Search results for: SSS equation.
852 Heat and Mass Transfer of Triple Diffusive Convection in a Rotating Couple Stress Liquid Using Ginzburg-Landau Model
Authors: Sameena Tarannum, S. Pranesh
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A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.
Keywords: Couple stress liquid, Ginzburg-Landau model, rotation, triple diffusive convection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1263851 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1401850 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem
Authors: Adil AL-Rammahi
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In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2477849 A New Version of Unscented Kalman Filter
Authors: S. A. Banani, M. A. Masnadi-Shirazi
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This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results.
Keywords: Extended Kalman Filter, Iterated EKF, Nonlinearstate estimator, Unscented Kalman Filter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2867848 On the Determination of a Time-like Dual Curve in Dual Lorentzian Space
Authors: Emin Özyılmaz
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In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1462847 Membrane Distillation Process Modeling: Dynamical Approach
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2843846 Development of Regression Equation for Surface Finish and Analysis of Surface Integrity in EDM
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2535845 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method
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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1410844 Thermodynamic Analysis of a Vapor Absorption System Using Modified Gouy-Stodola Equation
Authors: Gulshan Sachdeva, Ram Bilash
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3665843 Conduction Accompanied With Transient Radiative Heat Transfer Using Finite Volume Method
Authors: A. Ashok, K.Satapathy, B. Prerana Nashine
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The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.Keywords: Radiative transfer equation, finite volume method, conduction, transient radiation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1538842 A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement
Authors: Tudor Barbu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1293841 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation
Authors: Minghui Wang, Luping Xu, Juntao Zhang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1399840 Fast Short-Term Electrical Load Forecasting under High Meteorological Variability with a Multiple Equation Time Series Approach
Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 261839 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique
Authors: Mohamed M. Mousa, Aidarkhan Kaltayev
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4559838 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation
Authors: Tarun Kumar Rawat, Abhirup Lahiri, Ashish Gupta
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In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.
Keywords: Single-ended input differential amplifier, Noise, stochastic differential equation, mean and variance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1696837 Comprehensive Study on the Linear Hydrodynamic Analysis of a Truss Spar in Random Waves
Authors: Roozbeh Mansouri, Hassan Hadidi
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Truss spars are used for oil exploitation in deep and ultra-deep water if storage crude oil is not needed. The linear hydrodynamic analysis of truss spar in random sea wave load is necessary for determining the behaviour of truss spar. This understanding is not only important for design of the mooring lines, but also for optimising the truss spar design. In this paper linear hydrodynamic analysis of truss spar is carried out in frequency domain. The hydrodynamic forces are calculated using the modified Morison equation and diffraction theory. Added mass and drag coefficients of truss section computed by transmission matrix and normal acceleration and velocity component acting on each element and for hull section computed by strip theory. The stiffness properties of the truss spar can be separated into two components; hydrostatic stiffness and mooring line stiffness. Then, platform response amplitudes obtained by solved the equation of motion. This equation is non-linear due to viscous damping term therefore linearised by iteration method [1]. Finally computed RAOs and significant response amplitude and results are compared with experimental data.
Keywords: Truss Spar, Hydrodynamic analysis, Wave spectrum, Frequency Domain
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2406836 A New Time Discontinuous Expanded Mixed Element Method for Convection-dominated Diffusion Equation
Authors: Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao
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In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.
Keywords: Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1301835 Risk Assessment of Musculoskeletal Disorders in an Electronic Components Company
Authors: Sara Bragança, Eric Costa
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The work presented in this paper was performed for a workstation of an assembly section in a company that manufactures radio modules and air conditioning for cars. After performing a workstation analysis and a questionnaire to the operators it was possible to understand the need to investigate the risk of musculoskeletal disorders originated from both the handling of loads as the incorrect dimensioning of the workstation. Regarding the handling of loads the NIOSH Equation was used and it was verified that there was no risk of musculoskeletal disorders. As the operators expressed their lack of satisfaction regarding back pains due to posture adopted they were established the appropriate dimensions (to satisfy 97.5% of the population and using the table of anthropometric data of the Portuguese population) for the workstation and it was proposed the availability of a chair for the workers.
Keywords: Anthropometry, Musculoskeletal disorders, NIOSH Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1789834 Oscillation Criteria for Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales
Authors: Da-Xue Chen, Guang-Hui Liu
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In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.
Keywords: Oscillation, damped delay dynamic equation, time scale.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1267833 Investigation of Enhancement of Heat Transfer in Natural Convection Utilizing of Nanofluids
Authors: S. Etaig, R. Hasan, N. Perera
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This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.Keywords: Computational fluid Dynamics, Natural convection, Nanofluid and Thermal conductivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1830832 Characterization of the In0.53Ga0.47As n+nn+ Photodetectors
Authors: Fatima Zohra Mahi, Luca Varani
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We present an analytical model for the calculation of the sensitivity, the spectral current noise and the detective parameter for an optically illuminated In0.53Ga0.47As n+nn+ diode. The photocurrent due to the excess carrier is obtained by solving the continuity equation. Moreover, the current noise level is evaluated at room temperature and under a constant voltage applied between the diode terminals. The analytical calculation of the current noise in the n+nn+ structure is developed by considering the free carries fluctuations. The responsivity and the detection parameter are discussed as functions of the doping concentrations and the emitter layer thickness in one-dimensional homogeneous n+nn+ structure.
Keywords: Responsivity, detection parameter, photo-detectors, continuity equation, current noise.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2053831 Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model
Authors: Amadi Ugwulo Chinyere, Lewis D. Gbarayorks, Emem N. H. Inamete
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In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.
Keywords: DC pension fund, modified constant elasticity of variance, optimal investment strategies, voluntary contribution, administrative charges.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 355830 Identification of States and Events for the Static and Dynamic Simulation of Single Electron Tunneling Circuits
Authors: Sharief F. Babiker, Abdelkareem Bedri, Rania Naeem
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The implementation of single-electron tunneling (SET) simulators based on the master-equation (ME) formalism requires the efficient and accurate identification of an exhaustive list of active states and related tunnel events. Dynamic simulations also require the control of the emerging states and guarantee the safe elimination of decaying states. This paper describes algorithms for use in the stationary and dynamic control of the lists of active states and events. The paper presents results obtained using these algorithms with different SET structures.Keywords: Active state, Coulomb blockade, Master Equation, Single electron devices
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1379829 Assessment Tool for Social Responsibility Performance According to the ISO 26000
Authors: W. Fethallah, L. Chraibi, N. Sefiani
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The present paper is concerned with a statistical approach involving latent and manifest variables applied in order to assess the organization's social responsibility performance. The main idea is to develop an assessment tool and a measurement of the Social Responsibility Performance, enabling the company to characterize her performance regarding to the ISO 26000 standard's seven core subjects. For this, we conceptualize a structural equation modeling (SEM) which describes various causal connections between the Social Responsibility’s components. The SEM’s resolution is based on the Partial Least squares (PLS) method and the implementation is running in the XLSTAT software.Keywords: Corporate social responsibility, latent and manifest variable, partial least squares, structural equation model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1212828 Degradation Model of Optical Characteristics of Zno-Pigmented White Paint by Electron Radiation
Authors: Tian Hai, Yang Shengsheng, Jr., Wang Yi
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Based on an analysis of the mechanism of degradation of optical characteristics of the ZnO-pigmented white paint by electron irradiation, a model of single molecular color centers is built. An equation that explains the relationship between the changes of variation of the ZnO-pigmented white paint-s spectrum absorptance and electron fluence is derived. The uncertain parameters in the equation can be calculated using the curve fitting by experimental data. The result indicates that the model can be applied to predict the degradation of optical characteristics of ZnO-pigmented white paint by electron radiation.
Keywords: ZnO-pigmented white pain, effects of electron radiation, optical characteristics degradation, prediction model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1518827 Intrinsic Kinetics of Methanol Dehydration over Al2O3 Catalyst
Authors: Liang Zhang, Hai-Tao Zhang, W ei-Yong Ying, Ding-Ye Fang
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Dehydration of methanol to dimethyl ether (DME) over a commercial Al2O3 catalyst was studied in an isothermal integral fixed bed reactor. The experiments were performed on the temperature interval 513-613 K, liquid hourly space velocity (LHSV) of 0.9-2.1h-1, pressures between 0.1 and 1.0 MPa. The effect of different operation conditions on the dehydration of methanol was investigated in a laboratory scale experiment. A new intrinsic kinetics equation based on the mechanism of Langmuir-Hinshelwood dissociation adsorption was developed for the dehydration reaction by fitting the expressions to the experimental data. An activation energy of 67.21 kJ/mol was obtained for the catalyst with the best performance. Statistic test showed that this new intrinsic kinetics equation was acceptable.Keywords: catalyst, dimethyl ether, intrinsic kinetics, methanol
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4637826 On the Modeling and State Estimation for Dynamic Power System
Authors: A. Thabet, M. Boutayeb, M. N. Abdelkrim
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This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.
Keywords: Power system, Dynamic decoupled model, Extended Kalman Filter, Convergence analysis, Time computing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2723825 Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method
Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh
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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.
Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2886824 A Sliding Mesh Technique and Compressibility Correction Effects of Two-equation Turbulence Models for a Pintle-Perturbed Flow Analysis
Authors: J. Y. Heo, H. G. Sung
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Numerical simulations have been performed for assessment of compressibility correction of two-equation turbulence models suitable for large scale separation flows perturbed by pintle strokes. In order to take into account pintle movement, a sliding mesh method was applied. The chamber pressure, mass flow rate, and thrust have been analyzed, and the response lag and sensitivity at the chamber and nozzle were estimated for a movable pintle. The nozzle performance for pintle reciprocating as its insertion and extraction processes, were analyzed to better understand the dynamic performance of the pintle nozzle.
Keywords: Pintle, sliding mesh, turbulent model, compressibility correction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2254823 Einstein’s General Equation of the Gravitational Field
Authors: A. Benzian
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The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.
Keywords: Inertia, principle of equivalence, tensors, Riemannian geometry.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 743