Search results for: ahmed amin mousa

Authors: Ahmed M. Mansour, Ali M. El-Sawy, Ahmed T Sayed

Abstract:

Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving insights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

Keywords: Logarithms, log2, floor, iterative, CORDIC, Taylor series.

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Authors: F. Amin, S. Feizi

Abstract:

This paper describes the complex nature of organizational culture and its role in telecom organizations. To set the stage for culture change, the literature is reviewed for perspective on the role and function of culture in organizations. Organizational the­orists as well as business consultants report that a strong organizational culture is essential for success because the shared assumptions, values and culture of an organization influence the behavior of its individual members.

Keywords: Component, Telecommunication, Management, Cultural, Transformation.

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Authors: Ahmed Hossam_ ElDin, Ahmed Farag, Ibrahim Madi., Hanaa Karawia

Abstract:

In our modern society electricity is vital to our health, safety, comfort and well-being. While our daily use of electricity is often taken for granted, public concern has arisen about potential adverse health effects from electric and magnetic – electromagnetic – fields (EMFs) produced by our use of electricity. This paper aims to compare between the measured magnetic field values and the simulated models for the indoor medium to low voltage (MV/LV) distribution substations. To calculate the magnetic flux density in the substations, interactive software SUBCALC is used which is based on closed form solution of the Biot-Savart law with 3D conductor model. The comparison between the measured values and the simulated models was acceptable. However there were some discrepancies, as expected, may be due to the current variation during measurements.

Keywords: Distribution substation, magnetic field, measurement, simulation.

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Authors: Amin Chegenizadeh, Hamid Nikraz

Abstract:

Soil mechanics is a traditional course in any university. Management of lab classes is one of the main issues to deliver a proper outline. In Curtin University, different methods applied to check the efficiency of these methods. One of them was mainly rely on demonstration and the other one mainly on involving students in running tests. Comparison between these delivery methods also are outlined in summary section. The recommendation also made that the more satisfaction is reachable while the students engaged.

Keywords: Soil, Geomechanic, Laboratory.

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Authors: Mousa Mojarrad, Amir Masoud Rahmani, Mehrab Mohebi

Abstract:

Detection, feature extraction and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes and the high dimensionality of articulated body models and also the important field in Image, Signal and Vision Computing in recent years. In this paper, four types of people in 2D dimension image will be tested and proposed. The system will extract the size and the advantage of them (such as: tall fat, short fat, tall thin and short thin) from image. Fat and thin, according to their result from the human body that has been extract from image, will be obtained. Also the system extract every size of human body such as length, width and shown them in output.

Keywords: Analysis of Image Processing, Canny Edge Detection, Human Body Recognition, Measurement, Pose Estimation, 2D Human Dimension.

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Authors: Mohamed. A. Shrud, Ahmad H. Kharaz, Ahmed. S. Ashur, Ahmed Faris, Mustafa Benamar

Abstract:

This paper will focus on modeling, analysis and simulation of a 42V/14V dc/dc converter based architecture. This architecture is considered to be technically a viable solution for automotive dual-voltage power system for passenger car in the near further. An interleaved dc/dc converter system is chosen for the automotive converter topology due to its advantages regarding filter reduction, dynamic response, and power management. Presented herein, is a model based on one kilowatt interleaved six-phase buck converter designed to operate in a Discontinuous Conduction Mode (DCM). The control strategy of the converter is based on a voltagemode- controlled Pulse Width Modulation (PWM) with a Proportional-Integral-Derivative (PID). The effectiveness of the interleaved step-down converter is verified through simulation results using control-oriented simulator, MatLab/Simulink.

Keywords: Automotive, dc-to-dc power modules, design, interleaved, Matlab\Simulink and PID control.

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Authors: Moustafa Ahmed, Ahmed Bakry, Safwat W. Z. Mahmoud

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We model and simulate the combined effect of fiber dispersion and frequency chirp of a directly modulated high-speed laser diode on the figures of merit of a non-amplified 40-Gbps optical fiber link. We consider both the return to zero (RZ) and non-return to zero (NRZ) patterns of the pseudorandom modulation bits. The performance of the fiber communication system is assessed by the fiber-length limitation due to the fiber dispersion. We study the influence of replacing standard single-mode fibers by non-zero dispersion-shifted fibers on the maximum fiber length and evaluate the associated power penalty. We introduce new dispersion tolerances for 1-dB power penalty of the RZ and NRZ 40-Gbps optical fiber links.

Keywords: Bit error rate, dispersion, frequency chirp, fiber communications, semiconductor laser.

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Authors: Yousra Zakaria Ahmed, Ahmed El Gendy, Salah El Haggar

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In this paper, our methodology to assess sustainability of wastewater treatment technologies in Egypt is presented. The preliminary list of factors to be considered, as well as their ranking listed. The factors include, but are not limited to pollutants removal efficiency and energy consumption under the environmental dimension, construction cost, operation and maintenance costs and required land area cost under the economic dimension and public acceptance, noise and generating job opportunities for local residents. This methodology is intended to be a user-friendly screening tool to support the decision making process when investigating different wastewater treatment technologies in Egypt. Based on the research work results presented in this paper, it can be generally concluded that the categorization of some of the social and environmental aspects of sustainability is subjective and highly dependent on the local conditions and researchers’ background.

Keywords: Sustainability, wastewater treatment, sustainability assessment, Egypt.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

Keywords: Electrically conducting elastico-viscous fluid, symmetry solution, Homotopy perturbation method, Padé approximation, 4th order Runge–Kutta, Maple

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Authors: Elham Alaee, Mousa Shamsi, Hossein Ahmadi, Soroosh Nazem, Mohammadhossein Sedaaghi

Abstract:

Human face has a fundamental role in the appearance of individuals. So the importance of facial surgeries is undeniable. Thus, there is a need for the appropriate and accurate facial skin segmentation in order to extract different features. Since Fuzzy CMeans (FCM) clustering algorithm doesn’t work appropriately for noisy images and outliers, in this paper we exploit Possibilistic CMeans (PCM) algorithm in order to segment the facial skin. For this purpose, first, we convert facial images from RGB to YCbCr color space. To evaluate performance of the proposed algorithm, the database of Sahand University of Technology, Tabriz, Iran was used. In order to have a better understanding from the proposed algorithm; FCM and Expectation-Maximization (EM) algorithms are also used for facial skin segmentation. The proposed method shows better results than the other segmentation methods. Results include misclassification error (0.032) and the region’s area error (0.045) for the proposed algorithm.

Keywords: Facial image, segmentation, PCM, FCM, skin error, facial surgery.

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Authors: Moustafa Ahmed, Ahmed Bakry, Fumio Koyama

Abstract:

We report on the use of strong external optical feedback to enhance the modulation response of semiconductor lasers over a frequency passband around modulation frequencies higher than 60 GHz. We show that this modulation enhancement is a type of photon-photon resonance (PPR) of oscillating modes in the external cavity formed between the laser and the external reflector. The study is based on a time-delay rate equation model that takes into account both the strong feedback and multiple reflections in the external cavity. We examine the harmonic and intermodulation distortions associated with single and two-tone modulations in the mm-wave band of the resonant modulation. We show that compared with solitary lasers modulated around the carrier-photon resonance frequency, the present mm-wave modulated signal has lower distortions.

Keywords: Distortion, intensity modulation, optical feedback, semiconductor laser.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab

Abstract:

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.

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Authors: Metwally Abdel Aziz Ahmed, Ahmed Shaban Abdel Hay Gabr, Inas Mohamed Saleh

Abstract:

The main objective of structural design is to ensure safety and functional performance requirements of a structural system for its target reliability levels. In this study, the reliability index for the reinforcement concrete slender columns with rectangular cross section is studied. The variable parameters studied include the loads, the concrete compressive strength, the steel yield strength, the dimensions of concrete cross-section, the reinforcement ratio, and the location of steel placement. Risk analysis program was used to perform the analytical study. The effect of load eccentricity on the reliability index of reinforced concrete slender column was studied and presented. The results of this study indicate that the good quality control improve the performance of slender reinforced columns through increasing the reliability index β.

Keywords: Reliability, reinforced concrete, safety, slender column.

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Authors: Bernardo Cedano, Ahmed H. Eltom, Bob Hay, Jim Glass, Raga Ahmed

Abstract:

The deployment of smart grid devices such as smart meters and smart switches (SS) supported by a reliable and fast communications system makes automated distribution possible, and thus, provides great benefits to electric power consumers and providers alike. However, more research is needed before the full utility of smart switch data is realized. This paper presents new automated switching techniques using SS within the electric power grid. A concise background of the SS is provided, and operational examples are shown. Organization and presentation of data obtained from SS are shown in the context of the future goal of total automation of the distribution network. The description of application techniques, the examples of success with SS, and the vision outlined in this paper serve to motivate future research pertinent to disturbance analysis automation.

Keywords: Disturbance automation, electric power grid, smart grid, smart switch.

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Authors: Mohamed T. Sorour, Mohamed A. Abdellatif, Ahmed A. Ramadan, Ahmed A. Abo-Ismail

Abstract:

This paper describes the development of an autonomous robot for painting the interior walls of buildings. The robot consists of a painting arm with an end effector roller that scans the walls vertically and a mobile platform to give horizontal feed to paint the whole area of the wall. The painting arm has a planar twolink mechanism with two joints. Joints are driven from a stepping motor through a ball screw-nut mechanism. Four ultrasonic sensors are attached to the mobile platform and used to maintain a certain distance from the facing wall and to avoid collision with side walls. When settled on adjusted distance from the wall, the controller starts the painting process autonomously. Simplicity, relatively low weight and short painting time were considered in our design. Different modules constituting the robot have been separately tested then integrated. Experiments have shown successfulness of the robot in its intended tasks.

Keywords: Automated roller painting, Construction robots, Mobile robots, service robots, two link planar manipulator

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Authors: A. S. Mousa, R. I. Rajab, A. A. Pinto

Abstract:

An envy behavioral game theoretical model with two types of homogeneous players is considered in this paper. The strategy space of each type of players is a discrete set with only two alternatives. The preferences of each type of players is given by a discrete utility function. All envy strategies that form Nash equilibria and the corresponding envy Nash domains for each type of players have been characterized. We use geometry to construct two dimensional envy tilings where the horizontal axis reflects the preference for players of type one, while the vertical axis reflects the preference for the players of type two. The influence of the envy behavior parameters on the Cartesian position of the equilibria has been studied, and in each envy tiling we determine the envy Nash equilibria. We observe that there are 1024 combinatorial classes of envy tilings generated from envy chromosomes: 256 of them are being structurally stable while 768 are with bifurcation. Finally, some conditions for the disparate envy Nash equilibria are stated.

Keywords: Game theory, Nash Equilibrium, envy Nash Equilibrium, geometric tilings, bifurcation thresholds.

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Authors: A. Elsayed Ahmed, A. Hafez, A. N. Ouda, H. Eldin Hussein Ahmed, H. Mohamed Abd-Elkader

Abstract:

Unmanned aircraft systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. . In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized, and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end the model is checked by matching between the behavior of the states of the nonlinear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: Equations of motion, linearization, modeling, nonlinear model, UAV.

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Authors: T. M. Mousa-Balabel, M. A. Salama

Abstract:

The effect of shearing date on behaviors and performances of 20 pregnant Rahmani ewes was evaluated in four groups (5each). Ewes were shorn at 70, 100 and 130 days of pregnancy in the first three groups respectively, while the fourth group was maintained unshorn as a control. Some behavioral and physiological data related to ewes in addition, blood cortisol level were recorded. Results revealed a significant increase in the frequencies of comfort and eating behaviors, respiratory rate, pulse rate, lamb birth weight and blood cortisol level in early and mid pregnancy shorn ewes. Also, a slight increase in pregnancy period was observed for those ewes. On the other hand, social behaviors, and core temperature were not affected by shearing. These results conclude that prenatal shearing (early and mid-pregnancy) of ewes increases the frequencies of comfort and eating behaviors, and improves the survival rates of lambs by increasing their birth weights.

Keywords: behavior, blood cortisol, pregnant rahmani ewes, shearing.

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Authors: Ahmed N. Shmroukh, Ahmed Hamza H. Ali, Ali K. Abel-Rahman

Abstract:

Adsorption refrigeration working pair is a vital and is the main component in the adsorption refrigeration machine. Therefore the development key is laying on the adsorption pair that leads to the improvement of the adsorption refrigeration machine. In this study the state-of-the-art in the application of the adsorption refrigeration working pairs in both classical and modern adsorption pairs are presented, compared and summarized. It is found that the maximum adsorption capacity for the classical working pairs was 0.259kg/kg for activated carbon/methanol and that for the modern working pairs was 2kg/kg for maxsorb III/R-134a. The study concluded that, the performances of the adsorption working pairs of adsorption cooling systems are still need further investigations as well as developing adsorption pairs having higher sorption capacity with low or no impact on environmental, to build compact, efficient, reliable and long life performance adsorption chillier. Also, future researches need to be focused on designing the adsorption system that provide efficient heating and cooling for the adsorbent materials through distributing the adsorbent material over heat exchanger surface, to allow good heat and mass transfer between the adsorbent and the refrigerant.

Keywords: Adsorption, Adsorbent/Adsorbate Pairs, Refrigeration.

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Authors: Ahlam Elkilani, Bayan Elsheikh Ali, Rasha Abu Romman, Amjed Al-mousa, Belal Sababha

Abstract:

The amount of energy the world uses doubles every 20 years. Green homes play an important role in reducing the residential energy demand. This paper presents a platform that is intended to learn the behavior of home residents and build a profile about their habits and actions. The proposed resident aware home controller intervenes in the operation of home appliances in order to save energy without compromising the convenience of the residents. The presented platform can be used to simulate the actions and movements happening inside a home. The paper includes several optimization techniques that are meant to save energy in the home. In addition, several test scenarios are presented that show how the controller works. Moreover, this paper shows the computed actual savings when each of the presented techniques is implemented in a typical home. The test scenarios have validated that the techniques developed are capable of effectively saving energy at homes.

Keywords: Green Home, Resident Aware, Resident Profile, Activity Learning, Machine Learning.

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Authors: Raed Abendeh, Mousa Bani Baker, Zaydoun Abu Salem, Heham Ahmad

Abstract:

The using of waste materials in the construction industry can reduce the dependence on the natural aggregates which are going at the end to deplete. The glass waste is generated in a huge amount which can make one of its disposals in concrete industry effective not only as a green solution but also as an advantage to enhance the performance of mechanical properties and durability of concrete. This article reports the performance of concrete specimens containing different percentages of milled glass waste as a partial replacement of cement (Powder), when they are subject to cycles of freezing and thawing. The tests were conducted on 75-mm cubes and 75 x 75 x 300-mm prisms. Compressive strength based on laboratory testing and non-destructive ultrasonic pulse velocity test were performed during the action of freezing-thawing cycles (F/T). The results revealed that the incorporation of glass waste in concrete mixtures is not only feasible but also showed generally better strength and durability performance than control concrete mixture. It may be said that the recycling of waste glass in concrete mixes is not only a disposal way, but also it can be an exploitation in concrete industry.

Keywords: Durability, glass waste, freeze-thaw cycles, nondestructive test.

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Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

Thermal radiation plays a very important role in the heat transfer combination through the various components of the SOFC fuel cell operating at high temperatures. Lattice Boltzmann method is used for treating conduction-radiation heat transfer in the electrolyte. The thermal radiation heat transfer is coupled to the overall energy conservation equations through the divergence of the local radiative flux. The equation of energy in one dimension is numerically resolved by using the Lattice Boltzmann method. A computing program (FORTRAN) is developed locally for this purpose in order to obtain fields of temperature in every element of the cell. The parameters investigated are: functioning temperature, cell voltages and electrolyte thickness. The results show that the radiation effect increases with increasing the electrolyte thickness, also increases with increasing the functioning temperature and decreases with the increase of the voltage of the cell.

Keywords: SOFC, lattice Boltzmann method, conduction, radiation, planar medium.

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Authors: Pradip Peter Dey, Bhaskar Raj Sinha, Mohammad Amin, Hassan Badkoobehi

Abstract:

Mathematical, graphical and intuitive models are often constructed in the development process of computational systems. The Unified Modeling Language (UML) is one of the most popular modeling languages used by practicing software engineers. This paper critically examines UML models and suggests an augmented use case view with the addition of new constructs for modeling software. It also shows how a use case diagram can be enhanced. The improved modeling constructs are presented with examples for clarifying important design and implementation issues.

Keywords: Software architecture, software design, Unified Modeling Language (UML), user interface.

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Authors: Amin Hajizadeh, Ehsan Hajizadeh

Abstract:

This paper presents a multi-objective formulation for optimal siting and sizing of distributed generation (DG) resources in distribution systems in order to minimize the cost of power losses and energy not supplied. The implemented technique is based on particle swarm optimization (PSO) and weight method that employed to obtain the best compromise between these costs. Simulation results on 33-bus distribution test system are presented to demonstrate the effectiveness of the proposed procedure.

Keywords: Distributed generation, distribution networks, particle swarm optimization, reliability, weight method

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Authors: S. N. Moghaddas Tafreshi, S. M. Amin Ghotbi

Abstract:

This paper presents a numerical study for investigating the effectiveness of geocell reinforcement in reducing pressure and settlement over EPS geofoam blocks in road embankments. A 3-D FEM model of soil and geofoam was created in ABAQUS, and geocell was also modeled realistically using membrane elements. The accuracy of the model was tested by comparing its results with previous works. Sensitivity analyses showed that reinforcing the soil cover with geocell has a significant influence on the reduction of imposed stresses over geofoam and consequently decreasing its deformation.

Keywords: EPS geofoam, road embankments, geocell, reinforcement, lightweight fill.

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Authors: Nahid A. Ali, Salma H. Ahmed, ElShazali A. Mohamed, Isam A. Mohamed Ahmed, Elfadil E.Babiker

Abstract:

The effect of cross linking of the protein isolates of three legumes with the microbial enzyme transglutaminase (EC 2.3.2.13) on the functional properties at different NaCl concentration was studied. The reduction in the total free amino groups (OD340) of the polymerized protein showed that TGase treatment cross-linking the protein subunit of each legume. The solubility of the protein polymer of each legume was greatly improved at high concentration of NaCl. At 1.2 M NaCl the solubility of the native legumes protein was significantly decreased but after polymerization slightly improved. Cross linked proteins were less turbid on heating to higher temperature as compared to native proteins and the temperature at which the protein turns turbid also increased in the polymerized proteins. The emulsifying and foaming properties of the protein polymer were greatly improved at all concentrations of NaCl for all legumes.

Keywords: Functional properties, Legumes, Protein isolate, NaCl, Transglutaminase.

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Authors: F. Amin, A. H. Jahangir, H. Rasifard

Abstract:

With the widespread growth of applications of Wireless Sensor Networks (WSNs), the need for reliable security mechanisms these networks has increased manifold. Many security solutions have been proposed in the domain of WSN so far. These solutions are usually based on well-known cryptographic algorithms. In this paper, we have made an effort to survey well known security issues in WSNs and study the behavior of WSN nodes that perform public key cryptographic operations. We evaluate time and power consumption of public key cryptography algorithm for signature and key management by simulation.

Keywords: Wireless Sensor Networks, Security, Public Key Cryptography, Key Management.

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Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

This paper examines the natural convection in a square enclosure filled with a water-Al₂O₃ nanofluid and is subjected to a magnetic field. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra=10³ to 10⁶, Hartmann number varied from Ha=0 to 90, phase deviation (γ=0, π/4, π/2, 3π/4 and π) and the solid volume fraction of the nanoparticles between Ø = 0 and 6%. The results show that the heat transfer rate increases with an increase of the Rayleigh number but it decreases with an increase of the Hartmann number. For γ=π/2 and Ra=10⁵ the magnetic field augments the effect of nanoparticles. At Ha=0, the greatest effects of nanoparticles are obtained at γ = 0 and π/4 for Ra=10⁴ and 10⁵ respectively.

 

Keywords: Lattice Boltzmann Method, magnetic field, Natural convection, nanofluid, Sinusoidal temperature distribution.

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Authors: Ali Khaleel Kareem, Shian Gao, Ahmed Qasim Ahmed

Abstract:

A numerical investigation of unsteady mixed convection heat transfer in a 3D moving top wall enclosure, which has a central rotating cylinder and uses either artificial roughness on the bottom hot plate or smooth bottom hot plate to study the heat transfer enhancement, is completed for fixed circular cylinder, and anticlockwise and clockwise rotational speeds, -1 ≤ Ω ≤ 1, at Reynolds number of 5000. The top lid-driven wall was cooled, while the other remaining walls that completed obstructed cubic were kept insulated and motionless. A standard k-ε model of Unsteady Reynolds-Averaged Navier-Stokes (URANS) method is involved to deal with turbulent flow. It has been clearly noted that artificial roughness can strongly control the thermal fields and fluid flow patterns. Ultimately, the heat transfer rate has been dramatically increased by involving artificial roughness on the heated bottom wall in the presence of rotating cylinder.

Keywords: Artificial roughness, Lid-driven cavity, Mixed convection heat transfer, Rotating cylinder, URANS method.

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Authors: M. Zahid Hossain, M. Ashraful Amin

Abstract:

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.

Keywords: Convex hull, Approximation algorithm, Computational geometry, Linear time.

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