Search results for: energy balance equation

Authors: Arash Azizi-Mazreah, Mohammad T. Manzuri Shalmani, Hamid Barati, Ali Barati

Abstract:

The energy consumption and delay in read/write operation of conventional SRAM is investigated analytically as well as by simulation. Explicit analytical expressions for the energy consumption and delay in read and write operation as a function of device parameters and supply voltage are derived. The expressions are useful in predicting the effect of parameter changes on the energy consumption and speed as well as in optimizing the design of conventional SRAM. HSPICE simulation in standard 0.25μm CMOS technology confirms precision of analytical expressions derived from this paper.

Keywords: Read energy consumption, write energy consumption, read delay, write delay.

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Authors: Lei Danyang, Lu Jialiang

Abstract:

As nightlife is getting richer in urban area, urban nightscape has become an increasingly important part of the urban landscape. Understanding urban nightscape from the perspec­tive of pedestrian perception is very important to improve the livability and walkability of a city. The purpose of this study is to analyze the nightscapes of two different urban forms. The research methods are literature investigation and field investigation. From analyzing the lighting, sensory ex­perience, and night activities, this research studies the two streets, Pei Ho Street and Yen Chow Street West in Sham Shui Po. Results revealed that the two streets are on the two extremes of the two characters of the night and a better balance needs to be found between them. Because of the different land usage and stakeholders, the two streets should play different roles in the nightscape, so their balance points are also different. On the one hand, Pei Ho Street, which has a strong commercial atmos­phere, should not only retain its vitality and diversity but also ensure its function of relaxation at night; on the other hand, in Yen Chow Street West, it is necessary to develop its potential of reconnecting people with the darkness of the night while ensur­ing its safety. These findings may not only provide policymak­ers with information to help them improve the nightscape and livability of the Sham Shui Po area but also help bridge the gap between research and design. In the future, more attention should be paid to pedestrian preference and nightscape perception of vulnerable groups.

Keywords: Hong Kong, pedestrian perception, Sham Shui Po, urban form, urban nightscape.

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Authors: Sangbum Park, Youngjoon Han

Abstract:

This paper proposes a balance control scheme for a biped robot to trace an arbitrary path using image information. While moving, it estimates the zero moment point(ZMP) of the biped robot in the next step using a Kalman filter and renders an appropriate balanced pose of the robot. The ZMP can be calculated from the robot's pose, which is measured from the reference object image acquired by a CCD camera on the robot's head. For simplifying the kinematical model, the coordinates systems of individual joints of each leg are aligned and the robot motion is approximated as an inverted pendulum so that a simple linear dynamics, 3D-LIPM(3D-Linear Inverted Pendulum Mode) can be applied. The efficiency of the proposed algorithm has been proven by the experiments performed on unknown trajectory.

Keywords: Biped robot, Zero moment point, Balance control, Kalman filter.

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Authors: Ying Xin, Shigeki Kametani

Abstract:

This paper deals the energy saving performance of GHP (Gas engine heat pump) air conditioning system has improved with time-series variation. There are two types of air conditioning systems, VRF (Variable refrigerant flow) and central cooling and heating system. VRF is classified as EHP (Electric driven heat pump) and GHP. EHP drives the compressor with electric motor. GHP drives the compressor with the gas engine. The electric consumption of GHP is less than one tenth of EHP does.

In this study, the energy consumption data of GHP installed the junior high schools was collected. An annual and monthly energy consumption per rated thermal output power of each apparatus was calculated, and then their energy efficiency was analyzed. From these data, we investigated improvement of the energy saving of the GHP air conditioning system by the change in the generation.

Keywords: Energy-saving, VRF, GHP, EHP, Air Conditioning System.

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Authors: A. M. Hasna

Abstract:

Today global warming, climate change and energy supply are of greater concern as it is widely realized that the planet earth does not provide an infinite capacity for absorbing human industrialization in the 21st century. The aim of this paper is to analyze upstream and downstream electricity production in selected case studies: a coal power plant, a pump system and a microwave oven covering and consumption to explore the position of energy efficiency in engineering sustainability. Collectively, the analysis presents energy efficiency as a major pathway towards sustainability that requires an inclusive and a holistic supply chain response in the engineering design process.

Keywords: Sustainability, technology, efficiency, engineering, energy.

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Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati

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This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated.

Keywords: Membrane distillation, Dynamical modeling, Advection-diffusion equation, Thermal equilibrium, Heat equation.

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Authors: Md. Ashikur Rahman Khan, M. M. Rahman

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Electrical discharge machining (EDM) is a relatively modern machining process having distinct advantages over other machining processes and can machine Ti-alloys effectively. The present study emphasizes the features of the development of regression equation based on response surface methodology (RSM) for correlating the interactive and higher-order influences of machining parameters on surface finish of Titanium alloy Ti-6Al-4V. The process parameters selected in this study are discharge current, pulse on time, pulse off time and servo voltage. Machining has been accomplished using negative polarity of Graphite electrode. Analysis of variance is employed to ascertain the adequacy of the developed regression model. Experiments based on central composite of response surface method are carried out. Scanning electron microscopy (SEM) analysis was performed to investigate the surface topography of the EDMed job. The results evidence that the proposed regression equation can predict the surface roughness effectively. The lower ampere and short pulse on time yield better surface finish.

Keywords: Graphite electrode, regression model, response surface methodology, surface roughness.

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Authors: Shun-Kai Yang, Kuo-Feng Ssu

Abstract:

Target tracking and localization are important applications in wireless sensor networks. In these applications, sensor nodes collectively monitor and track the movement of a target. They have limited energy supplied by batteries, so energy efficiency is essential for sensor networks. Most existing target tracking protocols need to wake up sensors periodically to perform tracking. Some unnecessary energy waste is thus introduced. In this paper, an energy efficient protocol for target localization is proposed. In order to preserve energy, the protocol fixes the number of sensors for target tracking, but it retains the quality of target localization in an acceptable level. By selecting a set of sensors for target localization, the other sensors can sleep rather than periodically wake up to track the target. Simulation results show that the proposed protocol saves a significant amount of energy and also prolongs the network lifetime.

Keywords: Coverage, energy efficiency, target localization, wireless sensor network.

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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: M. Saravi, F. Ashrafi, S.R. Mirrajei

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As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Gulshan Sachdeva, Ram Bilash

Abstract:

In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy-Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

Keywords: Exergy analysis, Gouy-Stodola, refrigeration, vapor absorption.

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Authors: R. Geetha, G. Umarani Srikanth, S. Prabhu

Abstract:

Wireless sensor networks are resource constrained networks, where energy is the major resource in such networks. Therefore, energy conservation is major aspect in the deployment of Wireless Sensor Network. This work makes use of an extended Greedy Perimeter Stateless Routing (eGPSR) protocol that mainly focuses on energy efficient data transmission. This data transmission is based on the fact that the message that is sent to a distant node consumes more energy than the message that is sent to a short range transmission. Every cluster contains a head set that consists of many virtual cluster heads. Routing is decided by head set members. The energy level of the received signal is the major constraint to choose head set from its members. The experimental result shows that the use of eGPSR in routing has improved throughput with comparatively less delay.

Keywords: eGPSR, energy efficiency, routing, wireless sensor networks, WSN.

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Authors: Ahmad Rouhani

Abstract:

Iran has several potential for using renewable energies, so use them could significantly contribute to energy supply. The purpose of this paper is to identify the potential of the country and select the appropriate DG technologies with consideration the potential and primary energy resources in the regions. In this context, hybrid energy systems proportionate with the potential of different regions will be determined based on technical, economic, and environmental aspect. In the following the proposed structure will be optimized in terms of size and cost. DG technologies used in this project include photovoltaic system, wind turbine, diesel generator and battery bank. The HOMER software is applied for choosing the appropriate structure and the optimization of system sizing. The results have been analyzed in terms of technical and economic. The performance and the cost of each project demonstrate the appropriate structure of hybrid energy system in that region.

Keywords: Feasibility, Hybrid Energy System, Iran, Renewable Energy.

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Authors: Viktória Sugár, Attila Talamon, András Horkai, Michihiro Kita

Abstract:

The dense urban fabric of the 7^th district of Budapest -known as the former Jewish Quarter-, contains mainly historical style, multi-story tenement houses with courtyards. The high population density and the unsatisfactory energetic state of the buildings result high energy consumption. As a preliminary survey of a complex rehabilitation plan, the authors aim to determine the energy demand of the area. The energy demand was calculated by analyzing the structure and the energy consumption of each building by using Geographic Information System (GIS) methods. The carbon dioxide emission was also calculated, to assess the potential of reducing the present state value by complex structural and energetic rehabilitation. As a main focus of the survey, an energy intensity map has been created about the area.

Keywords: Carbon dioxide, energy intensity map, geographic information system, GIS, Hungary, Jewish quarter, rehabilitation.

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Authors: Yunyong Guo, Sudhakar Ganti, Bryan Guo

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The rapid growth of telehealth Internet of Things (IoT) devices has raised concerns about energy consumption and efficient data processing. This paper presents an energy-efficient model that integrates telehealth IoT devices with a fog and cloud computing-based platform, offering a sustainable and robust solution to overcome these challenges. Our model employs fog computing as a localized data processing layer while leveraging cloud computing for resource-intensive tasks, significantly reducing energy consumption. We incorporate adaptive energy-saving strategies. Simulation analysis validates our approach's effectiveness in enhancing energy efficiency for telehealth IoT systems integrated with localized fog nodes and both private and public cloud infrastructures. Future research will focus on further optimization of the energy-saving model, exploring additional functional enhancements, and assessing its broader applicability in other healthcare and industry sectors.

Keywords: Energy-efficient, fog computing, IoT, telehealth.

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Authors: Bahareh Gholamzadeh, Hooman Nabovati

Abstract:

Wireless sensor networks have been used in wide areas of application and become an attractive area for researchers in recent years. Because of the limited energy storage capability of sensor nodes, Energy consumption is one of the most challenging aspects of these networks and different strategies and protocols deals with this area. This paper presents general methods for designing low power wireless sensor network. Different sources of energy consumptions in these networks are discussed here and techniques for alleviating the consumption of energy are presented.

Keywords: Energy consumption, MAC protocol, Routing protocol, Sensor node, Topology control, Wireless sensor network.

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Authors: Norhayati Mat Wajid, Abdul Murad Zainal Abidin, Faiz Fadzil, Mohd Yusof Aizad Mukhtar

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One of the areas that present an opportunity to reduce the national carbon emission is the energy management of public buildings. To our present knowledge, there is no easy-to-use and centralized mechanism that enables the government to monitor the overall energy performance, as well as the carbon footprint, of Malaysia’s public buildings. Therefore, the Public Works Department Malaysia, or PWD, has developed a web-based energy performance reporting tool called JENOSYS (JKR Energy Online System), which incorporates a database of utility account numbers acquired from the utility service provider for analysis and reporting. For test case purposes, 23 buildings under PWD were selected and monitored for their monthly energy performance (in kWh), carbon emission reduction (in tCO₂eq) and utility cost (in MYR), against the baseline. This paper demonstrates the simplicity with which buildings without energy metering can be monitored centrally and the benefits that can be accrued by the government in terms of building energy disclosure and concludes with the recommendation of expanding the system to all the public buildings in Malaysia.

Keywords: Energy-efficient buildings. energy management systems, government buildings, JENOSYS.

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: Image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation scheme, finite differences.

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Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

In this paper, according to the classical algorithm LSQR for solving the least-squares problem, an iterative method is proposed for least-squares solution of constrained matrix equation. By using the Kronecker product, the matrix-form LSQR is presented to obtain the like-minimum norm and minimum norm solutions in a constrained matrix set for the symmetric arrowhead matrices. Finally, numerical examples are also given to investigate the performance.

Keywords: Symmetric arrowhead matrix, iterative method, like-minimum norm, minimum norm, Algorithm LSQR.

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Authors: Marco Morini, Nicolandrea Calabrese, Dario Chello

Abstract:

Despite the international commitment of Algeria towards the development of energy efficiency and renewable energy in the country, the internal energy demand has been continuously growing during the last decade due to the substantial increase of population and of living conditions, which in turn has led to an unprecedented expansion of the residential building sector. The RTB (Thermal Building Regulation) is the technical document that establishes the calculation framework for the thermal performance of buildings in Algeria, setting up minimum obligatory targets for the thermal performance of new buildings. An update of this regulation is due in the coming years and this paper discusses some proposals in this regard, with the aim to improve the energy efficiency of the building sector, particularly with regard to social housing. In particular, it proposes a methodology for drafting an energy performance label of new Algerian residential buildings, moving from the results of the thermal compliance verification and sizing of technical systems as defined in the RTB. Such an energy performance label – whose calculation method is briefly described in the paper – aims to raise citizens' awareness of the benefits of energy efficiency. It can represent the first step in a process of integrating technical installations into the calculation of the energy performance of buildings in Algeria.

Keywords: building, energy certification, energy efficiency, social housing, international cooperation, Mediterranean Region

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Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou

Abstract:

We present a multiple equation time series approach for the short-term load forecasting applied to the electrical power load consumption for the whole Quebec province, in Canada. More precisely, we take into account three meteorological variables — temperature, cloudiness and wind speed —, and we use meteorological measurements taken at different locations on the territory. Our final model shows an average MAPE score of 1.79% over an 8-years dataset.

Keywords: Short-term load forecasting, special days, time series, multiple equations, parallelization, clustering.

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Authors: M. Safa, S. Samarasinghe

Abstract:

An artificial neural network (ANN) approach was used to model the energy consumption of wheat production. This study was conducted over 35,300 hectares of irrigated and dry land wheat fields in Canterbury in the 2007-2008 harvest year.1 In this study several direct and indirect factors have been used to create an artificial neural networks model to predict energy use in wheat production. The final model can predict energy consumption by using farm condition (size of wheat area and number paddocks), farmers- social properties (education), and energy inputs (N and P use, fungicide consumption, seed consumption, and irrigation frequency), it can also predict energy use in Canterbury wheat farms with error margin of ±7% (± 1600 MJ/ha).

Keywords: Artificial neural network, Canterbury, energy consumption, modelling, New Zealand, wheat.

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Authors: M. S. Alrubaih, M. F. M. Zain, N. L. N. Ibrahim, M.A. Alghoul, K. I. Ben Sauod

Abstract:

Careful design and selection of daylighting systems can greatly help in reducing not only artificial lighting use, but also decrease cooling energy consumption and, therefore, potential for downsizing air-conditioning systems. This paper aims to evaluate the energy performance of two types of top-light daylighting systems due to the integration of daylight together with artificial lighting in an existing examinaton hall in University Kebangsaan Malaysia, based on a hot and humid climate. Computer simulation models have been created for building case study (base case) and the two types of toplight daylighting designs for building energy performance evaluation using the VisualDOE 4.0 building energy simulation program. The finding revealed that daylighting through top-light systems is a very beneficial design strategy in reducing annual lighting energy consumption and the overall total annual energy consumption.

Keywords: Academic buildings, Daylighting, Top-lighting, Energy savings, Tropical Climate

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Authors: Mukesh Kumar Awasth, Mohammad Tamsir

Abstract:

The effect of porous medium on the capillary instability of a cylindrical interface in the presence of axial electric field 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, viscosity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and porous medium both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Porous media, Axial electric field.

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Authors: Dayananda Pai, Shrikantha S. Rao, Savitha G.Kini

Abstract:

In this study, the effects of machining parameters on specific energy during surface grinding of 6061Al-SiC35P composites are investigated. Vol% of SiC, feed and depth of cut were chosen as process variables. The power needed for the calculation of the specific energy is measured from the two watt meter method. Experiments are conducted using standard RSM design called Central composite design (CCD). A second order response surface model was developed for specific energy. The results identify the significant influence factors to minimize the specific energy. The confirmation results demonstrate the practicability and effectiveness of the proposed approach.

Keywords: ANOVA, Metal matrix composites, Response surface methodology, Specific energy, Two watt meter method.

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Authors: Sandesh Achar

Abstract:

The cloud computing industry has set new goals for better service delivery and deployment, so anyone can access services such as computation, application, and storage anytime. Cloud computing promises new possibilities for approaching sustainable solutions to deploy and advance their services in this distributed environment. This work explores energy-efficient approaches and how cloud-based architecture can reduce energy consumption levels amongst enterprises leveraging cloud computing services. Adopting cloud-based networking, database, and server machines provide a comprehensive means of achieving the potential gains in energy efficiency that cloud computing offers. In energy-efficient cloud computing, virtualization is one aspect that can integrate several technologies to achieve consolidation and better resource utilization. Moreover, the Green Cloud Architecture for cloud data centers is discussed in terms of cost, performance, and energy consumption, and appropriate solutions for various application areas are provided.

Keywords: Greener Cloud, cloud computing, energy efficiency, energy consumption, metadata tags, Green Cloud Advisor.

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Authors: Rinlee Butch M. Cervera, Princess Stephanie P. Llanos

Abstract:

Lithium iron phosphate (LiFePO₄) is a potential cathode material for lithium-ion batteries due to its promising characteristics. In this study, pure LiFePO₄ (LFP) and carbon-coated nanograined LiFePO₄ (LFP-C) is synthesized and characterized for its microstructural properties. X-ray diffraction patterns of the synthesized samples can be indexed to an orthorhombic LFP structure with about 63 nm crystallite size as calculated by using Scherrer’s equation. Agglomerated particles that range from 200 nm to 300 nm are observed from scanning electron microscopy images. Transmission electron microscopy images confirm the crystalline structure of LFP and coating of amorphous carbon layer. Elemental mapping using energy dispersive spectroscopy analysis revealed the homogeneous dispersion of the compositional elements. In addition, galvanostatic charge and discharge measurements were investigated for the cathode performance of the synthesized LFP and LFP-C samples. The results showed that the carbon-coated sample demonstrated the highest capacity of about 140 mAhg^-1 as compared to non-coated and micrograined sized commercial LFP.

Keywords: Ceramics, microstructure, electrochemical measurements, energy storage, transmission electron microscope.

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Authors: V. Tawiwat, P. Jumnong

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting when combining the minimum energy and jerk of indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of the minimum energy, the minimum jerk and combining them together are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of state inputs employed by combining minimum energy and jerk designs. The numerical solution of minimum direct jerk and energy problem are exactly the same solution; however, the solutions from problem of minimum energy yield the similar solution especially in term of tendency.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: Bin Su

Abstract:

This study focuses on the impact of school building design factors on winter extra energy consumption which mainly includes space heating, water heating and other appliances related to winter indoor thermal conditions. A number of Auckland schools were randomly selected for the study which introduces a method of using real monthly energy consumption data for a year to calculate winter extra energy data of school buildings. The study seeks to identify the relationships between winter extra energy data related to school building design data related to the main architectural features, building envelope and elements of the sample schools. The relationships can be used to estimate the approximate saving in winter extra energy consumption which would result from a changed design datum for future school development, and identify any major energy-efficient design problems. The relationships are also valuable for developing passive design guides for school energy efficiency.

Keywords: Building energy efficiency, Building thermal design, Building thermal performance, School building design.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.

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