Search results for: Energy equation

Authors: A. Sherif, A. El Zafarany, R. Arafa

Abstract:

Hospitals, everywhere, are considered heavy energy consumers. Hospital Intensive Care Unit spaces pose a special challenge, where design guidelines requires the provision of external windows for daylighting and external view. Window protection strategies could be employed to reduce energy loads without detriment effect on comfort or health care. This paper addresses the effectiveness of using various window strategies on the annual cooling, heating and lighting energy use of a typical Hospital Intensive Unit space. Series of experiments were performed using the EnergyPlus simulation software for a typical Intensive Care Unit (ICU) space in Cairo, located in the Egyptian desert. This study concluded that the use of shading systems is more effective in conserving energy in comparison with glazing of different types, in the Cairo ICUs. The highest energy savings in the West and South orientations were accomplished by external perforated solar screens, followed by overhangs positioned at a protection angle of 45°.

Keywords: Energy, Hospital, Intensive Care Units, Shading.

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Authors: Kamalpreet Kaur, Harjit Pal Singh, Vikas Khullar

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In Wireless Sensor Network (WSN), the main limitation is generally inimitable energy consumption during processing of the sensor nodes. Cluster head (CH) election is one of the main issues that can reduce the energy consumption. Therefore, discovering energy saving routing protocol is the focused area for research. In this paper, fuzzy-based energy aware routing protocol is presented, which enhances the stability and network lifetime of the network. Fuzzy logic ensures the well-organized selection of CH by taking four linguistic variables that are concentration, energy, centrality, and distance to base station (BS). The results show that the proposed protocol shows better results in requisites of stability and throughput of the network.

Keywords: ERA, fuzzy logic, network model, WSN.

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Authors: Rooholah Hasanizadeh, Saadan Zokaei

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Energy efficient protocol design is the aim of current researches in the area of sensor networks where limited power resources impose energy conservation considerations. In this paper we care for Medium Access Control (MAC) protocols and after an extensive literature review, two adaptive schemes are discussed. Of them, adaptive-rate MACs which were introduced for throughput enhancement show the potency to save energy, even more than adaptive-power schemes. Then we propose an allocation algorithm for getting accurate and reliable results. Through a simulation study we validated our claim and showed the power saving of adaptive-rate protocols.

Keywords: Adaptive-rate, adaptive-power, MAC protocol, energy efficiency, sensor networks.

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Authors: A. Allirani, M. Suganthi

Abstract:

Data gathering is an essential operation in wireless sensor network applications. So it requires energy efficiency techniques to increase the lifetime of the network. Similarly, clustering is also an effective technique to improve the energy efficiency and network lifetime of wireless sensor networks. In this paper, an energy efficient cluster formation protocol is proposed with the objective of achieving low energy dissipation and latency without sacrificing application specific quality. The objective is achieved by applying randomized, adaptive, self-configuring cluster formation and localized control for data transfers. It involves application - specific data processing, such as data aggregation or compression. The cluster formation algorithm allows each node to make independent decisions, so as to generate good clusters as the end. Simulation results show that the proposed protocol utilizes minimum energy and latency for cluster formation, there by reducing the overhead of the protocol.

Keywords: Sensor networks, Low latency, Energy sorting protocol, data processing, Cluster formation.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: A. Soltani, M. Karimi Demneh

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In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Navid Javidtash, Abdolmohamad Davodi, Mojtaba Hakimzadeh, Abdolreza Roozbeh

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Economic dispatch (ED) is considered to be one of the key functions in electric power system operation. This paper presents a new hybrid approach based genetic algorithm (GA) to economic dispatch problems. GA is most commonly used optimizing algorithm predicated on principal of natural evolution. Utilization of chaotic queue with GA generates several neighborhoods of near optimal solutions to keep solution variation. It could avoid the search process from becoming pre-mature. For the objective of chaotic queue generation, utilization of tent equation as opposed to logistic equation results in improvement of iterative speed. The results of the proposed approach were compared in terms of fuel cost, with existing differential evolution and other methods in literature.

Keywords: Economic Dispatch(ED), Optimization, Fuel Cost, Genetic Algorithm (GA).

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

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Authors: Hairulliza M. Judi, Soon Y. Chee

Abstract:

This paper discusses the landscape design that could increase energy efficiency in a house. By planting trees in a house compound, the tree shades prevent direct sunlight from heating up the building, and it enables cooling off the surrounding air. The requirement for air-conditioning could be minimized and the air quality could be improved. During the life time of a tree, the saving cost from the mentioned benefits could be up to US $ 200 for each tree. The project intends to visually describe the landscape design in a house compound that could enhance energy efficiency and consequently lead to energy saving. The house compound model was developed in three dimensions by using AutoCAD 2005, the animation was programmed by using LightWave 3D softwares i.e. Modeler and Layout to display the tree shadings in the wall. The visualization was executed on a VRML Pad platform and implemented on a web environment.

Keywords: Tree planting, tree shading, energy efficiency, visualization.

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Authors: Saad F. Al Nuaimi

Abstract:

Energy consumption is a very important topic these days especially regarding air conditioning in residential buildings, since this takes the biggest amount of energy in buildings total consumption, residential buildings constitute the biggest percentage of energy consumption in Bahrain. This research reflects on the effects of shading percentage in different solar orientations on the energy consumption inside residential buildings (domestic dwellings). The research as found that, there are different effects of shading in changing building orientation: • 0.69% for the shading percentage 25% when the building is oriented to the north (0º); • 18.59% for 75% of shading in north-west orientation (325º); • The best effect for shading is in north-west orientation (315º); • The less effect for shading was in case of the building orientation is the north (0º).

Keywords: Bahraini buildings, Building shading, energy consumption, residential buildings, shading effects.

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Authors: M. Kouhirostamkolaei, M. Kouhirostami, M. Sam, J. Woo, A. T. Asutosh, J. Li, C. Kibert

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Construction is one of the most energy consumed activities in the urban environment that results in a significant amount of greenhouse gas emissions around the world. Thus, the impact of the construction industry on global warming is undeniable. Thus, reducing building energy consumption and mitigating carbon production can slow the rate of global warming. The purpose of this study is to determine the amount of energy consumption and carbon dioxide production during the operation phase and the impact of using new shells on energy saving and carbon footprint. Therefore, a residential building with a re-enforced concrete structure is selected in Babolsar, Iran. DesignBuilder software has been used for one year of building operation to calculate the amount of carbon dioxide production and energy consumption in the operation phase of the building. The primary results show the building use 61750 kWh of energy each year. Computer simulation analyzes the effect of changing building shells -using XPS polystyrene and new electrochromic windows- as well as changing the type of lighting on energy consumption reduction and subsequent carbon dioxide production. The results show that the amount of energy and carbon production during building operation has been reduced by approximately 70% by applying the proposed changes. The changes reduce CO₂e to 11345 kg CO₂/yr. The result of this study helps designers and engineers to consider material selection’s process as one of the most important stages of design for improving energy performance of buildings.

Keywords: Construction materials, green construction, energy simulation, carbon footprint, energy saving, concrete structure, DesignBuilder.

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: Zohreh Soltani, Seyedmohammadhossein Hosseinian

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Reduction of energy consumption in built infrastructure, through the installation of energy-efficient technologies, is a major approach to achieving sustainability. In practice, the viability of energy efficiency projects strongly depends on the cost reimbursement and profitability. These projects are subject to failure if the actual cost savings do not reimburse the project cost promptly. In such cases, refinancing could be a solution to benefit from the long-term returns of the project, if implemented wisely. However, very little is still known about the effect of refinancing options on financial performance of energy efficiency projects. In order to fill this gap, the present study investigates the financial behavior of energy efficiency projects with focus on refinancing options, such as Leveraged Loans. A System Dynamics (SD) model is introduced, and the model application is presented using an actual case-study data. The case study results indicate that while high-interest start-ups make using Leveraged Loan inevitable, refinancing can rescue the project and bring about profitability. This paper also presents some managerial implications of refinancing energy efficiency projects based on the case-study analysis. Results of this study help to implement financially viable energy efficiency projects so that the community could benefit from their environmental advantages widely.

Keywords: Energy efficiency projects, leveraged loan, refinancing, sustainability.

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Authors: Azadeh Maroufmashat, Sourena Sattari Khavas, Halle Bakhteeyar

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Multi-energy systems will enhance the system reliability and power quality. This paper presents an integrated approach for the design and operation of distributed energy resources (DER) systems, based on energy hub modeling. A multi-objective optimization model is developed by considering an integrated view of electricity and natural gas network to analyze the optimal design and operating condition of DER systems, by considering two conflicting objectives, namely, minimization of total cost and the minimization of environmental impact which is assessed in terms of CO2 emissions. The mathematical model considers energy demands of the site, local climate data, and utility tariff structure, as well as technical and financial characteristics of the candidate DER technologies. To provide energy demands, energy systems including photovoltaic, and co-generation systems, boiler, central power grid are considered. As an illustrative example, a hotel in Iran demonstrates potential applications of the proposed method. The results prove that increasing the satisfaction degree of environmental objective leads to increased total cost.

Keywords: Multi objective optimization, DER systems, Energy hub, Cost, CO2 emission.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

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The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Jalil Boudjadar

Abstract:

Dynamic Voltage and Frequency Scaling (DVFS) multicore platforms are promising execution platforms that enable high computational performance, less energy consumption and flexibility in scheduling the system processes. However, the resulting interleaving and memory interference together with per-core frequency tuning make real-time guarantees hard to be delivered. Besides, energy consumption represents a strong constraint for the deployment of such systems on energy-limited settings. Identifying the system configurations that would achieve a high performance and consume less energy while guaranteeing the system schedulability is a complex task in the design of modern embedded systems. This work studies the trade-off between energy consumption, cores utilization and memory bottleneck and their impact on the schedulability of DVFS multicore time-critical systems with a hierarchy of shared memories. We build a model-based framework using Parametrized Timed Automata of UPPAAL to analyze the mutual impact of performance, energy consumption and schedulability of DVFS multicore systems, and demonstrate the trade-off on an actual case study.

Keywords: Time-critical systems, multicore systems, schedulability analysis, performance, memory interference, energy consumption.

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Authors: Abdurrahim Dal, Tuncay Karaçay

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Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: M. Cañada-Soriano, C. Aparicio-Fernández, P. Sebastián Ferrer Gisbert, M. Val Field, J.-L. Vivancos-Bono

Abstract:

The lack of insulation along with the existence of air leakages constitute a meaningful impact on the energy performance of buildings. Both of them lead to increases in the energy demand through additional heating and/or cooling loads. Additionally, they cause thermal discomfort. In order to quantify these uncontrolled air currents, the Blower Door test can be used. It is a standardized procedure that determines the airtightness of a space by characterizing the rate of air leakages through the envelope surface. In this sense, the low-energy buildings complying with the Passive House design criteria are required to achieve high levels of airtightness. Due to the invisible nature of air leakages, additional tools are often considered to identify where the infiltrations take place such as the infrared thermography. The aim of this study is to assess the airtightness of a typical Mediterranean dwelling house, refurbished under the Passive House standard, using the Blower Door test. Moreover, the building energy performance modelling tools TRNSYS (TRaNsient System Simulation program) and TRNFlow (TRaNsient Flow) have been used to estimate the energy demand in different scenarios. In this sense, a sequential implementation of three different energy improvement measures (insulation thickness, glazing type and infiltrations) have been analyzed.

Keywords: Airtightness, blower door, TRNSYS, infrared thermography, energy demand.

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Authors: Emmanouel Koumoulas, Aikaterini Rokkou, Marios Moschakis

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Theagenio" in Thessaloniki exists and works for three centuries now as a hospital. Since 1975, it has been operating as an Integrated Special Cancer Hospital and since 1985 it has been integrated into the National Health System. "Theagenio" Cancer Hospital is located at the central web of Thessaloniki residential complex and consists of two buildings, the "Symeonidio Research Center", which was completed in 1962 and the Nursing Ward, a project that was later completed in 1975. This paper examines the design of the Hospital Unit according to the requirements of the energy design of buildings. Initially, the energy characteristics of the Hospital are recorded, followed by a detailed presentation of the electromechanical installations. After the existing situation has been captured and with the help of the software TEE-KENAK, different scenarios for the energy upgrading of the buildings have been studied. Proposals for upgrading concern both the shell, e.g. installation of external thermal insulation, replacement of frames, addition of shading systems, etc. as well as electromechanical installations, e.g. use of ceiling fans, improvements in heating and cooling systems, interventions in lighting, etc. The simulation calculates the future energy status of the buildings and presents the economic benefits of the proposed interventions with reference to the environmental profits that arise.

Keywords: Energy consumption in hospitals, energy saving interventions, energy upgrading, hospital facilities.

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Authors: J.-P. Skön, M. Johansson, O. Kauhanen, M. Raatikainen, K. Leiviskä, M. Kolehmainen

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The building sector is the largest energy consumer and CO2 emitter in the European Union (EU) and therefore the active reduction of energy consumption and elimination of energy wastage are among the main goals in it. Healthy housing and energy efficiency are affected by many factors which set challenges to monitoring, control and research of indoor air quality (IAQ) and energy consumption, especially in old buildings. These challenges include measurement and equipment costs, for example. Additionally, the measurement results are difficult to interpret and their usage in the ventilation control is also limited when taking into account the energy efficiency of housing at the same time. The main goal of this study is to develop a cost-effective building monitoring and control system especially for old buildings. The starting point or keyword of the development process is a wireless system; otherwise the installation costs become too high. As the main result, this paper describes an idea of a wireless building monitoring and control system. The first prototype of the system has been installed in 10 residential buildings and in 10 school buildings located in the City of Kuopio, Finland.

Keywords: Energy efficiency, Indoor air quality, Monitoring system, Building automation

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Authors: Hanen Nafaa, Maissa Farhat, Sina Ouriemi, Sbita Lassaad

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The use of renewable energies is growing significantly worldwide. Faced with the increasing demand for electrical energy, mainly for the needs of remote, deserted and mountainous regions, numerous applications use photovoltaic energy. In this sense, the proposed study concerns a mathematical modeling and an experimental validation for the recovery of essential oil by a steam distillation system using photovoltaic energy. In this paper, we proceed to a modeling of the solar system that includes a photovoltaic (PV) generator with an electronic power converter allowing a continuation of the optimum operating point. The results obtained are promising and are validated practically.

Keywords: Boiling in tubes, DC-DC converter, desalination, maximum power point tracking command, photovoltaic energy, solar generator.

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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: F. Behrouzi, A. Maimun, M. Nakisa

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The growth of population, rising fossil fuel prices (limited and decreasing day by day), pollution problem due to use of fossil fuels and increasing electrical demand are important factors that encourage the use of green and renewable energy technologies. Among the different renewable energy technologies, hydro power generation (large and small scale) is the prime choice in terms of contribution to the world's electricity generation by using water current turbines. Currently, researchers mainly focused on design and development of different kind of turbines to capture hydropower to generate electricity as clean and reliable energy. This paper is a review of the status of research on water current turbines carried out to generate electricity from hydrokinetic energy especially in places where there is no electricity, but there is access to flowing water.

Keywords: Turbines, Renewable Energy, Hydropower.

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Authors: Mohammad M. Toufigh, Ahad Ouria

Abstract:

This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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Authors: Doaa M. Atia, Faten H. Fahmy, Ninet M. Ahmed, Hassen T. Dorrah

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In this paper, the optimum design for renewable energy system powered an aquaculture pond was determined. Hybrid Optimization Model for Electric Renewable (HOMER) software program, which is developed by U.S National Renewable Energy Laboratory (NREL), is used for analyzing the feasibility of the stand alone and hybrid system in this study. HOMER program determines whether renewable energy resources satisfy hourly electric demand or not. The program calculates energy balance for every 8760 hours in a year to simulate operation of the system. This optimization compares the demand for the electrical energy for each hour of the year with the energy supplied by the system for that hour and calculates the relevant energy flow for each component in the model. The essential principle is to minimize the total system cost while HOMER ensures control of the system. Moreover the feasibility analysis of the energy system is also studied. Wind speed, solar irradiance, interest rate and capacity shortage are the parameters which are taken into consideration. The simulation results indicate that the hybrid system is the best choice in this study, yielding lower net present cost. Thus, it provides higher system performance than PV or wind stand alone systems.

Keywords: Wind stand-alone system, Photovoltaic stand-alone system, Hybrid system, Optimum system sizing, feasibility, Cost analysis.

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Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

Abstract:

Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: Graphic parameterization, green building design, mathematical model, U-shaped buildings.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

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The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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