

Alginite has been evaluated as an efficient pollution control material. In this paper, alginite from maar Pinciná (SR) for removal of Cd2+ ions from aqueous solution was studied. The potential sorbent was characterized by X-ray fluorescence analysis (RFA) analysis, Fourier transform infrared spectral analysis (FT-IR) and specific surface area (SSA) was also determined. The sorption process was optimized from the point of initial cadmium concentration effect and effect of pH value. The Freundlich and Langmuir models were used to interpret the sorption behavior of Cd2+ ions, and the results showed that experimental data were well fitted by the Langmuir equation. Alginite maximal sorption capacity (Qmax) for Cd2+ ions calculated from Langmuir isotherm was 34 mg/g. Sorption process was significantly affected by initial pH value in the range from 4.0-7.0. Alginite is a comparable sorbent with other materials for toxic metals removal. 

Keywords: Alginites, Cd2+, sorption, Qmax

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2782 Pd(II) Complex with 4-Bromo-Bis-Hydroxymethyl Phenol and Nicotinamide: Synthesis and Spectral Analysis

Authors: Özlen Altun, Zeliha Yoruç

Abstract:

In the present study, the reactions involving 4-bromo-2,6-bis-hydroxymethyl-phenol (BBHMP) and nicotinamide (NA) in the presence of Pd(II) ions were investigated. Optimum conditions for the reactions were established as pH = 7 and λ = 450 nm. According to absorbance measurements, the molar ratio of BBHMP: NA: Pd2+ was found to be 1: 2: 2. As a result of physicochemical, spectrophotometric and thermal analyses, the reactions of BBHMP and NA with Pd(II) are complexation reactions and one molecule of BBHMP and two molecules of NA react with two molecules of the Pd(II) ion.

Keywords: Nicotinamide, 4-bromo-2, 6-bis-hydroxymethyl-phenol, Pd(II), spectral analysis, synthesis.

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2781 Study of Damage in Beams with Different Boundary Conditions

Authors: Nilson Barbieri, Renato Barbieri

Abstract:

–In this paper the damage in clamped-free, clampedclamped and free-free beam are analyzed considering samples without and with structural modifications. The damage location is investigated by the use of the bispectrum and wavelet analysis. The mathematical models are obtained using 2D elasticity theory and the Finite Element Method (FEM). The numerical and experimental data are approximated using the Particle Swarm Optimizer (PSO) method and this way is possible to adjust the localization and the severity of the damage. The experimental data are obtained through accelerometers placed along the sample. The system is excited using impact hammer.

Keywords: Damage, beam, PSO, bispectrum, wavelet transform

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2780 Heat Transfer and Friction Factor Study for Triangular Duct Solar Air Heater Having Discrete V-Shaped Ribs

Authors: Varun

Abstract:

Solar energy is a good option among renewable energy resources due to its easy availability and abundance. The simplest and most efficient way to utilize solar energy is to convert it into thermal energy and this can be done with the help of solar collectors. The thermal performance of such collectors is poor due to less heat transfer from the collector surface to air. In this work, experimental investigations of single pass solar air heater having triangular duct and provided with roughness element on the underside of the absorber plate. V-shaped ribs are used for investigation having three different values of relative roughness pitch (p/e) ranges from 4- 16 for a fixed value of angle of attack (α), relative roughness height (e/Dh) and a relative gap distance (d/x) values are 60°, 0.044 and 0.60 respectively. Result shows that considerable augmentation in heat transfer has been obtained by providing roughness.

Keywords: Artificial roughness, Solar Air heater, Triangular duct, V-Shaped Ribs.

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2779 Quantitative Ranking Evaluation of Wine Quality

Authors: A. Brunel, A. Kernevez, F. Leclere, J. Trenteseaux

Abstract:

Today, wine quality is only evaluated by wine experts with their own different personal tastes, even if they may agree on some common features. So producers do not have any unbiased way to independently assess the quality of their products. A tool is here proposed to evaluate wine quality by an objective ranking based upon the variables entering wine elaboration, and analysed through principal component analysis (PCA) method. Actual climatic data are compared by measuring the relative distance between each considered wine, out of which the general ranking is performed.

Keywords: Wine, grape, vine, weather conditions, rating, climate, principal component analysis, metric analysis.

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2778 3D Object Model Reconstruction Based on Polywogs Wavelet Network Parametrization

Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3D object, optimization, parametrization, Polywog wavelets, reconstruction, wavelet networks.

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2777 Effects of Carbonation on the Microstructure and Macro Physical Properties of Cement Mortar

Authors: Son Tung Pham, William Prince

Abstract:

The objective of this work was to examine the changes in the microstructure and macro physical properties caused by the carbonation of normalised CEM II mortar. Samples were prepared and subjected to accelerated carbonation at 20°C, 65% relative humidity and 20% CO2 concentration. On the microstructure scale, the evolutions of the cumulative pore volume, pore size distribution, and specific surface area during carbonation were calculated from the adsorption desorption isotherms of nitrogen. We also examined the evolution of macro physical properties such as the porosity accessible to water, the gas permeability, and thermal conductivity. The conflict between the results of nitrogen porosity and water porosity indicated that the porous domains explored using these two techniques are different and help to complementarily evaluate the effects of carbonation. This is a multi-scale study where results on microstructural changes can help to explain the evolution of macro physical properties.

Keywords: Carbonation, cement mortar, microstructure, physical properties.

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2776 Effect of Lime on the California Bearing Ratio Behaviour of Fly Ash - mine Overburden Mixes

Authors: B. Behera, M. K. Mishra

Abstract:

Typically thermal power plants are located near to surface coal mines that produce huge amount of fly ash as a waste byproduct. Disposal of fly ash causes significant economic and environmental problems. Now-a-days, research is going on for bulk utilization of fly ash. In order to increase its percentage utilization, an investigation was carried out to evaluate its potential for haul road construction. This paper presents the laboratory California bearing ratio (CBR) tests and evaluates the effect of lime on CBR behavior of fly ash - mine overburden mixes. Tests were performed with different percentages of lime (2%, 3%, 6%, and 9%). The results show that the increase in bearing ratio of fly ash-overburden mixes was achieved by lime treatment. Scanning electron microscopy (SEM) analyses were conducted on 28 days cured specimens. The SEM study showed that the bearing ratio development is related to the microstructural development.

Keywords: California bearing ratio, Fly ash, Mine overburden, Lime.

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2775 A Study of Calcination and Carbonation of Cockle Shell

Authors: N.A. Rashidi, M. Mohamed, S.Yusup

Abstract:

Calcium oxide (CaO) as carbon dioxide (CO2) adsorbent at the elevated temperature has been very well-received thus far. The CaO can be synthesized from natural calcium carbonate (CaCO3) sources through the reversible calcination-carbonation process. In the study, cockle shell has been selected as CaO precursors. The objectives of the study are to investigate the performance of calcination and carbonation with respect to different temperature, heating rate, particle size and the duration time. Overall, better performance is shown at the calcination temperature of 850oC for 40 minutes, heating rate of 20oC/min, particle size of < 0.125mm and the carbonation temperature is at 650oC. The synthesized materials have been characterized by nitrogen physisorption and surface morphology analysis. The effectiveness of the synthesized cockle shell in capturing CO2 (0.72 kg CO2/kg adsorbent) which is comparable to the commercialized adsorbent (0.60 kg CO2/kg adsorbent) makes them as the most promising materials for CO2 capture.

Keywords: Calcination, Calcium oxide, Carbonation, Cockle shell

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2774 Existence and Uniqueness of Periodic Solution for a Discrete-time SIR Epidemic Model with Time Delays and Impulses

Authors: Ling Liu, Yuan Ye

Abstract:

In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.

Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.

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2773 Lightweight Mirrors for Space X-Ray Telescopes

Authors: M. Mika, L. Pina, M. Landova, L. Sveda, R. Havlikova, V. Marsikova, R. Hudec, A. Inneman

Abstract:

Future astronomical projects on large space x-ray imaging telescopes require novel substrates and technologies for the construction of their reflecting mirrors. The mirrors must be lightweight and precisely shaped to achieve large collecting area with high angular resolution. The new materials and technologies must be cost-effective. Currently, the most promising materials are glass or silicon foils. We focused on precise shaping these foils by thermal forming process. We studied free and forced slumping in the temperature region of hot plastic deformation and compared the shapes obtained by the different slumping processes. We measured the shapes and the surface quality of the foils. In the experiments, we varied both heat-treatment temperature and time following our experiment design. The obtained data and relations we can use for modeling and optimizing the thermal forming procedure.

Keywords: Glass, silicon, thermal forming, x-ray

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2772 Learning Factory for Changeability

Authors: Dennis Gossmann, Habil Peter Nyhuis

Abstract:

Amongst the consistently fluctuating conditions prevailing today, changeability represents a strategic key factor for a manufacturing company to achieve success on the international markets. In order to cope with turbulences and the increasing level of incalculability, not only the flexible design of production systems but in particular the employee as enabler of change provide the focus here. It is important to enable employees from manufacturing companies to participate actively in change events and in change decisions. To this end, the learning factory has been created, which is intended to serve the development of change-promoting competences and the sensitization of employees for the necessity of changes.

Keywords: Changeability, human resources, learning factory.

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2771 Periodicity for a Food Chain Model with Functional Responses on Time Scales

Authors: Kejun Zhuang

Abstract:

With the help of coincidence degree theory, sufficient conditions for existence of periodic solutions for a food chain model with functional responses on time scales are established.

Keywords: time scales, food chain model, coincidence degree, periodic solutions.

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2770 Field Investigation on Modification of Japanese Cedar Pollen Allergen in Urban Air-Polluted Area

Authors: Qingyue Wang, Jun Morita, Shinichi Nakamura, Di Wu, Xiumin Gong, Miho Suzuki, Makoto Miwa, Daisuke Nakajima

Abstract:

Cry j 1 is a causative substance of Japanese cedar pollinosis, and it may deteriorate by Cry j 1 invasion to a lower respiratory tract. We observed airborne particles containing Cry j 1 by an immunofluorescence technique using a fluorescence microscope, and we clarified that Cry j 1 exist as aggregates of airborne fine particles (< 1.1 μm) in the urban atmosphere. Airborne Cry j 1 may react with air pollutants and be denature to a substance deteriorated Japanese cedar pollinosis. Therefore, we applied a sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) to evaluate a Cry j 1 reacted with various air pollutants by liquid phase reaction, and calculated kinetics constants of Cry j 1 extracted from pollens collected in various sites and airborne fine particles containing Cry j 1 by using a surface plasmon resonance (SPR) method. As a result, it is suggested that Cry j 1 may be denatured by air pollutants during the transportation to the urban atmosphere.

Keywords: Cry j 1, Japanese cedar pollinosis, SDS-PAGE, SPR

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2769 Analysis of Model in Pregnant and Non-Pregnant Dengue Patients

Authors: R. Kongnuy, P. Pongsumpun

Abstract:

We used mathematical model to study the transmission of dengue disease. The model is developed in which the human population is separated into two populations, pregnant and non-pregnant humans. The dynamical analysis method is used for analyzing this modified model. Two equilibrium states are found and the conditions for stability of theses two equilibrium states are established. Numerical results are shown for each equilibrium state. The basic reproduction numbers are found and they are compared by using numerical simulations.

Keywords: Basic reproductive number, dengue disease, equilibrium states, pregnancy.

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2768 Banach Lattices with Weak Dunford-Pettis Property

Authors: Khalid Bouras, Mohammed Moussa

Abstract:

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results.

Keywords: Almost Dunford-Pettis operator, weak Dunford-Pettis operator, eak almost Dunford-Pettis operator, almost Dunford-Pettis operator, weak Dunford-Pettis operator

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2767 On-Line Geometrical Identification of Reconfigurable Machine Tool using Virtual Machining

Authors: Alexandru Epureanu, Virgil Teodor

Abstract:

One of the main research directions in CAD/CAM machining area is the reducing of machining time. The feedrate scheduling is one of the advanced techniques that allows keeping constant the uncut chip area and as sequel to keep constant the main cutting force. They are two main ways for feedrate optimization. The first consists in the cutting force monitoring, which presumes to use complex equipment for the force measurement and after this, to set the feedrate regarding the cutting force variation. The second way is to optimize the feedrate by keeping constant the material removal rate regarding the cutting conditions. In this paper there is proposed a new approach using an extended database that replaces the system model. The feedrate scheduling is determined based on the identification of the reconfigurable machine tool, and the feed value determination regarding the uncut chip section area, the contact length between tool and blank and also regarding the geometrical roughness. The first stage consists in the blank and tool monitoring for the determination of actual profiles. The next stage is the determination of programmed tool path that allows obtaining the piece target profile. The graphic representation environment models the tool and blank regions and, after this, the tool model is positioned regarding the blank model according to the programmed tool path. For each of these positions the geometrical roughness value, the uncut chip area and the contact length between tool and blank are calculated. Each of these parameters are compared with the admissible values and according to the result the feed value is established. We can consider that this approach has the following advantages: in case of complex cutting processes the prediction of cutting force is possible; there is considered the real cutting profile which has deviations from the theoretical profile; the blank-tool contact length limitation is possible; it is possible to correct the programmed tool path so that the target profile can be obtained. Applying this method, there are obtained data sets which allow the feedrate scheduling so that the uncut chip area is constant and, as a result, the cutting force is constant, which allows to use more efficiently the machine tool and to obtain the reduction of machining time.

Keywords: Reconfigurable machine tool, system identification, uncut chip area, cutting conditions scheduling.

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2766 Case on Manufacturing Cell Formation Using Production Flow Analysis

Authors: Vladimír Modrák

Abstract:

This paper offers a case study, in which methodological aspects of cell design for transformation the production process are applied. The cell redesign in this work is tightly focused to reach optimization of material flows under real manufacturing conditions. Accordingly, more individual techniques were aggregated into compact methodical procedure with aim to built one-piece flow production. Case study was concentrated on relatively typical situation of transformation from batch production to cellular manufacturing.

Keywords: Product/Quantity analysis, layout, design, manufacturing process.

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2765 Deterministic Method to Assess Kalman Filter Passive Ranging Solution Reliability

Authors: Ronald M. Yannone

Abstract:

For decades, the defense business has been plagued by not having a reliable, deterministic method to know when the Kalman filter solution for passive ranging application is reliable for use by the fighter pilot. This has made it hard to accurately assess when the ranging solution can be used for situation awareness and weapons use. To date, we have used ad hoc rules-of-thumb to assess when we think the estimate of the Kalman filter standard deviation on range is reliable. A reliable algorithm has been developed at BAE Systems Electronics & Integrated Solutions that monitors the Kalman gain matrix elements – and a patent is pending. The “settling" of the gain matrix elements relates directly to when we can assess the time when the passive ranging solution is within the 10 percent-of-truth value. The focus of the paper is on surface-based passive ranging – but the method is applicable to airborne targets as well.

Keywords: Electronic warfare, extended Kalman filter (EKF), fighter aircraft, passive ranging, track convergence.

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2764 Zno Nanocomposites: Control of Enviromental Effects for Preservation of old Manuscripts

Authors: Maryam Afsharpour, Saleh Imani, Shahrzad Abdolmohammadi

Abstract:

We investigate the ZnO role in the inherent protection of old manuscripts to protect them against environmental damaging effect of ultraviolet radiation, pollutant gasses, mold and bacteria. In this study a cellulosic nanocomposite of ZnO were used as protective coating on the surface of paper fibers. This layered nanocomposite can act as a consolidate materials too. Furthermore, to determine how well paper works screen objects from the damaging effects, two accelerated aging mechanisms due to light and heat are discussed. Results show good stability of papers with nanocomposite coating. Also, a good light stability was shown in the colored paper that treated with this nanocomposite. Furthermore, to demonstrate the degree of antifungal and antibacterial properties of coated papers, papers was treated with four common molds and bacteria and the good preventive effects of coated paper against molds and bacteria are described.

Keywords: Enviromental effects, Manuscript, Nanocomposite, Zinc oxide.

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2763 Characterization of Adhesive Layers in Sandwich Composites by Nondestructive Technique

Authors: E. Barkanov, E. Skukis, M. Wesolowski, A. Chate

Abstract:

New nondestructive technique, namely an inverse technique based on vibration tests, to characterize nonlinear mechanical properties of adhesive layers in sandwich composites is developed. An adhesive layer is described as a viscoelastic isotropic material with storage and loss moduli which are both frequency dependent values in wide frequency range. An optimization based on the planning of experiments and response surface technique to minimize the error functional is applied to decrease considerably the computational expenses. The developed identification technique has been tested on aluminum panels and successfully applied to characterize viscoelastic material properties of 3M damping polymer ISD-112 used as a core material in sandwich panels.

Keywords: Adhesive layer, finite element method, inverse technique, sandwich panel, vibration test, viscoelastic material properties.

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2762 Anthropometric Profile as a Factor of Impact on Employee Productivity in Manufacturing Industry of Tijuana, Mexico

Authors: J. A. López, J. E. Olguín, C. W. Camargo, G. A. Quijano, R. Martínez

Abstract:

This paper presents an anthropometric study conducted to 300 employees in a maquiladora industry that belongs to the cluster of medical products as part of a research project to pretend simulate workplace conditions under which operators conduct their activities. This project is relevant because traditionally performed a study to design ergonomic workspaces according to anthropometric profile of users, however, this paper demonstrates the importance of making decisions when the infrastructure cannot be adapted for economic whichever put emphasis on user activity.

Keywords: Anthropometry, Biomechanics, Design, Ergonomics, Productivity.

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2761 Construction Technology of Modified Vacuum Pre-Loading Method for Slurry Dredged Soil

Authors: Ali H. Mahfouz, Gao Ming-Jun, Mohamad Sharif

Abstract:

Slurry dredged soil at coastal area has a high water content, poor permeability, and low surface intensity. Hence, it is infeasible to use vacuum preloading method to treat this type of soil foundation. For the special case of super soft ground, a floating bridge is first constructed on muddy soil and used as a service road and platform for implementing the modified vacuum preloading method. The modified technique of vacuum preloading and its construction process for the super soft soil foundation improvement is then studied. Application of modified vacuum preloading method shows that the technology and its construction process are highly suitable for improving the super soft soil foundation in coastal areas.

Keywords: Super soft foundation, dredger fill, vacuum preloading, foundation treatment, construction technology.

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2760 Numerical Modeling of Natural Convection on Various Configuration of Rectangular Fin Arrays on Vertical Base Plates

Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian

Abstract:

In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.

Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.

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2759 Existence and Exponential Stability of Almost Periodic Solution for Cohen-Grossberg SICNNs with Impulses

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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2758 Techno-Economic Analysis Framework for Wave Energy Conversion Schemes under South African Conditions: Modeling and Simulations

Authors: Siyanda S. Biyela, Willie A. Cronje

Abstract:

This paper presents a desktop study of comparing two different wave energy to electricity technologies (WECs) using a techno-economic approach. This techno-economic approach forms basis of a framework for rapid comparison of current and future technologies. The approach also seeks to assist in investment and strategic decision making expediting future deployment of wave energy harvesting in South Africa.

Keywords: Cost of energy, tool, wave energy converter, WEC-Sim.

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2757 Characterization of Solutions of Nonsmooth Variational Problems and Duality

Authors: Juan Zhang, Changzhao Li

Abstract:

In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established.

Keywords: Variational problem, Nonsmooth pseudo-invex, Nonsmooth quasi-invex, Critical point, Duality

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