Search results for: Linear fredholm equations

Authors: Babak Tashakori Bafghi, Laleh Tashakori, Reza Allahyari Soeini, Mohammad Mokhtari

Abstract:

Supplier selection is a multi criteria decision-making process that comprises tangible and intangible factors. The majority of previous supplier selection techniques do not consider strategic perspective. Besides, uncertainty is one of the most important obstacles in supplier selection. For the first, time in this paper, the idea of the algorithm " Knapsack " is used to select suppliers Moreover, an attempt has to be made to take the advantage of a simple numerical method for solving model .This is an innovation to resolve any ambiguity in choosing suppliers. This model has been tried in the suppliers selected in a competitive environment and according to all desired standards of quality and quantity to show the efficiency of the model, an industry sample has been uses.

Keywords: Knapsack, linear programming, supplier select, supply chain management.

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Authors: M. Tahani, G. Karimi

Abstract:

In this paper after reviewing some previous studies, in order to optimize the above knee prosthesis, beside the inertial properties a new controlling parameter is informed. This controlling parameter makes the prosthesis able to act as a multi behavior system when the amputee is opposing to different environments. This active prosthesis with the new controlling parameter can simplify the control of prosthesis and reduce the rate of energy consumption in comparison to recently presented similar prosthesis “Agonistantagonist active knee prosthesis". In this paper three models are generated, a passive, an active, and an optimized active prosthesis. Second order Taylor series is the numerical method in solution of the models equations and the optimization procedure is genetic algorithm. Modeling the prosthesis which comprises this new controlling parameter (SEP) during the swing phase represents acceptable results in comparison to natural behavior of shank. Reported results in this paper represent 3.3 degrees as the maximum deviation of models shank angle from the natural pattern. The natural gait pattern belongs to walking at the speed of 81 m/min.

Keywords: Above knee prosthesis, active controlling parameter, ballistic motion, swing phase.

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Authors: Mohammadreza Nezamirad, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

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In this study OpenFOAM 4.4.2 was used to investigate flow inside the coronary artery of the heart. This step is the first step of our future project, which is to include conjugate heat transfer of the heart with three main coronary arteries. Three different velocities were used as inlet boundary conditions to see the effect of velocity increase on velocity, pressure, and wall shear of the coronary artery. Also, three different fluids, namely the University of Wisconsin solution, gelatin, and blood was used to investigate the effect of different fluids on flow inside the coronary artery. A code based on Reynolds Stress Navier Stokes (RANS) equations was written and implemented with the real boundary condition that was calculated based on MRI images. In order to improve the accuracy of the current numerical scheme, hex dominant mesh is utilized. When the inlet velocity increases to 0.5 m/s, velocity, wall shear stress, and pressure increase at the narrower parts.

Keywords: CFD, heart, simulation, OpenFOAM.

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Authors: Ping Yuan, Mu-Sheng Chiang, Syu-Fang Liu, Shih-Bin Wang, Ming-Jun Kuo

Abstract:

This study investigates the electrical performance of a planar solid oxide fuel cell unit with cross-flow configuration when the fuel utilization gets higher and the fuel inlet flow are non-uniform. A software package in this study solves two-dimensional, simultaneous, partial differential equations of mass, energy, and electro-chemistry, without considering stack direction variation. The results show that the fuel utilization increases with a decrease in the molar flow rate, and the average current density decreases when the molar flow rate drops. In addition, non-uniform Pattern A will induce more severe happening of non-reaction area in the corner of the fuel exit and the air inlet. This non-reaction area deteriorates the average current density and then deteriorates the electrical performance to –7%.

Keywords: Performance, Solid oxide fuel cell, non-uniform, fuelutilization

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Authors: F.Ebrahimi, A.Rastgo

Abstract:

Analytical investigation of the free vibration behavior of circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the circular FG plate based on the classical plate theory (CPT) is presented in this paper. The material properties of the functionally graded substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and Numerical investigations are performed for FG plates with two surface-bonded piezoelectric layers. Emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from threedimensional finite element analyses.

Keywords: Circular plate, CPT, Functionally graded, Piezoelectric.

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Authors: Hassan M. Elkamchouchi, Samy H. Darwish, Yasser H. Elkamchouchi, M. E. Morsy

Abstract:

Methodology is suggested to design a linear rectangular microstrip array antenna based on Yagi antenna theory. The antenna with different directors' lengths as parasitic elements were designed, simulated, and analyzed using HFSS. The calculus and results illustrate the effectiveness of using specific parasitic elements to improve the directivity and gain for microstrip array antenna. The results have shown that the suggested methodology has the potential to be applied for improving the antenna performance. Maximum radiation intensity (Umax) of the order of 0.47w/st was recorded, directivity of 6.58dB, and gain better than 6.07dB are readily achievable for the antenna that working.

Keywords: Directivity, director, gain improvement, microstrip antenna.

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Authors: R. Mahjoub, K. Maghsoudi Mehraban

Abstract:

In recent years, solid oxide fuel cells have been used as one of the main technologies for the production of electrical energy with high-efficiency ratio, which is used hydrogen and other hydrocarbons as fuels. The fuel cell technology can be used either alone or in hybrid gas turbines systems. In this study, thermodynamics analysis for GT-SOFC hybrid system is developed, and then mass balance and exergy equations have been applied not only on the process but also on the individual components of the hybrid system, which enable us to estimate the thermal efficiency of the hybrid systems. Furthermore, various sources of irreversibility in the solid oxide fuel cell system are discussed, and modeling and parametric analyses like heat and pressure are carried out. This study enables us to consider the irreversible effects of solid oxide fuel cells, and also it leads to the specification of efficiency of the system accurately. Next in the study, both methane and hydrogen as a fuel for SOFC are used and implemented, and finally, our results are compared with other references.

Keywords: hybrid system, gas turbine, entropy and exergy analysis, irreversibility analysis

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Authors: Ping Du, Masaki Sagehashi, Akihiko Terada, Masaaki Hosomi

Abstract:

Prediction of benzene transport in soil and volatilization from soil to the atmosphere is important for the preservation of human health and management of contaminated soils. The adequacy of a simple numerical model, assuming two-phase diffusion and equilibrium of liquid/solid adsorption, was investigated by experimental data of benzene concentration in a flux chamber (with headspace) where Andosol and sand were filled. Adsorption experiment for liquid phase was performed to determine an adsorption coefficient. Furthermore, adequacy of vapor phase adsorption was also studied through two runs of experiment using sand with different water content. The results show that the model adequately predicted benzene transport and volatilization from Andosol and sand with water content of 14.0%. In addition, the experiment additionally revealed that vapor phase adsorption should be considered in diffusion model for sand with very low water content.

Keywords: Benzene; Transport Model, Adsorption, Soil Contaminant.

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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Authors: Norihan Md Arifin, Norfifah Bachok

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The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the internal heating, depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with internal heating are studied in detail.

Keywords: Linear stability, Marangoni convection, Internal Heatgeneration.

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Authors: Andrey D. Andreev, Ilona I. Iatcheva, Dimitar N. Karastoyanov, Rumena D. Stancheva

Abstract:

A study of electromagnetic flow meter is presented in the paper. Comparison has been made between the analytical and the numerical results by the use of FEM numerical analysis (Quick Field 5.6) for determining polarization voltage through the circle cross section of the polarization transducer. Exciting and geometrical parameters increasing its effectiveness has been examined. The aim is to obtain maximal output signal. The investigations include different variants of the magnetic flux density distribution around the tube: homogeneous field of magnitude Bm, linear distribution with maximal value Bm and trapezium distribution conserving the same exciting magnetic energy as the homogeneous field.

Keywords: Effectiveness, electromagnetic flow meter, finite element method, polarization voltage.

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

Abstract:

Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: 6-DOF robots, motion planning, trigonometric function, kinematic constraints

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Authors: A. M. Tahsini, S. T. Mousavi

Abstract:

The purpose of this paper is to elucidate the flow unsteady behavior for moving plug in convergent-divergent variable thrust nozzle. Compressible axisymmetric Navier-Stokes equations are used to study this physical phenomenon. Different velocities are set for plug to investigate the effect of plug movement on flow unsteadiness. Variation of mass flow rate and thrust are compared under two conditions: First, the plug is placed at different positions and flow is simulated to reach the steady state (quasi steady simulation) and second, the plug is moved with assigned velocity and flow simulation is coupled with plug movement (unsteady simulation). If plug speed is high enough and its movement time scale is at the same order of the flow time scale, variation of the mass flow rate and thrust level versus plug position demonstrate a vital discrepancy under the quasi steady and unsteady conditions. This phenomenon should be considered especially from response time viewpoints in thrusters design. 

Keywords: Nozzle, Numerical study, Unsteady, Variable thrust.

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Authors: Kai-Long Hsiao, BorMing Lee

Abstract:

In this study, an analysis has been performed for conjugate heat and mass transfer of a steady laminar boundary-layer mixed convection of magnetic hydrodynamic (MHD) flow with radiation effect of second grade subject to suction past a stretching sheet. Parameters E Nr, Gr, Gc, Ec and Sc represent the dominance of the viscoelastic fluid heat and mass transfer effect which have presented in governing equations, respectively. The similar transformation and the finite-difference method have been used to analyze the present problem. The conjugate heat and mass transfer results show that the non-Newtonian viscoelastic fluid has a better heat transfer effect than the Newtonian fluid. The free convection with a larger r G or c G has a good heat transfer effect better than a smaller r G or c G , and the radiative convection has a good heat transfer effect better than non-radiative convection.

Keywords: Conjugate heat and mass transfer, Radiation effect, Magnetic effect, Viscoelastic fluid, Viscous dissipation, Stretchingsheet.

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Authors: K. Kajsanthia, J. Wittayakun, S. Prayoonpokarach

Abstract:

An optical chemical sensing film based on immobilizing of 1,1′- diethyl 2,2′-cyanine (pseudocyanine iodide) in nafion film was developed for the determination of Fe(III). The sensing film was homogeneous, transparent, and mechanically stable. Decrease of the absorbance measured at 518 nm was observed when the sensing film was immersed in a solution of Fe(III). The optimum response of the sensing film to Fe(III) was obtained in a solution with pH 4.0. Linear calibration curve over an Fe(III) concentration range of 1-30 ppm with a limit of detection of 0.71 ppm was obtained. Cd(II) is the major interference. The sensing film exhibited good stability for 2 months and high reproducibility. The proposed method was applied for the determination of Fe(III) in water samples with satisfactory results.

Keywords: iron(III), _nafion, optical sensing film, pseudocyanine iodide

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Authors: Hyoup-Sang Yoon

Abstract:

The quality of video transmitted by mobile ad hoc networks (MANETs) can be influenced by several factors, including protocol layers; parameter settings of each protocol. In this paper, we are concerned with understanding the functional relationship between these influential factors and objective video quality in MANETs. We illustrate a systematic statistical design of experiments (DOE) strategy can be used to analyze MANET parameters and performance. Using a 2^k factorial design, we quantify the main and interactive effects of 7 factors on a response metric (i.e., mean opinion score (MOS) calculated by PSNR with Evalvid package) we then develop a first-order linear regression model between the influential factors and the performance metric.

Keywords: Evalvid, full factorial design, mobile ad hoc networks, ns-2.

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Authors: O. Tovide, N. Jahed, N. Mohammed, C. E. Sunday, H. R. Makelane, R. F. Ajayi, K. M. Molapo, A. Tsegaye, M. Masikini, S. Mailu, A. Baleg, T. Waryo, P. G. Baker, E. I. Iwuoha

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A graphenated–polyaniline (GR-PANI) nanocomposite sensor was constructed and used for the determination of anthracene. The direct electro-oxidation behavior of anthracene on the GR-PANI modified glassy carbon electrode (GCE) was used as the sensing principle. The results indicate thatthe response profile of the oxidation of anthracene on GR-PANI-modified GCE provides for the construction of sensor systems based onamperometric and potentiometric signal transductions. A dynamic linear range of 0.12- 100 µM anthracene and a detection limit of 0.044 µM anthracene were established for the sensor system.

Keywords: Electrochemical sensors, environmental pollutants, graphenated-polymers, polyaromatic hydrocarbon.

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Authors: T. Theodosiou, P. Polychronidou, A. G. Karasavvoglou

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The latest years the number of immigrants at Greece has increased dramatically. Their impact on the National Health System (NHS) has not been yet thoroughly investigated. This paper analyses the cost of immigrants to the NHS hospitals of the region of Eastern Macedonia and Thrace. The data are collected from 2005 to 2011 from five different hospitals and are analysed using linear mixed effects models in order to investigate the effects of nationality and year on the cost of hospitalization and treatment. The results show that generally the Greek nationality patients have a higher mean cost of hospitalization compared to the immigrants and that there is an increasing trend for the cost except for the year 2010.

Keywords: Cost, Eastern Macedonia, Thrace, immigrants, national health system.

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Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

Abstract:

The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Non-isothermal wedge, thermal radiation, nanofluid, magnetic field, Soret and Dufour effects.

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Authors: A. O. Ogunlela, B. Adelodun

Abstract:

Flood routing is used in estimating the travel time and attenuation of flood waves as they move downstream a river or channel. The routing procedure is usually classified as hydrologic or hydraulic. Hydraulic methods utilize the equations of continuity and motion. Kinematic routing, a hydraulic technique was used in routing Asa River at Ilorin. The river is of agricultural and industrial importance to Ilorin, the capital of Kwara State, Nigeria. This paper determines the kinematic parameters of kinematic wave velocity, time step, time required to traverse, weighting factor and change in length. Values obtained were 4.67 m/s, 19 secs, 21 secs, 0.75 and 100 m, respectively. These parameters adequately reflect the watershed and flow characteristics essential for the routing. The synthetic unit hydrograph was developed using the Natural Resources Conservation Service (NRCS) method. 24-hr 10yr, 25yr, 50yr and 100yr storm hydrographs were developed from the unit hydrograph using convolution procedures and the outflow hydrographs were obtained for each of 24-hr 10yr, 25yr, 50yr and 100yr indicating 0.11 m³/s, 0.10 m³/s, 0.10 m³/s and 0.10 m³/s attenuations respectively.

Keywords: Asa River, Kinematic parameters, Routing

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Authors: Pang Ying Han, Hiew Fu San, Ooi Shih Yin

Abstract:

Linearization of graph embedding has been emerged as an effective dimensionality reduction technique in pattern recognition. However, it may not be optimal for nonlinearly distributed real world data, such as face, due to its linear nature. So, a kernelization of graph embedding is proposed as a dimensionality reduction technique in face recognition. In order to further boost the recognition capability of the proposed technique, the Fisher-s criterion is opted in the objective function for better data discrimination. The proposed technique is able to characterize the underlying intra-class structure as well as the inter-class separability. Experimental results on FRGC database validate the effectiveness of the proposed technique as a feature descriptor.

Keywords: Face recognition, Fisher discriminant, graph embedding, kernelization.

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Authors: Tijani Delleji, Mourad Zribi, Ahmed Ben Hamida

Abstract:

This paper discusses EM algorithm and Bootstrap approach combination applied for the improvement of the satellite image fusion process. This novel satellite image fusion method based on estimation theory EM algorithm and reinforced by Bootstrap approach was successfully implemented and tested. The sensor images are firstly split by a Bayesian segmentation method to determine a joint region map for the fused image. Then, we use the EM algorithm in conjunction with the Bootstrap approach to develop the bootstrap EM fusion algorithm, hence producing the fused targeted image. We proposed in this research to estimate the statistical parameters from some iterative equations of the EM algorithm relying on a reference of representative Bootstrap samples of images. Sizes of those samples are determined from a new criterion called 'hybrid criterion'. Consequently, the obtained results of our work show that using the Bootstrap EM (BEM) in image fusion improve performances of estimated parameters which involve amelioration of the fused image quality; and reduce the computing time during the fusion process.

Keywords: Satellite image fusion, Bayesian segmentation, Bootstrap approach, EM algorithm.

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Authors: R. Chakib, A. Essadki, M. Cherkaoui

Abstract:

This paper proposes the study of a robust control of the doubly fed induction generator (DFIG) used in a wind energy production. The proposed control is based on the linear active disturbance rejection control (ADRC) and it is applied to the control currents rotor of the DFIG, the DC bus voltage and active and reactive power exchanged between the DFIG and the network. The system under study and the proposed control are simulated using MATLAB/SIMULINK.

Keywords: Doubly fed induction generator DFIG, Active disturbance rejection control ADRC, Vector control, MPPT, Extended state observer, back to back converter, Wind turbine.

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Authors: Heesung Lee, Joonkyung Sung, Euntai Kim

Abstract:

This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.

Keywords: Error correcting codes, genetic algorithm, non-linearpower optimization, Hamming code, Hsiao code.

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Authors: R. Saini, R. Lal

Abstract:

The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: Bilinear thickness, generalized differential quadrature (GDQ), non-homogeneous, Rectangular.

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Authors: Mohamed Amine Belmiloud, Nord Eddine Sad Chemloul

Abstract:

In this study, we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity ε and the varying of the Richardson number Ri on the variation of average Nusselt number Nu. The vertical walls of the cavity are differentially heated, the left wall is maintained at a uniform temperature higher than the right wall, and the two horizontal walls are adiabatic. The finite volume method is used for solving the dimensionless Governing Equations. Emissivity values used in this study are ranged between 0 and 1, the Richardson number in the range 0.1 to 10. The Rayleigh number is fixed to Ra=104 and the Prandtl number is maintained constant Pr=0.71. Streamlines, isothermal lines and the average Nusselt number are presented according to the surface emissivity. The results of this study show that the Richardson number Ri and emissivity ε affect the average Nusselt number.

Keywords: Numerical study, mixed convection, square cavity, wall emissivity, lid-driven.

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Authors: Wint Thida Zaw, Thinn Thu Naing

Abstract:

One of the essential sectors of Myanmar economy is agriculture which is sensitive to climate variation. The most important climatic element which impacts on agriculture sector is rainfall. Thus rainfall prediction becomes an important issue in agriculture country. Multi variables polynomial regression (MPR) provides an effective way to describe complex nonlinear input output relationships so that an outcome variable can be predicted from the other or others. In this paper, the modeling of monthly rainfall prediction over Myanmar is described in detail by applying the polynomial regression equation. The proposed model results are compared to the results produced by multiple linear regression model (MLR). Experiments indicate that the prediction model based on MPR has higher accuracy than using MLR.

Keywords: Polynomial Regression, Rainfall Forecasting, Statistical forecasting.

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Authors: Md. Nasir Uddin, M. A. Alim, M. M. K. Chowdhury

Abstract:

This analysis is performed to study the momentum, heat and mass transfer characteristics of MHD mixed convective flow past inclined porous plate in porous medium, including the effect of fluid suction. The fluid is assumed to be steady, incompressible and dense. Similarity solution is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically by using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. Numerical results for the various types of parameters entering into the problem for velocity, temperature and concentration distributions are presented graphically and analyzed thereafter. Moreover, expressions for the skin-friction, heat transfer co-efficient and mass transfer co-efficient are discussed with graphs against streamwise distance for various governing parameters.

Keywords: Fluid suction, heat and mass transfer, inclined porous plate, MHD, mixed convection, porous medium.

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Authors: Durga C. Dalal, Swapan K. Pandit

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In this paper, a numerical study has been made to analyze the transient 2-D flows of a viscous incompressible fluid through channels with forward or backward constriction. Problems addressed include flow through sudden contraction and sudden expansion channel geometries with rounded and increasingly sharp reentrant corner. In both the cases, numerical results are presented for the separation and reattachment points, streamlines, vorticity and flow patterns. A fourth order accurate compact scheme has been employed to efficiently capture steady state solutions of the governing equations. It appears from our study that sharpness of the throat in the channel is one of the important parameters to control the strength and size of the separation zone without modifying the general flow patterns. The comparison between the two cases shows that the upstream geometry plays a significant role on vortex growth dynamics.

Keywords: Forward and backward constriction, HOC scheme, Incompressible viscous flows, Separation and reattachment points.

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Authors: Antonio Carlos Marques Alvim, Fernando Carvalho da Silva, Aquilino Senra Martinez

Abstract:

For a quick and accurate calculation of spatial neutron distribution in nuclear power reactors 3D nodal codes are usually used aiming at solving the neutron diffusion equation for a given reactor core geometry and material composition. These codes use a second order polynomial to represent the transverse leakage term. In this work, a nodal method based on the well known nodal expansion method (NEM), developed at COPPE, making use of this polynomial expansion was modified to treat the transverse leakage term for the external surfaces of peripheral reflector nodes. The proposed method was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of this modified treatment of peripheral nodes for practical purposes in PWR reactors.

Keywords: Transverse leakage, nodal expansion method, power density, PWR reactors

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