Search results for: waves equations

Authors: Hesham A. Elkaranshawy, Amr Abdelrazek, Hosam Ezzat

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This paper analyzes a single point rough collision in three dimensional rigid-multibody systems. A set of nonlinear different equations describing the progress and outcome of the impact are obtained. Specifically in case of the tangential, referred to as sliding, component of impact velocity is of great importance. Numerical methods are used to solve this problem. In this work, all these possible sliding behaviors during impact are identified, conditions leading to each behavior are specified, and an appropriate numerical procedure is suggested. A case of a four-degrees-of-freedom spatial robot that collides with its environment is investigated. The phase portrait of the tangential velocity, which presents the flow trajectories for different initial conditions, is calculated. Using the coefficient of friction as a control parameter, few phase portraits are drawn, each for a specific value of this coefficient. In addition, the bifurcation associated with the variation of this coefficient will be investigated.

Keywords: friction impact, three-dimensional rigid multibody systems, sliding velocity, nonlinear ordinary differential equations, phase portrait

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Authors: Olga Santesteban, Glorisa Canino, Hector R. Bird, Cristiane S. Duarte

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Objective: To address whether harsh discipline is associated with disruptive behavior disorders (DBD) in Puerto Rican children over time. Background: Both cross-sectional and longitudinal studies report that rates of DBD vary by gender, age and other demographics, being more frequent among boys, later in life and among those who live in urban areas. Also, the literature supports the direct, positive association between harsh discipline and externalizing behaviors. Nevertheless, scholars have underscored the important role of race and ethnicity in understanding discipline effects on children. The impact of harsh discipline in a Puerto Rican population remains to be studied. Methods: Sample: This is a secondary analysis of the Boricua Youth Study which assessed yearly (3 times) Puerto Rican children aged 5-15 in two different sites: San Juan (Puerto Rico) and the South Bronx (NY), N=2951. Participants that did not have scores of harsh discipline in the 3 waves were excluded for this analysis (N=2091). Main Measures: a) Harsh Discipline (Parent report) was measured using 6 items from the “Parental Discipline Scale” that measures various forms of punishment, including physical and verbal abuse, and withholding affection; b) Disruptive Behavior Disorder (Parent report): Parent version of the Diagnostic Interview Schedule for Children-IV (DISC-IV) was used to asses children’s conduct disorders; c) Demographic factors: Child gender, child age, family income, marital status; d) Parental factors: parental psychopathology, parental monitoring, familism, parent support; e) Children characteristics: Controlling for any diagnostic at wave 1 (internalizing or externalizing). Data Analysis: Logistic regression was carried out relating the likelihood of DBD to harsh discipline along waves controlling for potential confounders as demographics, child and parent characteristics. Results: There were no significant differences in harsh discipline by site in wave 1 and wave 2 but there was a significant difference in wave 3. Also, there were no significant differences in DBD by site in wave 1 and wave 2 but there was a significant difference in wave 3. There was a significant difference of discipline by gender and age in all the waves. We calculated unadjusted (OR) and adjusted (AOD) and 95% confidence intervals (95%CI) showing the relation between harsh discipline at wave 1 and the presence of child disruptive behavior disorder at wave 3 for both South Bronx and Puerto Rico. There was an association between harsh discipline and the likelihood of having DBD in The Bronx (AOR=1.76; 95%CI=1.13-2.74, p.013) and in Puerto Rico (AOR=2.17; 95%CI=1.28-3.67, p.004) having controlled for demographic, parental and individual factors. Conclusions: Context may be an important differential factor shaping the potential risk of harsh discipline toward DBD for Puerto Rican children.

Keywords: disruptive behavior disorders, harsh discipline, puerto rican, psychological education

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Authors: Naghmeh Zamani, Ashkan Pourkand, David Grow

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This paper presents the design and mechanical model of a hybrid impedance/admittance haptic device optimized for applications, like bone drilling, spinal awl probe use, and other surgical techniques were high force is required in the tool-axial direction, and low impedance is needed in all other directions. The performance levels required cannot be satisfied by existing, off-the-shelf haptic devices. This design may allow critical improvements in simulator fidelity for surgery training. The device consists primarily of two low-mass (carbon fiber) plates with a rod passing through them. Collectively, the device provides 6 DOF. The rod slides through a bushing in the top plate and it is connected to the bottom plate with a universal joint, constrained to move in only 2 DOF, allowing axial torque display the user’s hand. The two parallel plates are actuated and located by means of four cables pulled by motors. The forward kinematic equations are derived to ensure that the plates orientation remains constant. The corresponding equations are solved using the Newton-Raphson method. The static force/torque equations are also presented. Finally, we present the predicted distribution of location error, cables velocity, cable tension, force and torque for the device. These results and preliminary hardware fabrication indicate that this design may provide a revolutionary approach for haptic display of many surgical procedures by means of an architecture that allows arbitrary workspace scaling. Scaling of the height and width can be scaled arbitrarily.

Keywords: cable direct driven robot, haptics, parallel plates, bone drilling

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Authors: A. D. Rao, Sachiko Mohanty

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The Internal Waves (IWs) are generated by the flow of barotropic tide over the rapidly varying and steep topographic features like continental shelf slope, subsurface ridges, and the seamounts, etc. The IWs of the tidal frequency are generally known as internal tides. These waves have a significant influence on the vertical density and hence causes mixing in the region. Such waves are also important in submarine acoustics, underwater navigation, offshore structures, ocean mixing and biogeochemical processes, etc. over the shelf-slope region. The seasonal variability of internal tides in the Bay of Bengal with special emphasis on its energetics is examined by using three-dimensional MITgcm model. The numerical simulations are performed for different periods covering August-September, 2013; November-December, 2013 and March-April, 2014 representing monsoon, post-monsoon and pre-monsoon seasons respectively during which high temporal resolution in-situ data sets are available. The model is initially validated through the spectral estimates of density and the baroclinic velocities. From the estimates, it is inferred that the internal tides associated with semi-diurnal frequency are more dominant in both observations and model simulations for November-December and March-April. However, in August, the estimate is found to be maximum near-inertial frequency at all the available depths. The observed vertical structure of the baroclinic velocities and its magnitude are found to be well captured by the model. EOF analysis is performed to decompose the zonal and meridional baroclinic tidal currents into different vertical modes. The analysis suggests that about 70-80% of the total variance comes from Mode-1 semi-diurnal internal tide in both observations as well as in the model simulations. The first three modes are sufficient to describe most of the variability for semidiurnal internal tides, as they represent 90-95% of the total variance for all the seasons. The phase speed, group speed, and wavelength are found to be maximum for post-monsoon season compared to other two seasons. The model simulation suggests that the internal tide is generated all along the shelf-slope regions and propagate away from the generation sites in all the months. The model simulated energy dissipation rate infers that its maximum occurs at the generation sites and hence the local mixing due to internal tide is maximum at these sites. The spatial distribution of available potential energy is found to be maximum in November (20kg/m²) in northern BoB and minimum in August (14kg/m²). The detailed energy budget calculation are made for all the seasons and results are analysed.

Keywords: available potential energy, baroclinic energy flux, internal tides, Bay of Bengal

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Authors: Nini Johana Marín Rodríguez, William Fernando Oquendo Patino

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In this work, we model a coupled system where we explore the effects of steady and random behavior on a linear system like an extension of the classic Strogatz model. This is exemplified by modeling a couple love dynamics as a linear system of two coupled differential equations and studying its stability for four types of lovers chosen as CC='Cautious- Cautious', OO='Only other feelings', OP='Opposites' and RR='Romeo the Robot'. We explore the effects of, first, introducing saturation, and second, adding a random variation to one of the CC-type lover, which will shape his character by trying to model how its variability influences the dynamics between love and hate in couple in a long run relationship. This work could also be useful to model other kind of systems where interactions can be modeled as linear systems with external or internal random influence. We found the final results are not easy to predict and a strong dependence on initial conditions appear, which a signature of chaos.

Keywords: differential equations, dynamical systems, linear system, love dynamics

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Authors: Anuar Ishak

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The characteristics of stagnation point flow of a nanofluid towards a stretching/shrinking sheet are investigated. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.

Keywords: dual solutions, heat transfer, forced convection, nanofluid, stability analysis

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

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Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.

Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique

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Authors: A. T. Kuda, J. J. Dayya, A. Jimoh

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This paper investigates the fault detection and Isolation technique of measurement data sets from a three tank system using analytical model-based temporal redundancy which is based on residual generation using parity equations/space approach. It further briefly outlines other approaches of model-based residual generation. The basic idea of parity space residual generation in temporal redundancy is dynamic relationship between sensor outputs and actuator inputs (input-output model). These residuals where then used to detect whether or not the system is faulty and indicate the location of the fault when it is faulty. The method obtains good results by detecting and isolating faults from the considered data sets measurements generated from the system.

Keywords: fault detection, fault isolation, disturbing influences, system failure, parity equation/relation, structured parity equations

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: P. C. Tewari, Parveen Kumar

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The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.

Keywords: availability modeling, Markov process, milling system, rice milling plant

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Authors: Yohannes Yirga, Daniel Tesfay

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The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, and chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: heat and mass transfer, magnetohydrodynamics, nanofluid, fluid dynamics

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Authors: Quznetsov Gunn

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In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

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Authors: Shrikant Ghadage

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Study of shock waves generated in the Scramjet engine is typically restricted to pressure, temperature, density, entropy and Mach number variation across the shock wave. The present work discusses the impact of inlet shock wave angles on the specific impulse of the Scramjet engine. A mathematical analysis has done for the isentropic hypersonic flow of air flowing through a Scramjet with hydrogen fuel at an altitude of 30 km. Analysis has been done in order to get optimum shock wave angle to achieve maximum impulse. Since external drag has excluded from the analysis, the losses due to friction are not considered for the present analysis. When Mach number of the airflow at the entry of the nozzle reaches unity, then that flow is choked. This condition puts limitations on increasing the inlet shock wave angle. As inlet shock wave angle increases, speed of the flow entering into the nozzle decreases, which results in an increase in the specific impulse of the engine. When the speed of the flow at the entry of the nozzle reduces below sonic speed, then there is no further increase in the specific impulse of the engine. Here the Conclusion is the thrust and specific impulse of a scramjet engine, which increases gradually with an increase in inlet shock wave angle up to the condition when airflow speed reaches sonic velocity at the exit of the combustor. In addition to that, variation in drag force at the inlet of the scramjet and variation in hypersonic flow conditions at every stage of the scramjet also studied in order to understand variation on flow characteristics with respect to flow deflection angle. Essentially, it helps in designing inlet profile for the Scramjet engine to achieve optimum specific impulse.

Keywords: hypersonic flow, scramjet, shock waves, specific impulse, mathematical analysis

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Authors: Hamid Maidat, Khedidja Bouhadef, Djamel Eddine Ameziani, Azzedine Abdedou

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This work consists of a numerical simulation of convective heat transfer in a vertical plane channel filled with a heat generating porous medium, in the absence of local thermal equilibrium. The walls are maintained to a constant temperature and the inlet velocity is uniform. The dynamic range is described by the Darcy-Brinkman model and the thermal field by two energy equations model. A dimensionless formulation is developed for performing a parametric study based on certain dimensionless groups such as, the Biot interstitial number, the thermal conductivity ratio and the volumetric heat generation. The governing equations are solved using the finite volume method, gave rise to a multitude of results concerning in particular the thermal field in the porous channel and the existence or not of the local thermal equilibrium.

Keywords: local thermal non equilibrium model, mixed convection, porous medium, power generation

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Authors: Vikas Kumar

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The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. Thus, the obtained results are presented numerically and graphically in the paper.

Keywords: axi-symmetric, ferrofluid, magnetic field, porous rotating disk

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Authors: Jianyang Zhu, Lin Jiang, Tixian Tian

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Inspired by the increasing interesting on the wind power associated with production of clear electric power, a numerical experiment is applied to investigate the aerodynamic performance of straight type vertical axis wind turbine with different thickness and solidity, where the incompressible Navier-Stokes (N-S) equations coupled with dynamic mesh technique is solved. By analyzing the flow field, as well as energy coefficient of different thickness and solidity turbine, it is found that the thickness and solidity can significantly influence the performance of vertical axis wind turbine. For the turbine under low tip speed, the mean energy coefficient increase with the increasing of thickness and solidity, which may improve the self starting performance of the turbine. However for the turbine under high tip speed, the appropriate thickness and smaller solidity turbine possesses better performance. In addition, delay stall and no interaction of the blade and previous separated vortex are observed around appropriate thickness and solidity turbine, therefore lead better performance characteristics.

Keywords: vertical axis wind turbine, N-S equations, dynamic mesh technique, thickness, solidity

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Authors: Titinan Pothong, Prasit Wangpakapattanawong, Stephen Elliott

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Shifting cultivation is an indigenous agricultural practice among upland people and has long been one of the major land-use systems in Southeast Asia. As a result, fallows and secondary forests have come to cover a large part of the region. However, they are increasingly being replaced by monocultures, such as corn cultivation. This is believed to be a main driver of deforestation and forest degradation, and one of the reasons behind the recurring winter smog crisis in Thailand and around Southeast Asia. Accurate biomass estimation of trees is important to quantify valuable carbon stocks and changes to these stocks in case of land use change. However, presently, Thailand lacks proper tools and optimal equations to quantify its carbon stocks, especially for secondary evergreen forests, including fallow areas after shifting cultivation and smaller trees with a diameter at breast height (DBH) of less than 5 cm. Developing new allometric equations to estimate biomass is urgently needed to accurately estimate and manage carbon storage in tropical secondary forests. This study established new equations using a destructive method at three study sites: approximately 50-year-old secondary forest, 4-year-old fallow, and 7-year-old fallow. Tree biomass was collected by harvesting 136 individual trees (including coppiced trees) from 23 species, with a DBH ranging from 1 to 31 cm. Oven-dried samples were sent for carbon analysis. Wood density was calculated from disk samples and samples collected with an increment borer from 79 species, including 35 species currently missing from the Global Wood Densities database. Several models were developed, showing that aboveground biomass (AGB) was strongly related to DBH, height (H), and wood density (WD). Including WD in the model was found to improve the accuracy of the AGB estimation. This study provides insights for reforestation management, and can be used to prepare baseline data for Thailand’s carbon stocks for the REDD+ and other carbon trading schemes. These may provide monetary incentives to stop illegal logging and deforestation for monoculture.

Keywords: aboveground biomass, allometric equation, carbon stock, secondary forest

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

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Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: rotating shaft, flexible blades, centrifugal stiffness, stability

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Authors: Win Ko Ko, A. N. Temnov

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The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: M. Ahmed, Javed Mallick, Mohammad Abul Hasan

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The flexural tensile strength of concrete is an important parameter for determining cracking behavior of concrete structure and to compute deflection under flexure. Many factors have been shown to influence the flexural tensile strength, particularly the level of concrete strength, size of member, age of concrete and confinement to flexure member etc. Empirical equations have been suggested to relate the flexural tensile strength and compressive strength. Limited literature is available for relationship between flexural tensile strength and compressive strength giving consideration to the factors affecting the flexural tensile strength specially the concrete confinement factor. The concrete member such as slabs, beams and columns critical locations are under confinement effects. The paper presents the experimental study to predict the flexural tensile strength and compressive strength empirical relations using statistical procedures considering the effect of confinement and age of concrete for wide range of concrete strength (from 35 to about 100 MPa). It is concluded from study that due consideration of confinement should be given in deriving the flexural tensile strength and compressive strength proportionality equations.

Keywords: compressive strength, flexural tensile strength, modulus of rupture, statistical procedures, concrete confinement

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Authors: Alicia Kamischke, Souhail Elhouar, Yasser Khodair

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The American Institute of Steel Construction (AISC) Specification (360-10) provides equations for calculating the capacity of a W-shaped steel member to resist concentrated forces applied to its flange. In the case of flange local bending, the capacity equations were primarily formulated for an interior point along the member, which is defined to be at a distance larger than ten flange thicknesses away from the member’s end. When a concentrated load is applied within ten flange thicknesses from the member’s end, AISC requires a fifty percent reduction to be applied to the flange bending capacity. This reduction, however, is not supported by any research. In this study, finite element modeling is used to investigate the actual reduction in capacity near the end of such a steel member. The results indicate that the AISC equation for flange local bending is quite conservative for forces applied at less than ten flange thicknesses from the member’s end and a new equation is suggested for the evaluation of available flange local bending capacity within that distance.

Keywords: flange local bending, concentrated forces, column, flange capacity

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Authors: M. Kashfi, K. Jahani

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Sound attenuation in absorptive silencers has been analyzed in this paper. The structure of such devices is as follows. When the rigid duct of an expansion chamber has been lined by a packed absorptive material under a perforated membrane, incident sound waves will be dissipated by the absorptive liners. This kind of silencer, usually are applicable for medium to high frequency ranges. Several conditions for different absorptive materials, variety in their thicknesses, and different shapes of the expansion chambers have been studied in this paper. Also, graphs of sound attenuation have been compared between empty expansion chamber and duct of silencer with applying liner. Plane waves have been assumed in inlet and outlet regions of the silencer. Presented results that have been achieved by applying finite element method (FEM), have shown the dependence of the sound attenuation spectrum to flow resistivity and the thicknesses of the absorptive materials, and geometries of the cross section (configuration of the silencer). As flow resistivity and thickness of absorptive materials increase, sound attenuation improves. In this paper, diagrams of the transmission loss (TL) for absorptive silencers in five different cross sections (rectangle, circle, ellipse, square, and rounded rectangle as the main geometry) have been presented. Also, TL graphs for silencers using different absorptive material (glass wool, wood fiber, and kind of spongy materials) as liner with three different thicknesses of 5 mm, 15 mm, and 30 mm for glass wool liner have been exhibited. At first, the effect of substances of the absorptive materials with the specific flow resistivity and densities on the TL spectrum, then the effect of the thicknesses of the glass wool, and at last the efficacy of the shape of the cross section of the silencer have been investigated.

Keywords: transmission loss, absorptive material, flow resistivity, thickness, frequency

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Authors: Abdulrahman Abdulrahman

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The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

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Authors: Binyam Teferi

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In this paper, a theoretical analysis of blood flow in the presence of thermal radiation and chemical reaction under the influence of time dependent magnetic field intensity has been studied. The unsteady non linear partial differential equations of blood flow considers time dependent stretching velocity, the energy equation also accounts time dependent temperature of vessel wall, and concentration equation includes time dependent blood concentration. The governing non linear partial differential equations of motion, energy, and concentration are converted into ordinary differential equations using similarity transformations solved numerically by applying ode45. MATLAB code is used to analyze theoretical facts. The effect of physical parameters viz., permeability parameter, unsteadiness parameter, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter, and Schmidt number on flow variables viz., velocity of blood flow in the vessel, temperature and concentration of blood has been analyzed and discussed graphically. From the simulation study, the following important results are obtained: velocity of blood flow increases with both increment of permeability and unsteadiness parameter. Temperature of the blood increases in vessel wall as Prandtl number and Hartmann number increases. Concentration of the blood decreases as time dependent chemical reaction parameter and Schmidt number increases.

Keywords: stretching velocity, similarity transformations, time dependent magnetic field intensity, thermal radiation, chemical reaction

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Authors: Kuniyoshi Abe

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Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Selahattin Gultekin

Abstract:

Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

Procedia PDF Downloads 311

Authors: S. Ali, M. Baccar

Abstract:

In this work, numerical simulations were carried out using a specific CFD code in order to study the performance of an innovative Scraped Surface Heat Exchanger (SSHE) with helical ribbons for Bingham fluids (threshold fluids). The resolution of three-dimensional form of the conservation equations (continuity, momentum and energy equations) was carried out basing on the finite volume method (FVM). After studying the effect of dimensionless numbers (axial Reynolds, rotational Reynolds and Oldroyd numbers) on the hydrodynamic and thermal behaviors within SSHE, a parametric study was developed, by varying the width of the helical ribbon, the clearance between the stator wall and the tip of the ribbon and the number of turns of the helical ribbon, in order to improve the heat transfer inside the exchanger. The effect of these geometrical numbers on the hydrodynamic and thermal behaviors was discussed.

Keywords: heat transfer, helical ribbons, hydrodynamic behavior, parametric study, SSHE, thermal behavior

Procedia PDF Downloads 210

Authors: Rafael Muñoz, Juan Melchor, Alicia Valera, Laura Peralta, Guillermo Rus

Abstract:

A torsional piezoelectric ultrasonic transducer design is proposed to measure shear moduli in soft tissue with direct access availability, using shear wave elastography technique. The measurement of shear moduli of tissues is a challenging problem, mainly derived from a) the difficulty of isolating a pure shear wave, given the interference of multiple waves of different types (P, S, even guided) emitted by the transducers and reflected in geometric boundaries, and b) the highly attenuating nature of soft tissular materials. An immediate application, overcoming these drawbacks, is the measurement of changes in cervix stiffness to estimate the gestational age at delivery. The design has been optimized using a finite element model (FEM) and a semi-analytical estimator of the probability of detection (POD) to determine a suitable geometry, materials and generated waves. The technique is based on the time of flight measurement between emitter and receiver, to infer shear wave velocity. Current research is centered in prototype testing and validation. The geometric optimization of the transducer was able to annihilate the compressional wave emission, generating a quite pure shear torsional wave. Currently, mechanical and electromagnetic coupling between emitter and receiver signals are being the research focus. Conclusions: the design overcomes the main described problems. The almost pure shear torsional wave along with the short time of flight avoids the possibility of multiple wave interference. This short propagation distance reduce the effect of attenuation, and allow the emission of very low energies assuring a good biological security for human use.

Keywords: cervix ripening, preterm birth, shear modulus, shear wave elastography, soft tissue, torsional wave

Procedia PDF Downloads 344