Search results for: Faddeev equations

Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Gyo Woo Lee, Man Young Kim

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The blocked-off formulations for the analysis of radiative heat transfer are formulated and examined in order to find the solutions in a two-dimensional complex enclosure. The final discretization equations using the step scheme for spatial differencing practice are proposed with the additional source term to incorporate the blocked-off procedure. After introducing the implementation for inactive region into the general discretization equation, three different problems are examined to find the performance of the solution methods.

Keywords: radiative heat transfer, Finite Volume Method (FVM), blocked-off solution procedure, body-fitted coordinate

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Authors: Waleed Al-Nuaimy, Luke Anastassiou, Manjinder Kainth

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As the process of teaching has evolved with the advent of new technologies over the ages, so has the process of learning. Educators have perpetually found themselves on the lookout for new technology-enhanced methods of teaching in order to increase learning efficiency and decrease ever expanding workloads. Shortly after the invention of the internet, web-based learning started to pick up in the late 1990s and educators quickly found that the process of providing learning material and marking assignments could change thanks to the connectivity offered by the internet. With the creation of early web-based virtual learning environments (VLEs) such as SPIDER and Blackboard, it soon became apparent that VLEs resulted in higher reported computer self-efficacy among students, but at the cost of students being less satisfied with the learning process . It may be argued that the impersonal nature of VLEs, and their limited functionality may have been the leading factors contributing to this reported dissatisfaction. To this day, often faced with the prospects of assigning colossal engineering cohorts their homework and assessments, educators may frequently choose optimally curated assessment formats, such as multiple-choice quizzes and numerical answer input boxes, so that automated grading software embedded in the VLEs can save time and mark student submissions instantaneously. A crucial skill that is meant to be learnt during most science and engineering undergraduate degrees is gaining the confidence in using, solving and deriving mathematical equations. Equations underpin a significant portion of the topics taught in many STEM subjects, and it is in homework assignments and assessments that this understanding is tested. It is not hard to see that this can become challenging if the majority of assignment formats students are engaging with are multiple-choice questions, and educators end up with a reduced perspective of their students’ ability to manipulate equations. Artificial intelligence (AI) has in recent times been shown to be an important consideration for many technologies. In our paper, we explore the use of new AI based software designed to work in conjunction with current VLEs. Using our experience with the software, we discuss its potential to solve a selection of problems ranging from impersonality to the reduction of educator workloads by speeding up the marking process. We examine the software’s potential to increase learning efficiency through its features which claim to allow more customized and higher-quality feedback. We investigate the usability of features allowing students to input equation derivations in a range of different forms, and discuss relevant observations associated with these input methods. Furthermore, we make ethical considerations and discuss potential drawbacks to the software, including the extent to which optical character recognition (OCR) could play a part in the perpetuation of errors and create disagreements between student intent and their submitted assignment answers. It is the intention of the authors that this study will be useful as an example of the implementation of AI in a practical assessment scenario insofar as serving as a springboard for further considerations and studies that utilise AI in the setting and marking of science and engineering assignments.

Keywords: engineering education, assessment, artificial intelligence, optical character recognition (OCR)

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Authors: Mohammed A. Hajeeh

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This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: repairable models, imperfect, availability, exponential distribution

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Authors: Mohammadreza DaqiqShirazi, Rouhollah Torabi, Alireza Riasi, Ahmad Nourbakhsh

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In this paper, the flow in a sidewall gap of an impeller which belongs to a centrifugal pump is studied using numerical method. The flow in sidewall gap forms internal leakage and is the source of “disk friction loss” which is the most important cause of reduced efficiency in low specific speed centrifugal pumps. Simulation is done using CFX software and a high quality mesh, therefore the modeling error has been reduced. Navier-Stokes equations have been solved for this domain. In order to predict the turbulence effects the SST model has been employed.

Keywords: numerical study, centrifugal pumps, disk friction loss, sidewall gap

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Authors: Jin Zhi

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This study focuses on a green screen keying method developed especially for film visual effects. There are a series of ways of using existing tools for creating mattes from green or blue screen plates. However, it is still a time-consuming process, and the results vary especially when it comes to retaining tiny details, such as hair and fur. This paper introduces an alternative concept and method for retaining edge details of characters on a green screen plate, also, a number of connected mathematical equations are explored. At the end of this study, a simplified process of applying this method in real productions is also introduced.

Keywords: green screen, visual effects, compositing, matte

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Authors: Habibis Saleh, Ishak Hashim

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Combined surface tension and natural convection heat transfer in an open cavity is studied numerically in this article. The cavity is filled with water-{Cu} nanofluids. The left wall is kept at low temperature, the right wall at high temperature and the bottom and top walls are adiabatic. The top free surface is assumed to be flat and non--deformable. Finite difference method is applied to solve the dimensionless governing equations. It is found that the insignificant effect of adding the nanoparticles were obtained about $Ma_{bf}=250$.

Keywords: natural convection, marangoni convection, nanofluids, square open cavity

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Authors: E. Arcos, E. Bautista, F. Méndez

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In this work, a scaling analysis of the liquefaction phenomena is presented. The characteristic scales are obtained by balancing term by term of the well-known partial dynamics governing equations, (U − P). From the above, the order of magnitude of the horizontal displacement is very smaller compared with the vertical displacement and therefore the governing equation is only a function of the dependent vertical variables. The U − P approximation is reduced and presented in its dimensionless version. This scaling analysis can be used to obtain analytical solutions of the liquefaction phenomena under the action of the water waves.

Keywords: approximation U-P, porous seabed, scaling analysis, water waves

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Authors: Mujde Turkkan, Nurkan Yagiz

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The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: active suspension system, air suspension, bus model, sliding mode control

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Authors: D. S. Nagesh, G. L. Datta

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In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases, design of experiments technique to postulate multiple linear regression equations have been used. Nowadays, Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: smaw, genetic algorithm, bead geometry, optimization/inverse mapping

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Authors: D. S. Nagesh, G. L. Datta

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In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases design of experiments technique to postulate multiple linear regression equations have been used. Nowadays Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: SMAW, genetic algorithm, bead geometry, optimization/inverse mapping

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Authors: Larry Wang

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The aim of this paper is to demonstrate how an online homework system is integrated in teaching and learning mathematics and how it improves the student success rates in some gateway mathematics courses. WeBWork provided by the Mathematical Association of America is adopted as the online homework system. During the period of 2010-2015, the system was implemented in classes of precalculus, calculus, probability and statistics, discrete mathematics, linear algebra, and differential equations. As a result, the passing rates of the sections with WeBWork are well above other sections without WeBWork (about 7-10% higher). The paper also shows how the WeBWork system was used.

Keywords: gateway mathematics, online grading, pass rate, WeBWorK

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Authors: Yasaman Esfandiari

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Mechanical engineering has always dealt with amplification of the input power in power trains. One of the ways to achieve this goal is to use gears to change the amplitude and direction of the torque and the speed. However, the gears should be optimally designed to best achieve these objectives. In this study, helical gear systems are optimized to achieve maximum power. Material selection, space restriction, available facilities for manufacturing, the probability of tooth breakage, and tooth wear are taken into account and governing equations are derived. Finally, a Matlab code was generated to solve the optimization problem and the results are verified.

Keywords: design, gears, Matlab, optimization

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Authors: A. Bekbaev, M. Dzhamanbaev, R. Abitaeva, A. Karbozova, G. Nabyeva

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In this paper, the regression dependence of dancing intensity from wind speed and length of span was established due to the statistic data obtained from multi-year observations on line wires dancing accumulated by power systems of Kazakhstan and the Russian Federation. The lower and upper limitations of the equations parameters were estimated, as well as the adequacy of the regression model. The constructed model will be used in research of dancing phenomena for the development of methods and means of protection against dancing and for zoning plan of the territories of line wire dancing.

Keywords: power lines, line wire dancing, dancing intensity, regression equation, dancing area intensity

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Authors: Ese Urhie, Olabisi Popoola, Obindah Gershon

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Several policies and programs initiated to address the challenge of unemployment in Nigeria seem to be inadequate. The desired structural transformation which is expected to absorb the excess labour in the economy is yet to be achieved. The agricultural sector accounts for almost half of the labour force with very low productivity. This could partly explain why the much anticipated structural transformation has not been achieved. A major reason for the low productivity is the fact that the production process is predominantly based on the use of traditional tools. In view of the underdeveloped nature of the agricultural sector, Nigeria still has huge potentials for productivity enhancement through modern technology. Aside from productivity enhancement, modern agriculture also stimulates both backward and forward linkages that promote investment and thus generate employment. Contrary to the apprehension usually expressed by many stake-holders about the adoption of modern technology by labour-abundant less-developed countries, this study showed that though there will be job loss initially, the reverse will be the case in the long-run. The outcome of this study will enhance the understanding of all stakeholders in the sector and also encourage them to adopt modern techniques of farming. It will also aid policy formulation at both sectoral and national levels. The recursive model and analysis adopted in the study is useful because it exhibits a unilateral cause-and-effect relationship which most simultaneous equation models do not. It enables the structural equations to be ordered in such a way that the first equation includes only predetermined variables on the right-hand side, while the solution for the final endogenous variable is completely determined by all equations of the system. The study examines the transmission channels and effect of modern agriculture on agricultural productivity and employment growth in Nigeria, via its forward and backward linkages. Using time series data spanning 1980 to 2014, the result of the analyses shows that: (i) a significant and positive relationship between agricultural productivity growth and modern agriculture; (ii) a significant and negative relationship between export price index and agricultural productivity growth; (iii) a significant and positive relationship between export and investment; and (iv) a significant and positive relationship between investment and employment growth. The unbalanced growth theory will be a good strategy to adopt by developing countries such as Nigeria.

Keywords: employment, modern agriculture, productivity, recursive model

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Authors: Diego Liberati

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Standard molecular modeling is traditionally done through Schroedinger equations via the help of powerful tools helping to manage them atom by atom, often needing High Performance Computing. Here, a full portfolio of new tools, conjugating statistical inference in the so called eXplainable Artificial Intelligence framework (in the form of Machine Learning of understandable rules) to the more traditional modeling and simulation control theory of mixed dynamic logic hybrid processes, is offered as quite a general purpose even if making an example to a popular chemical physics set of problems.

Keywords: understandable rules ML, k-means, PCA, PieceWise Affine Auto Regression with eXogenous input

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Authors: H. S. Kang

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Coupled electrical and optical model for conversion of electrical energy into coherent optical energy for transmitter-receiver link by solid state device is presented. Probability distribution for travelling laser beam switching time intervals and the number of switchings in the time interval is obtained. Selector function mapping is employed to regulate optical data transmission speed. It is established that regulated laser transmission from PhotoActive Laser transmitter follows principal of invariance. This considerably simplifies design of PhotoActive Laser Transmission networks.

Keywords: computational mathematics, finite difference Markov chain methods, sequence spaces, singularly perturbed differential equations

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Authors: Kachout Mnaouer, Bel Hadj Tahar Jamel, Choubani Fethi

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In this paper, three electric equivalent models to evaluate crosstalk between three-conductor transmission lines are proposed. First, electric equivalent models for three-conductor transmission lines are presented. Secondly, rigorous equations to calculate the per-unit length inductive and capacitive parameters are developed. These models allow us to calculate crosstalk between conductors. Finally, to validate the presented models, we compare the theoretical results with simulation data. Obtained results show that proposed models can be used to predict crosstalk performance.

Keywords: near-end crosstalk, inductive parameter, L, Π, T models

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Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

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In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the numerical solution of the Navier-Stokes equations and the vortex panel method. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method

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Authors: Si Abdallah Mayouf

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In this work, the effects of the wavy surface on free convection heat transfer boundary layer flow between two parallel wavy plates have been studied numerically. The two plates are considered at a constant temperature. The equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm. The important parameters in this problem are the amplitude of the wavy surfaces and the distance between the two wavy plates. Results are presented as velocity profiles, temperature profiles and local Nusselt number according to the important parameters.

Keywords: free convection, wavy surface, parallel plates, fluid dynamics

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Authors: L. Hammadi, D. Boukhaloua

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In this study, a numerical model was developed to predict cavitation phenomena around a NACA0009 profile. The equations of the Rayleigh-Plesset and modified Rayleigh-Plesset are used to modeling the cavitation by bubble around a NACA0009 profile. The study shows that the distributions of pressures around extrados and intrados of profile for angle of incidence equal zero are the same. The study also shows that the increase in the angle of incidence makes it possible to differentiate the pressures on the intrados and the extrados.

Keywords: cavitation, NACA0009 profile, flow, pressure coefficient

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Authors: Ayubi Wirara, Ardya Suryadinata

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Improper application of the RSA algorithm scheme can cause vulnerability to attacks. The attack utilizes the relationship between broadcast messages sent to the user with some fixed polynomial functions that belong to each user. Scheme attacks carried out by applying the Chinese Remainder Theorem to obtain a general polynomial equation with the same modulus. The formation of the general polynomial becomes a first step to get back the original message. Furthermore, to solve these equations can use Coppersmith's theorem.

Keywords: RSA algorithm, broadcast message, Chinese Remainder Theorem, Coppersmith’s theorem

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Authors: Daniel Y. Abebe, Jaehyouk Choi

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The objective of this paper is to investigate, through an analytical study, the behavior of both stiffened and un-stiffened removable shear link with perforated web considering different number and size of web openings. Removable shear link with perforated web is a novel shear link beam proposed to be used in eccentrically braced frame (EBF). The proposed link overcomes the difficulties during construction slab due to less cross-sectional areas of the link to control the plastic deformation on the conventional EBF with removable shear link. Finite element analyses were conducted under both cyclic and monotonic loading and from the results obtained design equations are developed.

Keywords: eccentrically braced frame, removable shear link, perforated web, non-linear FE analysis

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Authors: Alemayehu Mengesha, Solomon Belay

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We determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength. Currently, we are doing the numerical analysis of this work.

Keywords: astrophysical, magnetic field, instability, MHD, wavelength, viscosity

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Authors: Aliakbar Sayadi, Thomas Neitzert, Charles Clifton

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The hydration process of a green concrete with differences on fly ash and the poly-lactic acid ratio was investigated using electrical resistivity measurement. The results show that the hydration process of proposed concrete was significantly different with concrete containing petroleum aggregate. Moreover, a microstructure analysis corresponding to each hydration stage is conducted with scanning microscope for ploy-lactic acid and expanded polystyrene concrete. In addition, specific equations using the variables of this study were developed to understand and predict the relationship between setting time and resistivity development of proposed concrete containing eco-friendly aggregate.

Keywords: green concrete, SEM, hydration mechanism, eco-friendly aggregate

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Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

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The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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Authors: Zahra Neffah, Henda Kahalerras

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A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.

Keywords: chemical reaction, heat and mass transfer, oscillating flow, porous channel

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