Search results for: parallel plate

Authors: A. Satour, F. Boubenider, R. Halimi, A. Badidibouda

Abstract:

Sandwich plates are finding an increasing range of application in the aircraft industry. The inspection of honeycomb composite structure by conventional ultrasonic technique is complex and very time consuming. The present study demonstrates a technique using guided Lamb waves at low frequencies to predict de-bond defects in aluminum skin-honeycomb core sandwich structure used in aeronautics. The numerical method was investigated for drawing the dispersion and displacement curves of ultrasonic Lamb wave propagated in Aluminum plate. An experimental study was carried out to check the theoretical prediction. The detection of unsticking between the skin and the core was tested by the two first modes for a low frequency. It was found that A0 mode is more sensitive to delamination defect compared to S0 mode.

Keywords: Damage detection, delamination, guided waves, Sandwich structure.

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Authors: Homayon Ahmad Panahi, Hossein Sid Kalal, Atyeh Rahimi

Abstract:

A high performance thin layer chromatography system (HPTLC) for the separation of vitamin B2 and B12 has been developed. The separation was successfully using a solvent system of methanol, water, ammonia 7.3.1 (V/V) as mobile phase on HPTLC plates impregnated with boric acid. The effect of other mobile phases on the separation of vitamins was also examined. The method is based on different behavior of investigated compounds in impregnated TLC plates with different amount of boric acid. The Rf values of vitamin B2 and B12 are considered on non impregnated and impregnated silica gel HPTLC plate with boric acid. The effect of boric acid in the mobile phase and on HPTLC plates on the RF values of the vitamins has also been studied.

Keywords: High performance thin layer chromatography, HPTLC, Vitamin B2, Vitamin B12, Separation.

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Authors: T. K. Das, N. Senapatil, R. K. Dhal

Abstract:

An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.

Keywords: MHD, Mixed convective, Elastic-viscous incompressible, rotational, heat transfer, mass transfer, suction and injection.

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Authors: M. Invigorito, G. Elia, M. Panelli

Abstract:

Hybrid propulsion combines beneficial properties of both solid and liquid rockets, such as multiple restarts, throttability as well as simplicity and reduced costs. A nitrous oxide (N₂O)/paraffin-based hybrid rocket engine demonstrator is currently under development at the Italian Aerospace Research Center (CIRA) within the national research program HYPROB, funded by the Italian Ministry of Research. Nitrous oxide belongs to the class of self-pressurizing propellants that exhibit a high vapor pressure at standard ambient temperature. This peculiar feature makes those fluids very attractive for space rocket applications because it avoids the use of complex pressurization systems, leading to great benefits in terms of weight savings and reliability. To avoid feed-system-coupled instabilities, the phase change is required to occur through the injectors. In this regard, the oxidizer is stored in liquid condition while target chamber pressures are designed to lie below vapor pressure. The consequent cavitation and flash vaporization constitute a remarkably complex phenomenology that arises great modelling challenges. Thus, it is clear that the design of the injection system is fundamental for the full exploitation of hybrid rocket engine throttability. The Analytical Hierarchy Process has been used to select the injection architecture as best compromise among different design criteria such as functionality, technology innovation and cost. The impossibility to use engineering simplified relations for the dimensioning of the injectors led to the needs of applying a numerical approach based on OpenFOAM^®. The numerical tool has been validated with selected experimental data from literature. Quantitative, as well as qualitative comparisons are performed in terms of mass flow rate and pressure drop across the injector for several operating conditions. The results show satisfactory agreement with the experimental data. Modeling assumptions, together with their impact on numerical predictions are discussed in the paper. Once assessed the reliability of the numerical tool, the injection plate has been designed and sized to guarantee the required amount of oxidizer in the combustion chamber and therefore to assure high combustion efficiency. To this purpose, the plate has been designed with multiple injectors whose number and diameter have been selected in order to reach the requested mass flow rate for the two operating conditions of maximum and minimum thrust. The overall design has been finally verified through three-dimensional computations in cavitating non-reacting conditions and it has been verified that the proposed design solution is able to guarantee the requested values of mass flow rates.

Keywords: Hybrid rocket, injection system design, OpenFOAM®, cavitation

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Authors: Y. Kobayashi, T. Shirochi, Y. Yasuda, T. Morita

Abstract:

This paper describes a method for preparing metallic Cu nanoparticles in aqueous solution, and a metal-metal bonding technique using the Cu particles.Preparation of the Cu particle colloid solution was performed in water at room temperature in air using a copper source (0.01 M Cu(NO₃)₂), a reducing reagent (0.2 - 1.0 M hydrazine), and stabilizers (0.5×10^-3 M citric acid and 5.0×10^-3 M cetyltrimethylammonium bromide). The metallic Cu nanoparticles with sizes of ca. 60nm were prepared at all the hydrazine concentrations examined. A stage and a plate of metallic Cu were successfully bonded under annealing at 400^oC and pressurizing at 1.2 MPa for 5min in H₂ gas with help of the metallic Cu particles. A shear strength required for separating the bonded Cu substrates reached the maximum value at a hydrazine concentration of 0.8M, and it decreased beyond the concentration. Consequently, the largest shear strength of 22.9 MPa was achieved at the 0.8 M hydrazine concentration.

Keywords: Aqueous solution, Bonding, Colloid, Copper, Nanoparticle.

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Authors: H. E. Michail, V. N. Thanasoulis, G. A. Panagiotakopoulos, A. P. Kakarountas, C. E. Goutis

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In this paper an efficient implementation of Ripemd- 160 hash function is presented. Hash functions are a special family of cryptographic algorithms, which is used in technological applications with requirements for security, confidentiality and validity. Applications like PKI, IPSec, DSA, MAC-s incorporate hash functions and are used widely today. The Ripemd-160 is emanated from the necessity for existence of very strong algorithms in cryptanalysis. The proposed hardware implementation can be synthesized easily for a variety of FPGA and ASIC technologies. Simulation results, using commercial tools, verified the efficiency of the implementation in terms of performance and throughput. Special care has been taken so that the proposed implementation doesn-t introduce extra design complexity; while in parallel functionality was kept to the required levels.

Keywords: Hardware implementation, hash functions, Ripemd-160, security.

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Authors: W. Hasan, H. Farhat, A. Alhilo, L. Tamimi

Abstract:

Oil in water (O/W) emulsions are utilized extensively for cooling and lubricating cutting tools during parts machining. A robust Lattice Boltzmann (LBM) thermal-surfactants model, which provides a useful platform for exploring complex emulsions’ characteristics under variety of flow conditions, is used here for the study of the fluid behavior during conventional tools cooling. The transient thermal capabilities of the model are employed for simulating the effects of the flow conditions of O/W emulsions on the cooling of cutting tools. The model results show that the temperature outcome is slightly affected by reversing the direction of upper plate (workpiece). On the other hand, an important increase in effective viscosity is seen which supports better lubrication during the work.

Keywords: Hybrid lattice Boltzmann method, Gunstensen model, thermal, surfactant-covered droplet, Marangoni stress.

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Authors: B. Ghosh, H. Sahoo, K. K. Mondal

Abstract:

Propagation of arbitrary amplitude nonlinear Alfven waves has been investigated in low but finite β electron-positron-ion plasma including full ion dynamics. Using Sagdeev pseudopotential method an energy integral equation has been derived. The Sagdeev potential has been calculated for different plasma parameters and it has been shown that inclusion of ion parallel motion along the magnetic field changes the nature of slow shear Alfven wave solitons from dip type to hump type. The effects of positron concentration, plasma-β and obliqueness of the wave propagation on the solitary wave structure have also been examined.

Keywords: Alfven waves, Sagdeev potential, Solitary waves.

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Authors: D. Gåsvaer, J. von Axelson

Abstract:

Considering today-s increasing speed of change, radical and innovative improvement - Kaikaku, is a necessity parallel to continuous incremental improvement - Kaizen, especially for SME-s in order to attain the competitive edge needed to be profitable. During 2011, a qualitative single case study with the objective of realizing a kaikaku in production has been conducted. The case study was run as a one year project using a collaborative approach including both researchers and company representatives. The case study was conducted with the purpose of gaining further knowledge about kaikaku realization as well as its implications. The empirical results provide insights about the great productivity results achieved by applying a specific kaikaku realization approach. However, it also sheds light on the difficulty and contradiction of combining innovation management and production system development.

Keywords: Kaikaku, Radical improvement, manufacturing, innovation capability

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Authors: Srinath Shetty K., Shivashankar R., Rashmi P. Shetty

Abstract:

Earth reinforcing techniques have become useful and economical to solve problems related to difficult grounds and provide satisfactory foundation performance. In this context, this paper uses radial basis function neural network (RBFNN) for predicting the bearing pressure of strip footing on reinforced granular bed overlying weak soil. The inputs for the neural network models included plate width, thickness of granular bed and number of layers of reinforcements, settlement ratio, water content, dry density, cohesion and angle of friction. The results indicated that RBFNN model exhibited more than 84 % prediction accuracy, thereby demonstrating its application in a geotechnical problem.

Keywords: Bearing pressure, granular bed, radial basis function neural network, strip footing.

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Authors: Pradeep Kumar K

Abstract:

We propose the use of magneto-optic Kerr effect (MOKE) to realize single-qubit quantum gates. We consider longitudinal and polar MOKE in reflection geometry in which the magnetic field is parallel to both the plane of incidence and surface of the film. MOKE couples incident TE and TM polarized photons and the Hamiltonian that represents this interaction is isomorphic to that of a canonical two-level quantum system. By varying the phase and amplitude of the magnetic field, we can realize Hadamard, NOT, and arbitrary phase-shift single-qubit quantum gates. The principal advantage is operation with magnetically non-transparent materials.

Keywords: Quantum computing, qubit, magneto-optic kerr effect (MOKE), magneto-optical interactions, continuous variables.

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Authors: Mohammad Reza Ghasemi, Ali Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimization, Neural Networks, RBFNN.

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Authors: Salah Aljbour, Hiroshi Yamada, Tomohiko Tagawa

Abstract:

A microchannel with two inlets and two outlets was tested as a potential reactor to carry out two-phase catalytic phase transfer reaction with phase separation at the exit of the microchannel. The catalytic phase transfer reaction between benzyl chloride and sodium sulfide was chosen as a model reaction. The effect of operational time on the conversion was studied. By utilizing a multiphase parallel flow inside the microchannel reactor with the aid of a guideline structure, the catalytic phase reaction followed by phase separation could be ensured. The organic phase could be separated completely from one exit and part of the aqueous phase was separated purely and could be reused with slightly affecting the catalytic phase transfer reaction.

Keywords: Green engineering, microchannel reactor, multiphase reaction, process intensification.

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Susmita Ghosh, Bhaskar Bhowmick

Abstract:

Market is an important factor for start-ups to look into during decision-making in product development and related areas. Emerging country markets are more uncertain in terms of information availability and institutional supports. The literature review of market uncertainty reveals the need for identifying factors representing the market uncertainty. This paper identifies factors for market uncertainty using Exploratory Factor Analysis (EFA) and confirmed the number of factor retention using an alternative factor retention criterion ‘Parallel Analysis’. 500 entrepreneurs, engaged in start-ups from all over India participated in the study. This paper concludes with the factor structure of ‘market uncertainty’ having dimensions of uncertainty in industry orientation, uncertainty in customer orientation and uncertainty in marketing orientation.

Keywords: Uncertainty, market, orientation, competitor, demand.

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Authors: Archana S. Nanoty, A. R. Chudasama

Abstract:

Three-phase induction machines are today a standard for industrial electrical drives. Cost, reliability, robustness and maintenance free operation are among the reasons these machines are replacing dc drive systems. The development of power electronics and signal processing systems has eliminated one of the greatest disadvantages of such ac systems, which is the issue of control. With modern techniques of field oriented vector control, the task of variable speed control of induction machines is no longer a disadvantage. The need to increase system performance, particularly when facing limits on the power ratings of power supplies and semiconductors, motivates the use of phase number other than three, In this paper a novel scheme of connecting two, three phase induction motors in parallel fed by two inverters; viz. VSI and CSI and their vector control is presented.

Keywords: Field oriented control, multiphase induction motor, power electronics converter.

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Authors: Stepan Kuchar, Martin Golasowski, Radim Vavrik, Michal Podhoranyi, Boris Sir, Jan Martinovic

Abstract:

The main goal of this article is to describe the online flood monitoring and prediction system Floreon+ primarily developed for the Moravian-Silesian region in the Czech Republic and the basic process it uses for running automatic rainfall-runoff and hydrodynamic simulations along with their calibration and uncertainty modeling. It takes a long time to execute such process sequentially, which is not acceptable in the online scenario, so the use of a high performance computing environment is proposed for all parts of the process to shorten their duration. Finally, a case study on the Ostravice River catchment is presented that shows actual durations and their gain from the parallel implementation.

Keywords: Flood prediction process, High performance computing, Online flood prediction system, Parallelization.

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Authors: Dimitri Perrin, Heather J. Ruskin, Martin Crane

Abstract:

We report on the development of a model to understand why the range of experience with respect to HIV infection is so diverse, especially with respect to the latency period. To investigate this, an agent-based approach is used to extract highlevel behaviour which cannot be described analytically from the set of interaction rules at the cellular level. A network of independent matrices mimics the chain of lymph nodes. Dealing with massively multi-agent systems requires major computational effort. However, parallelisation methods are a natural consequence and advantage of the multi-agent approach and, using the MPI library, are here implemented, tested and optimized. Our current focus is on the various implementations of the data transfer across the network. Three communications strategies are proposed and tested, showing that the most efficient approach is communication based on the natural lymph-network connectivity.

Keywords: HIV, Immune modelling, MPI, Parallelisation.

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Authors: A.Mosavi

Abstract:

A novel methodology has been used to design an evaporator coil of a refrigerant. The methodology used is through a complete Computer Aided Design /Computer Aided Engineering approach, by means of a Computational Fluid Dynamic/Finite Element Analysis model which is executed many times for the thermal-fluid exploration of several designs' configuration by an commercial optimizer. Hence the design is carried out automatically by parallel computations, with an optimization package taking the decisions rather than the design engineer. The engineer instead takes decision regarding the physical settings and initializing of the computational models to employ, the number and the extension of the geometrical parameters of the coil fins and the optimization tools to be employed. The final design of the coil geometry found to be better than the initial design.

Keywords: Multi-objective shape optimization, Heat Transfer, multi-physics structures, modeFRONTIER

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Authors: Yashvir Singh, Mayank Joshi

Abstract:

A lateral trench-gate power metal-oxide-semiconductor on 4H-SiC is proposed. The device consists of two separate trenches in which two gates are placed on both sides of P-body region resulting two parallel channels. Enhanced current conduction and reduced-surface-field effect in the structure provide substantial improvement in the device performance. Using two dimensional simulations, the performance of proposed device is evaluated and compare of with that of the conventional device for same cell pitch. It is demonstrated that the proposed structure provides two times higher output current, 11% decrease in threshold voltage, 70% improvement in transconductance, 70% reduction in specific ON-resistance, 52% increase in breakdown voltage, and nearly eight time improvement in figure-of-merit over the conventional device.

Keywords: 4H-SiC, lateral, trench-gate, power MOSFET.

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Authors: Yousef Amer, Mehdi Moayyedian, Zeinab Hajiabolhasani, Lida Moayyedian

Abstract:

Moulded parts contribute to more than 70% of components in products. However, common defects particularly in plastic injection moulding exist such as: warpage, shrinkage, sink marks, and weld lines. In this paper Taguchi experimental design methods are applied to reduce the warpage defect of thin plate Acrylonitrile Butadiene Styrene (ABS) and are demonstrated in two levels; namely, orthogonal arrays of Taguchi and the Analysis of Variance (ANOVA). Eight trials have been run in which the optimal parameters that can minimize the warpage defect in factorial experiment are obtained. The results obtained from ANOVA approach analysis with respect to those derived from MINITAB illustrate the most significant factors which may cause warpage in injection moulding process. Moreover, ANOVA approach in comparison with other approaches like S/N ratio is more accurate and with the interaction of factors it is possible to achieve higher and the better outcomes.

Keywords: Analysis of variance, ANOVA, plastic injection mould, Taguchi methods, Warpage.

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Authors: Praveen Saraswat, Vipin Kumar Verma, Rudraman Singh

Abstract:

The unsteady transient free convection flow of an incompressible dissipative viscous fluid between parallel plates at different distances have been investigated under porous medium. Due to presence of heat flux under the influence of uniform transverse magnetic field the velocity distribution and the temperature distribution, is shown graphically. Since exact solution is not possible so we find parametrical solution by perturbation technique. The result is shown in graph for different parameters. We notice that heat generation effects fluid velocity keeping in which of free convection which cools.

Keywords: Transient, Convection, MHD, Viscous, Porous.

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Authors: Dhahri Maher, Aouinet Hana

Abstract:

The presence of bubbles in the boundary layer introduces corrections into the log law, which must be taken into account. In this work, a logarithmic wall law was presented for bubbly two phase flows. The wall law presented in this work was based on the postulation of additional turbulent viscosity associated with bubble wakes in the boundary layer. The presented wall law contained empirical constant accounting both for shear induced turbulence interaction and for non-linearity of bubble. This constant was deduced from experimental data. The wall friction prediction achieved with the wall law was compared to the experimental data, in the case of a turbulent boundary layer developing on a vertical flat plate in the presence of millimetric bubbles. A very good agreement between experimental and numerical wall friction prediction was verified. The agreement was especially noticeable for the low void fraction when bubble induced turbulence plays a significant role.

Keywords: Bubbly flows, log law, boundary layer.

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Authors: Yanhui Zhang, Wenyu Yang

Abstract:

One of the difficulties of the vibration-based damage identification methods is the nonuniqueness of the results of damage identification. The different damage locations and severity may cause the identical response signal, which is even more severe for detection of the multiple damage. This paper proposes a new strategy for damage detection to avoid this nonuniqueness. This strategy firstly determines the approximates damage area based on the statistical pattern recognition method using the dynamic strain signal measured by the distributed fiber Bragg grating, and then accurately evaluates the damage information based on the Bayesian model updating method using the experimental modal data. The stochastic simulation method is then used to compute the high-dimensional integral in the Bayesian problem. Finally, an experiment of the plate structure, simulating one part of mechanical structure, is used to verify the effectiveness of this approach.

Keywords: Bayesian method, damage detection, fiber Bragg grating, structural health monitoring.

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Authors: Anastasia Katsamaki, Nikolaos Bilalis, Vassilis Dedoussis

Abstract:

This work proposes a set of actions to assist redesign procedure in existing products of Electric and Electronic Equipment (EEE). The aim is to improve their environmental behavior after their withdrawal in the End-of-Life (EOL) phase. In the beginning data collection takes place. Then follows selection and implementation of the optimal EOL Treatment Strategy (EOL_TS) and its results- evaluation concerning the environment. In parallel, product design characteristics that can be altered are selected based on their significance for the environment in the EOL stage. All results from the previous stages are combined and possible redesign actions are formulated for further examination and afterwards configuration in the design stage. The applied method to perform these tasks is Lean Thinking (LT). At the end, results concerning the application of the proposed method on a distribution transformer are presented.

Keywords: End-of-life treatment, Lean thinking, WEEE

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Authors: S. Shaaban, T. McNamara, S. Hudson

Abstract:

This paper reports on the performance of deliberately unbalanced, reliable, non-automated and assembly lines that merge, whose workstations differ in terms of their mean operation times. Simulations are carried out on 5- and 8-station lines with 1, 2 and 4 buffer capacity units, % degrees of line imbalance of 2, 5 and 12, and 24 different patterns of means imbalance. Data on two performance measures, namely throughput and average buffer level were gathered, statistically analysed and compared to a merging balanced line counterpart. It was found that the best configurations are a balanced line arrangement and a monotone decreasing order for each of the parallel merging lines, with the first generally resulting in a lower throughput and the second leading to a lower average buffer level than those of a balanced line.

Keywords: Average buffer level, merging lines, simulation, throughput, unbalanced.

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Authors: Dalvir Singh, Somnath Chattopadhyaya

Abstract:

During welding or flame cutting of metals, the prediction of heat affected zone (HAZ) is critical. There is need to develop a simple mathematical model to calculate the temperature variation in HAZ and derivative analysis can be used for this purpose. This study presents analytical solution for heat transfer through conduction in mild steel plate. The homogeneous and nonhomogeneous boundary conditions are single variables. The full field analytical solutions of temperature measurement, subjected to local heating source, are derived first by method of separation of variables followed with the experimental visualization using infrared imaging. Based on the present work, it is suggested that appropriate heat input characteristics controls the temperature distribution in and around HAZ.

Keywords: Conduction Heat Transfer, Heat Affected Zone (HAZ), Infra-Red Imaging, Numerical Method, Orthogonal Function, Plasma Arc Cutting, Separation of Variables, Temperature Measurement.

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Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: Se Kyung Oh, Ary Bachtiar Krishna Putra, Soo Whan Ahn

Abstract:

A numerical study on the turbulent flow and heat transfer characteristics in the rectangular channel with different types of baffles is carried out. The inclined baffles have the width of 19.8 cm, the square diamond type hole having one side length of 2.55 cm, and the inclination angle of 5o. Reynolds number is varied between 23,000 and 57,000. The SST turbulence model is applied in the calculation. The validity of the numerical results is examined by the experimental data. The numerical results of the flow field depict that the flow patterns around the different baffle type are entirely different and these significantly affect the local heat transfer characteristics. The heat transfer and friction factor characteristics are significantly affected by the perforation density of the baffle plate. It is found that the heat transfer enhancement of baffle type II (3 hole baffle) has the best values.

Keywords: Turbulent flow, rectangular channel, inclined baffle, heat transfer, friction factor.

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

Abstract:

This paper aims to analysis the behavior of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Currentvoltage curves are particularly analyzed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: Electrostatic precipitator, current-voltage characteristics, Least Squares method, electric field, magnetic field.

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