Search results for: load balance

Authors: K. Kamalanand, P. Mannar Jawahar

Abstract:

Methods of contemporary mathematical physics such as chaos theory are useful for analyzing and understanding the behavior of complex biological and physiological systems. The three dimensional model of HIV/AIDS is the basis of active research since it provides a complete characterization of disease dynamics and the interaction of HIV-1 with the immune system. In this work, the behavior of the HIV system is analyzed using the three dimensional HIV model and a chaotic measure known as the Hurst exponent. Results demonstrate that Hurst exponents of CD4, CD8 cells and viral load vary nonlinearly with respect to variations in system parameters. Further, it was observed that the three dimensional HIV model can accommodate both persistent (H>0.5) and anti-persistent (H<0.5) dynamics of HIV states. In this paper, the objectives of the study, methodology and significant observations are presented in detail.

Keywords: HIV/AIDS, mathematical model, chaos theory, Hurst exponent

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Authors: H. Fallah, Z. Naddaf Baghdadabadi

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Planning of economic activities development has various dimensions one of which determines adequate capacity of economic activities in provinces regarding the government-s goals. Paralleling planning goals of economic activities development including subjects being focused on the view statement is effective to better realize the statement's goals. Current paper presents a native framework for economic activities development in provincial level. Triple steps within the framework are concordant with the view statement-s goals achievement. At first step of the proposed framework, economic activities are being prioritized in terms of employment indices, and secondly economic activities regarding to the province's relative advantages are being recognized. In the third step, desirable capacity of economic activities is determined with regards to the government's goals and effective constraints in economic activities development. Development of economic activities related to the provinces- relative advantages, contributes on regional balance and on equal development of economic activities. Furthermore, results of the framework enable more confident investment, affect employment development and remove unemployment concern as the main goals of the view statement.

Keywords: Development, economic activity, regional planning, view statement.

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Authors: Abdolamir Nekoubin

Abstract:

The line start permanent magnet motor (LSPMM) combines a permanent magnet rotor for a better motor efficiency during synchronous running with an induction motor squirrel cage rotor to permit the motor starting by direct coupling to power source. In this paper effect of the rotor structure on a line start synchronous permanent magnet motor (LSPMM) is analyzed. LSPMM motor with three different structures for rotor is designed by using RMxprt software; efficiency and line current of LSPMM motor for different structures in full-load condition have been presented. The results indicate that with correct choosing of rotor structure, maximum efficiency can be found.

Keywords: Permanent magnets, LSPMM motor, rotor.

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Authors: İsmail Aksoy, Hacı Bodur, Nihan Altıntas

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This paper introduces a boost converter with a new active snubber cell. In this circuit, all of the semiconductor components in the converter softly turns on and turns off with the help of the active snubber cell. Compared to the other converters, the proposed converter has advantages of size, number of components and cost. The main feature of proposed converter is that the extra voltage stresses do not occur on the main switches and main diodes. Also, the current stress on the main switch is acceptable level. Moreover, the proposed converter can operates under light load conditions and wide input line voltage. In this study, the operating principle of the proposed converter is presented and its operation is verified with the Proteus simulation software for a 1 kW and 100 kHz model.

Keywords: Active snubber cell, boost converter, zero current switching, zero voltage switching.

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Authors: Shao-Ku Kao

Abstract:

This paper presents an active rectifier with time-domain delay compensation to enhance the efficiency. A delay calibration circuit is designed to convert delay time to voltage and adaptive control on/off delay in variable input voltage. This circuit is designed in 0.18 mm CMOS process. The input voltage range is from 2 V to 3.6 V with the output voltage from 1.8 V to 3.4 V. The efficiency can maintain more than 85% when the load from 50 Ω ~ 1500 Ω for 3.6 V input voltage. The maximum efficiency is 92.4 % at output power to be 38.6 mW for 3.6 V input voltage.

Keywords: Wireless power transfer, active diode, delay compensation, time to voltage converter, PCE.

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Authors: H. Dardour, S. Mazouz, A. Bellagi

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For many industrial applications plate heat exchangers are demonstrating a large superiority over the other types of heat exchangers. The efficiency of such a device depends on numerous factors the effect of which needs to be analysed and accurately evaluated. In this paper we present a theoretical analysis of a cocurrent plate heat exchanger and the results of its numerical simulation. Knowing the hot and the cold fluid streams inlet temperatures, the respective heat capacities mCp and the value of the overall heat transfer coefficient, a 1-D mathematical model based on the steady flow energy balance for a differential length of the device is developed resulting in a set of N first order differential equations with boundary conditions where N is the number of channels.For specific heat exchanger geometry and operational parameters, the problem is numerically solved using the shooting method. The simulation allows the prediction of the temperature map in the heat exchanger and hence, the evaluation of its performances. A parametric analysis is performed to evaluate the influence of the R-parameter on the e-NTU values. For practical purposes effectiveness-NTU graphs are elaborated for specific heat exchanger geometry and different operating conditions.

Keywords: Plate heat exchanger, thermal performance, NTU, effectiveness.

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Authors: Rossi A. Hassad

Abstract:

There is widespread emphasis on reform in the teaching of introductory statistics at the college level. Underpinning this reform is a consensus among educators and practitioners that traditional curricular materials and pedagogical strategies have not been effective in promoting statistical literacy, a competency that is becoming increasingly necessary for effective decision-making and evidence-based practice. This paper explains the historical context of, and rationale for reform-oriented teaching of introductory statistics (at the college level) in the health, social and behavioral sciences (evidence-based disciplines). A firm understanding and appreciation of the basis for change in pedagogical approach is important, in order to facilitate commitment to reform, consensus building on appropriate strategies, and adoption and maintenance of best practices. In essence, reform-oriented pedagogy, in this context, is a function of the interaction among content, pedagogy, technology, and assessment. The challenge is to create an appropriate balance among these domains.

Keywords: Reform-oriented, reform, introductory statistics, health, behavioral sciences, evidence-based, psychology, teaching, learning.

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Authors: Carmen E. Zapata, José F. Jiménez, Mauricio Ramiréz, Natalia A. Cano

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The majority of the urban areas in Latin America face the challenges associated with city planning and development problems, attributed to human, technical, and economical factors; therefore, we cannot ignore the issues related to climate change because the city modifies the natural landscape in a significant way transforming the radiation balance and heat content in the urbanized areas. These modifications provoke changes in the temperature distribution known as “the heat island effect”. According to this phenomenon, we have the need to conceive the urban planning based on climatological patterns that will assure its sustainable functioning, including the particularities of the climate variability. In the present study, it is identified the Local Climate Zones (LCZ) in the Metropolitan Area of the Aburrá Valley (Colombia) with the objective of relocate the air quality monitoring stations as a partial solution to the problem of how to measure representative air quality levels in a city for a local scale, but with instruments that measure in the microscale.

Keywords: Air quality, monitoring, local climatic zones, valley, monitoring stations.

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Authors: Ç. Erdoğan, T. Turan

Abstract:

Pediatric cancer patients experience multiple distressing, challenges, physical symptom such as fatigue, pain, sleep disturbance, and balance impairment that continue years after treatment completion. In recent years, yoga is often used in children with cancer to cope with these symptoms. Yoga practice is defined as a unique physical activity that combines physical practice, breath work and mindfulness/meditation. Yoga is an increasingly popular mind-body practice also characterized as a mindfulness mode of exercise. This study aimed to evaluate the impact of yoga intervention of children with cancer. This article planned searching the literature in this field. It has been determined that individualized yoga is feasible and provides benefits for inpatient children, improves health-related quality of life, physical activity levels, physical fitness. After yoga program, children anxiety score decreases significantly. Additionally, individualized yoga is feasible for inpatient children receiving intensive chemotherapy. As a result, yoga is an alternative and complementary medicine that can be safely used in children with cancer.

Keywords: Cancer treatment, children, nursing, yoga.

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Authors: Cédric Damour, Michel Benne, Brigitte Grondin-Perez, Jean-Pierre Chabriat

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Monitoring and control of cane sugar crystallization processes depend on the stability of the supersaturation (σ ) state. The most widely used information to represent σ is the electrical conductivity κ of the solutions. Nevertheless, previous studies point out the shortcomings of this approach: κ may be regarded as inappropriate to guarantee an accurate estimation of σ in impure solutions. To improve the process control efficiency, additional information is necessary. The mass of crystals in the solution ( c m ) and the solubility (mass ratio of sugar to water / s w m m ) are relevant to complete information. Indeed, c m inherently contains information about the mass balance and / s w m m contains information about the supersaturation state of the solution. The main problem is that c m and / s w m m are not available on-line. In this paper, a model based soft-sensor is presented for a final crystallization stage (C sugar). Simulation results obtained on industrial data show the reliability of this approach, c m and the crystal content ( cc ) being estimated with a sufficient accuracy for achieving on-line monitoring in industry

Keywords: Soft-sensor, on-line monitoring, cane sugarcrystallization.

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Authors: Min Goo Lee, Yong Kuk Park, Kyung Kwon Jung, Jun Jae Yoo

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This paper describes the smart energy monitoring system with a wireless sensor network for monitoring of electrical usage in smart house. Proposed system is composed of wireless plugs and energy control wallpad server. The wireless plug integrates an AC power socket, a relay to switch the socket ON/OFF, a Hall effect sensor to sense current of load appliance and a Kmote. The Kmote is a wireless communication interface based on TinyOS. We evaluated wireless plug in a laboratory, analyzed and presented energy consumption data from electrical appliances for 3 months in home.

Keywords: smart house, energy monitoring, wireless plug, wireless sensor network, current consumption.

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Authors: H. Zengin, M. E. Turan, Y. Turen, H. Ahlatci, Y. Sun

Abstract:

This study aimed for improving wear resistance of AM60 magnesium alloy by Ti addition (0, 0.2, 0.5, 1wt%Ti). An electric resistance furnace was used to produce alloys. Pure Mg together with Al, Al-Ti and Al-Mn were melted at 750 ⁰C in a stainless steel crucible under controlled Ar gas atmosphere and then poured into a metal mould preheated at 250 ⁰C. Microstructure characterizations were performed by light optical (LOM) and scanning electron microscope (SEM) after the wear test. Wear rates and friction coefficients were measured with a pin-on-disk type UTS-10 Tribometer test device under a load of 20N. The results showed that Ti addition altered the morphology and the amount of b-Mg₁₇Al₁₂ phase in the microstructure of AM60 alloy. b-Mg₁₇Al₁₂ phases on the grain boundaries were refined with increasing amount of Ti. An improvement in wear resistance of AM60 alloy was observed due to the alteration in the microstructure by Ti addition.

Keywords: Magnesium alloy, titanium, SEM, wear.

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Authors: Antônio P. de Araújo Neto, Ruy D. A. da Silva Neto, Juliana R. de Souza, Salete K. P. de Medeiros, João T. N. de Medeiros

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The tribological test with Pin-On-Disc configuration measures friction and wear properties in dry or lubricated sliding surfaces of a variety of materials and coatings. Polymeric matrix composites loaded with mineral filler were used, 1%, 3%, 10%, 30%, and 50% mass percentage of filler, to reduce the material cost by using mineral tailings. Using a pin-on-disc tribometer to quantify coefficient of friction and wear resistance of the specimens. The parameters known to performing the test were 300 rpm rotation, normal load of 16N and duration of 33.5 minutes. The composite with 10% mineral filler performed better, considering that the wear resistance was good when compared to the other compositions and an average low coefficient of friction, in the order of μ ≤ 0.15.

Keywords: Microcomposites, microparticles tailings of scheelite, PTFE, tribology.

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Authors: D. B. Gohil

Abstract:

Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: Experimentation, forging, process modeling, strain distribution.

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Authors: F. Gurkalo, K. Poutos

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Earthquakes produce some of the most violent loading situations that a structure can be subjected to and if a structure fails under these loads then inevitably human life is put at risk. One of the most common methods by which a structure fails under seismic loading is at the connection of structural elements. The research presented in this paper investigates the interlock systems as a novel method for building structures. The main objective of this experimental study wasto determine the dynamic characteristics and the seismic behaviour of the proposed structures compared to conventional structural systemsduring seismic motions. Results of this study indicate that the interlock mechanism of the panels influences the behaviour of lateral load-resisting systems of the structures during earthquakes, contributing to better structural flexibility and easier maintenance.

Keywords: Watertower, earthquake, seismic, interlocked panels

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: Wood waste ash, characterization, mechanical properties, finite element analysis, flexural behavior, bending tests.

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Authors: Ravit Gautam, Dipen A. Mistry, Manmohan Singh Meena, Bhupelly Dheeraj, Suresh Mikkili

Abstract:

Due to the increased use of the power electronic equipment, harmonics in the power system has increased to a greater extent. These harmonics results a poor power quality causing a major effect on the customers. Shunt active filters (SHAF) are used for the mitigations of the current harmonics and to maintain constant DC link voltage. PI and Fuzzy logic controllers (FLC) were used to control the performance of the shunt active filter under both balance and unbalance source voltage condition. The results found were not satisfying the IEEE-519 standards of THD to be less than 5%. Hysteresis band current control was used to obtain the gating signals for SHAF, though it has some drawbacks and thus to obtain a better performance of the SHAF to mitigate the harmonics, adaptive hysteresis band current control scheme is implemented. Adaptive hysteresis based SHAF is used to obtain better compensation of current harmonics and to regulate the DC link voltage in a better way.

Keywords: DC Link Voltage, Fuzzy Logic Controller, Adaptive Hysteresis, Harmonics, Shunt Active Filter.

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Authors: D. K. Tiwari, Mukesh Kumar Awasthi, G. S. Agrawal

Abstract:

The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Heat and mass transfer, Axial electric field.

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Authors: Amjaad Alsalamah, Liyakathunsia Syed

Abstract:

Transportation is an essential need for many people to go to their work, school, and home. In particular, the main common method inside many cities is to drive the car. Driving a car can be an easy job to reach the destination and load all stuff in a reasonable time. However, deciding to find a parking lot for a car can take a long time using the traditional system that can issue a paper ticket for each customer. The old system cannot guarantee a parking lot for all customers. Also, payment methods are not always available, and many customers struggled to find their car among a numerous number of cars. As a result, this research focuses on providing an online smart parking system in order to save time and budget. This system provides a flexible management system for both parking owner and customers by receiving all request via the online system and it gets an accurate result for all available parking and its location.

Keywords: Smart parking system, IoT, tracking system, process model, cost, time.

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Authors: D. H. Park, Y. H. Tak, H. H. Kwon, G. J. Kwon, H. G. Kim

Abstract:

The purpose of this study is to develop a forging process of automotive parts that satisfies the deformation characteristics. The analyses of temperature variation and deformation behavior of the material are important to obtain the optimal forging products. The hot compression test was carried out to know formability at high temperature. In order to define the optimum forging conditions including material temperature, strain and forging load, the commercial finite element analysis code was used to simulate the forging procedure of engine mounting parts. Experimental results were compared with the simulation results by finite element analysis. Test results were in good agreement with the simulations.

Keywords: Cold forging, hot forging, engine mounting, automotive parts, optimization.

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Authors: S. Al Dandachli, F. Perales, Y. Monerie, F. Jamin, M. S. El Youssoufi, C. Pelissou

Abstract:

The goal of this research is to study the fracture process and mechanical behavior of concrete under I–II mixed-mode stress, which is essential for ensuring the safety of concrete structures. For this purpose, two-dimensional simulations of three-point bending tests under variable load and geometry on notched cement paste samples of composite samples (cement paste/siliceous aggregate) are modeled by employing Cohesive Zone Models (CZMs). As a result of experimental validation of these tests, the CZM model demonstrates its capacity to predict fracture propagation at the local scale.

Keywords: Concrete, cohesive zone model, microstructure, fracture, three-point flexural test bending.

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Authors: Ali Reza Pouladkhan, Jalil Emadi, Hamed Habibolahiyan

Abstract:

This paper presents an exact solution and a finite element method (FEM) for a Piezoceramic Rod under static load. The cylindrical rod is made from polarized ceramics (piezoceramics) with axial poling. The lateral surface of the rod is traction-free and is unelectroded. The two end faces are under a uniform normal traction. Electrically, the two end faces are electroded with a circuit between the electrodes, which can be switched on or off. Two cases of open and shorted electrodes (short circuit and open circuit) will be considered. Finally, a finite element model will be used to compare the results with an exact solution. The study uses ABAQUS (v.6.7) software to derive the finite element model of the ceramic rod.

Keywords: Finite element method, Ceramic rod; Axial poling, Normal traction, Short circuit, Open circuit.

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Authors: I. O. Nascimento, J. T. Manzi

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The drying process is an important operation in the chemical industry and it is widely used in the food, grain industry and fertilizer industry. However, for demanding a considerable consumption of energy, such a process requires a deep energetic analysis in order to reduce operating costs. This paper deals with thermodynamic optimization applied to rotary dryers based on the entropy production minimization, aiming at to reduce the energy consumption. To do this, the mass, energy and entropy balance was used for developing a relationship that represents the rate of entropy production. The use of the Second Law of Thermodynamics is essential because it takes into account constraints of nature. Since the entropy production rate is minimized, optimals conditions of operations can be established and the process can obtain a substantial gain in energy saving. The minimization strategy had been led using classical methods such as Lagrange multipliers and implemented in the MATLAB platform. As expected, the preliminary results reveal a significant energy saving by the application of the optimal parameters found by the procedure of the entropy minimization It is important to say that this method has shown easy implementation and low cost.

Keywords: Drying, entropy minimization, modeling dryers, thermodynamic optimization.

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Authors: Jong-Bae Lee, Seongsoo Lee

Abstract:

This paper proposes an adaptive discharge time control method to balance cell voltages in alternating battery cell discharging method. In the alternating battery cell discharging method, battery cells are periodically discharged in turn. Recovery effect increases battery output voltage while the given battery cell rests without discharging, thus battery operation time of target system increases. However, voltage mismatch between cells leads two problems. First, voltage difference between cells induces inter-cell current with wasted power. Second, it degrades battery operation time, since system stops when any cell reaches to the minimum system operation voltage. To solve this problem, the proposed method adaptively controls cell discharge time to equalize both cell voltages. In the proposed method, battery operation time increases about 19%, while alternating battery cell discharging method shows about 7% improvement.

Keywords: Battery, Recovery Effect, Low-Power, Alternating Battery Cell Discharging, Adaptive Discharge Time Control.

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Authors: Bobbie Green, James A. Nelson

Abstract:

Innovations in technology have created new ethical challenges. Essential use of electronic communication in the workplace has escalated at an astronomical rate over the past decade. As such, legal and ethical dilemmas confronted by both the employer and the employee concerning managerial control and ownership of einformation have increased dramatically in the USA. From the employer-s perspective, ownership and control of all information created for the workplace is an undeniable source of economic advantage and must be monitored zealously. From the perspective of the employee, individual rights, such as privacy, freedom of speech, and freedom from unreasonable search and seizure, continue to be stalwart legal guarantees that employers are not legally or ethically entitled to abridge in the workplace. These issues have been the source of great debate and the catalyst for legal reform. The fine line between ethical and legal has been complicated by emerging technologies. This manuscript will identify and discuss a number of specific legal and ethical issues raised by the dynamic electronic workplace and conclude with suggestions that employers should follow to respect the delicate balance between employees- legal rights to privacy and the employer's right to protect its knowledge systems and infrastructure.

Keywords: Information, ethics, legal, privacy

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Authors: S. P. Sharma, Som Nath Saha

Abstract:

This paper presents the performance, based on exergy analysis of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater based on energy balance equations has been presented and the results obtained have been compared with that of a conventional flat-plate solar air heater. The double flow corrugated absorber solar air heater performs thermally better than the flat plate double flow and conventional flat-plate solar air heater under same operating conditions. However, the corrugated absorber leads to higher pressure drop thereby increasing pumping power. The results revealed that the energy and exergy efficiencies of double flow corrugated absorber solar air heater is much higher than conventional solar air heater with the concept involving of increase in heat transfer surface area and turbulence in air flow. The results indicate that the energy efficiency increases, however, exergy efficiency decreases with increase in mass flow rate.

Keywords: Corrugated absorber, double flow, exergy efficiency, solar air heater.

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Authors: Idris Elfeituri

Abstract:

In the current study, energy and exergy analysis of a 65 MW steam power plant was carried out. This study investigated the effect of variations of overall conductance of the super heater on the performance of an existing steam power plant located in Derna, Libya. The performance of the power plant was estimated by a mathematical modelling which considers the off-design operating conditions of each component. A fully interactive computer program based on the mass, energy and exergy balance equations has been developed. The maximum exergy destruction has been found in the steam generation unit. A 50% reduction in the design value of overall conductance of the super heater has been achieved, which accordingly decreases the amount of the net electrical power that would be generated by at least 13 MW, as well as the overall plant exergy efficiency by at least 6.4%, and at the same time that would cause an increase of the total exergy destruction by at least 14 MW. The achieved results showed that the super heater design and operating conditions play an important role on the thermodynamics performance and the fuel utilization of the power plant. Moreover, these considerations are very useful in the process of the decision that should be taken at the occasions of deciding whether to replace or renovate the super heater of the power plant.

Keywords: Exergy, super-heater, fouling, steam power plant, off-design.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

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This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Jairo Aparecido Martins, Estaner Claro Romão

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This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: Aluminum, industrial clutch, static and dynamic loading, numerical simulation.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

Abstract:

This paper presents a simple three phase power flow method for solution of three-phase unbalanced radial distribution system (RDN) with voltage dependent loads. It solves a simple algebraic recursive expression of voltage magnitude, and all the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily understood. Mutual coupling between the phases has been included in the mathematical model. The proposed algorithm has been tested with several unbalanced radial distribution networks and the results are presented in the article. 8- bus and IEEE 13 bus unbalanced radial distribution system results are in agreements with the literature and show that the proposed model is valid and reliable.

Keywords: radial distribution networks, load flow, circuitmodel, three-phase four-wire, unbalance.

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