Search results for: Boundary layer equation

Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

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This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Junji Kaneko, Shigeyuki Haruyama, Ken Kaminishi, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: System Model, Physical Models, Empirical Models, Conservation Law, Differential Algebraic Equation, Object-Oriented.

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Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: Zhao Wang, Hong Yan

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In this paper, a unified-gas kinetic scheme (UGKS) for the gas-particle flow is constructed. UGKS is a direct modeling method for both continuum and rarefied flow computations. The dynamics of particle and gas are described as rarefied and continuum flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook (BGK) equation for the particle distribution function. For the gas phase, the gas kinetic scheme for Navier-Stokes equation is solved. The momentum transfer between gas and particle is achieved by the acceleration term added to the BGK equation. The new scheme is tested by a 2cm-in-thickness dense bed comprised of glass particles with 1.5mm in diameter, and reasonable agreement is achieved.

Keywords: Gas-particle flow, unified gas-kinetic scheme, momentum transfer, shock-induced fluidization.

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Authors: Jawad Al Khaburi, Abbas A. Dehghani-Sanij, E. Andrea Nelson, Jerry Hutchinson

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Medical compression bandages are widely used in the treatment of chronic venous disorder. In order to design effective compression bandages, researchers have attempted to describe the interface pressure applied by multi-layer bandages using mathematical models. This paper reports on the work carried out to compare and validate the mathematical models used to describe the interface pressure applied by multi-layer bandages. Both analytical and experimental results showed that using simple multiplication of a number of bandage layers with the pressure applied by one layer of bandage or ignoring the increase in the limb radius due to former layers of bandage will result in overestimating the pressure. Experimental results showed that the mathematical models, which take into consideration the increase in the limb radius due to former bandage layers, are more accurate than the one which does not.

Keywords: Compression bandages, FlexiForce, interface pressure, venous ulcer

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Authors: Shilpa N. Kulkarni, Sujata R. Patrikar

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In the present work, an attempt is made to understand electromagnetic field confinement in a subwavelength waveguide structure using concepts of quantum mechanics. Evanescent field in the waveguide is looked as inability of the photon to get confined in the waveguide core and uncertainty of position is assigned to it. The momentum uncertainty is calculated from position uncertainty. Schrödinger wave equation for the photon is written by incorporating position-momentum uncertainty. The equation is solved and field distribution in the waveguide is obtained. The field distribution and power confinement is compared with conventional waveguide theory. They were found in good agreement with each other.

Keywords: photon localization in waveguide, photon tunneling, quantum confinement of light, Schrödinger wave equation, uncertainty principle.

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Authors: A. Bahmanikashkouli, O.R. Bahadori Nezhad

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In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

Keywords: Generalized Differential Quadrature method, Nonlinear consolidation, Nonlinear system of equations, Time-varied drainage

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Authors: T. S. Ozsahin, V. Kahya, A. Birinci, A. O. Cakiroglu

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In this study, the contact problem of a layered composite which consists of two materials with different elastic constants and heights resting on two rigid flat supports with sharp edges is considered. The effect of gravity is neglected. While friction between the layers is taken into account, it is assumed that there is no friction between the supports and the layered composite so that only compressive tractions can be transmitted across the interface. The layered composite is subjected to a uniform clamping pressure over a finite portion of its top surface. The problem is reduced to a singular integral equation in which the contact pressure is the unknown function. The singular integral equation is evaluated numerically and the results for various dimensionless quantities are presented in graphical forms.

Keywords: Frictionless contact, Layered composite, Singularintegral equation, The theory of elasticity.

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Authors: Shen-Kuei Du, Jen-Chieh Chang, Chia-Hong Kao, Tzu-Chen Hung, Chii-Ray Lin

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This study experimentally investigates the heat transfer effects of forced convection and natural convection under different substrate openings design. A computational fluid dynamics (CFD) model was established and implemented to verify and explain the experimental results and heat transfer behavior. It is found that different opening position will destroy the growth of the boundary layer on substrates to alter the cooling ability for both forced under low Reynolds number and natural convection. Nevertheless, having too many opening may reduce heat conduction and affect the overall heat transfer performance. This study provides future researchers with a guideline on designing and electronic package manufacturing.

Keywords: electronic cooling, experiment, opening concept, CFD.

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Authors: Anupma Bansal

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We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

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Authors: Mohammad Taghi Shervani Tabar, Zahra Poursharifi

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The interaction of the blade tip with the casing boundary layer and the leakage flow may lead to a kind of cavitation namely tip vortex cavitation. In this study, the onset of tip vortex cavitation was experimentally investigated in an axial flow pump. For a constant speed and a fixed angle of attack and by changing the flow rate, the pump head, input power, output power and efficiency were calculated and the pump characteristic curves were obtained. The cavitation phenomenon was observed with a camera and a stroboscope. Finally, the critical flow region, which tip vortex cavitation might have occurred, was identified. The results show that just by adjusting the flow rate, out of the specified region, the possibility of occurring tip vortex cavitation, decreases to a great extent.

Keywords: Axial flow pump, Gap cavitation, Leakage vortex, Tip vortex cavitation.

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Authors: E. Mat Tokit, Yusoff M. Z, Mohammed H.

Abstract:

Numerical investigation on the generality of nanoparticle velocity equation had been done on the previous published work. The three dimensional governing equations (continuity, momentum and energy) were solved using finite volume method (FVM). Parametric study of thermal performance between pure water-cooled and nanofluid-cooled are evaluated for volume fraction in the range of 1% to 4%, and nanofluid type of gamma-Al₂O₃ at Reynolds number range of 67.41 to 286.77. The nanofluid is modeled using single and two phase approach. Three different existing Brownian motion velocities are applied in comparing the generality of the equation for a wide parametric condition. Deviation in between the Brownian motion velocity is identified to be due to the different means of mean free path and constant value used in diffusion equation.

Keywords: Brownian nanoparticle velocity, heat transfer enhancement, nanofluid, two phase model.

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Authors: P. G. Siddheshwar, B. R. Revathi

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The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.

Keywords: Dielectric liquid, Nusselt number, amplitude equation.

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Authors: Kasra Ghaemi, Syeda Tasnim, Shohel Mahmud

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One of the main issues affecting the quality and shelf life of food products is temperature fluctuation during transportation and storage. Packaging plays an important role in protecting food from environmental conditions, especially thermal variations. In this study, the performance of using microencapsulated Phase Change Material (PCM) as a promising thermal buffer layer in smart food packaging is investigated. The considered insulation layer is evaluated for different thicknesses and the absorbed heat from the environment. The results are presented in terms of the melting time of PCM or provided thermal protection period.

Keywords: Food packaging, phase change material, thermal buffer, protection time.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: Un-Hwan Park, Jun-Hyeok Heo, In-Sung Lee, Tae-Hyeon Oh, Dae-Kyu Park

Abstract:

Sound absorbing material is used as automotive interior material. Sound absorption coefficient should be predicted to design it. But it is difficult to predict sound absorbing coefficient because it is comprised of several material layers. So, its targets are achieved through many experimental tunings. It causes a lot of cost and time. In this paper, we propose the process to estimate the sound absorption coefficient with multi-layer structure. In order to estimate the coefficient, physical properties of each material are used. These properties also use predicted values by Foam-X software using the sound absorption coefficient data measured by impedance tube. Since there are many physical properties and the measurement equipment is expensive, the values predicted by software are used. Through the measurement of the sound absorption coefficient of each material, its physical properties are calculated inversely. The properties of each material are used to calculate the sound absorption coefficient of the multi-layer material. Since the absorption coefficient of multi-layer can be calculated, optimization design is possible through simulation. Then, we will compare and analyze the calculated sound absorption coefficient with the data measured by scaled reverberation chamber and impedance tubes for a prototype. If this method is used when developing automotive interior materials with multi-layer structure, the development effort can be reduced because it can be optimized by simulation. So, cost and time can be saved.

Keywords: Optimization design, multi-layer nonwoven, sound absorption coefficient, scaled reverberation chamber, impedance tubes.

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Authors: Ngozi Nwogu, Edward Gobina

Abstract:

A dip-coating process has been used to form an asymmetric silica membrane with improved membrane performance and reproducibility. First, we deposited repeatedly silica on top of a commercial alumina membrane support to improve its structural make up. The membrane is further processed under clean room conditions to avoid dust impurity and subsequent drying in an oven for high thermal, chemical and physical stability. The resulting asymmetric membrane exhibits a gradual change in the membrane layer thickness. Compared to the support, the dual-layer process improves the gas flow rates. For the scientific applications for natural gas purification, CO2, CH4 and H2 gas flow rates were. In addition, the membrane selectively separated hydrogen.

Keywords: Gas permeation, Silica membrane, separation factor, membrane layer thickness.

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Authors: Zongyan Li, Matt Best

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This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: Correlation analysis, F-ratio, Levenberg-Marquardt, MSE, NARX, neural network, optimisation.

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Authors: M. Nassereddine, J. Rizk, G. Nasserddine

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Performing High Voltage (HV) tasks with a multi craft work force create a special set of safety circumstances. This paper aims to present vital information relating to when it is acceptable to use a single or a two-layer soil structure. Also it discusses the implication of the high voltage infrastructure on the earth grid and the safety of this implication under a single or a two-layer soil structure. A multiple case study is investigated to show the importance of using the right soil resistivity structure during the earthing system design.

Keywords: Earth Grid, EPR, High Voltage, Soil Resistivity Structure, Step Voltage, Touch Voltage.

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Authors: Loay A. Al-Zu'be, Asma A. Al-Tamimi, Thakir D. Al-Momani, Ayat J. Alkarala, Maryam A. Alzawahreh

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A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.

Keywords: Body Configurations, Equations of Motion, Mathematical Modeling, Movement Trajectories.

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Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: M. H. Kargarnovin, K. Momeni

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The study of the stress distribution on a hollow cylindrical fiber placed in a composite material is considered in this work and an analytical solution for this stress distribution has been constructed. Finally some parameters such as fiber-s thickness and fiber-s length are considered and their effects on the distribution of stress have been investigated. For finding the governing relations, continuity equations for the axisymmetric problem in cylindrical coordinate (r,o,z) are considered. Then by assuming some conditions and solving the governing equations and applying the boundary conditions, an equation relates the stress applied to the representative volume element with the stress distribution on the fiber has been found.

Keywords: Axial Loading, Composite, Hollow CylindricalFiber, Stress Distribution.

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Authors: F. Imanshoar, M. R. M. Tabatabai, Y. Hassanzadeh, M. Rostamipoor

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Subsurface erosion in river banks and its details, in spite of its occurrence in various parts of the world has rarely been paid attention by researchers. In this paper, quantitative concept of the subsurface bank erosion has been investigated for vertical banks. Vertical banks were simulated experimentally by considering a sandy erodible layer overlaid by clayey one under uniformly distributed constant overhead pressure. Results of the experiments are indicated that rate of sandy layer erosion is decreased by an increase in overburden; likewise, substituting 20% of coarse (3.5 mm) sand layer bed material by fine material (1.4 mm) may lead to a decrease in erosion rate by one-third. This signifies the importance of the bed material composition effect on sandy layers erosion due to subsurface erosion in river banks.

Keywords: Subsurface Erosion, Vertical Banks, Bed Material Size

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Authors: Magdy G. Asaad

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The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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Authors: Ya-Fen Lee, Yun-Yao Chi

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The study aims to explore the relationship between risk perception of rockfall and revisit intention using a Structural Equation Modeling (SEM) analysis. A total of 573 valid questionnaires are collected from travelers to Taroko National Park, Taiwan. The findings show the majority of travelers have the medium perception of rockfall risk, and are willing to revisit the Taroko National Park. The revisit intention to Taroko National Park is influenced by hazardous preferences, willingness-to-pay, obstruction and attraction. The risk perception has an indirect effect on revisit intention through influencing willingness-to-pay. The study results can be a reference for mitigation the rockfall disaster.

Keywords: Risk perception, rockfall, revisit intention, structural equation modeling.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

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Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: Snehasis Kundu, Koeli Ghoshal

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In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

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