Search results for: boundary integral equation

Authors: G. Sarojamma, K. Vendabai

Abstract:

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: Casson nanofluid, Boundary layer flow, Internal heat generation/absorption, Exponentially stretching cylinder, Heat transfer, Brownian motion, Thermophoresis.

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Authors: Yoichi Hikino, Mutsuto Kawahara

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The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

Abstract:

The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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Authors: Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

Abstract:

As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Keywords: periodic solution, neutral Rayleigh equation, variable sign, Deviating argument, p-Laplacian, Mawhin’s continuation.

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Authors: Reza Mollapourasl, Majid Haghi

Abstract:

In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: Radial basis functions, Hermite finite difference, Helmholtz equation, stability.

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Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

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This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.

Keywords: Chaos synchronization, Nonlinear sliding surface, Control gains, Sliding mode control.

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Authors: Ali Rafiee, Ahad Salimi, Ali Reza Roosta

Abstract:

Prostate cancer is one of the most frequent cancers in men and is a major cause of mortality in the most of countries. In many diagnostic and treatment procedures for prostate disease accurate detection of prostate boundaries in transrectal ultrasound (TRUS) images is required. This is a challenging and difficult task due to weak prostate boundaries, speckle noise and the short range of gray levels. In this paper a novel method for automatic prostate segmentation in TRUS images is presented. This method involves preprocessing (edge preserving noise reduction and smoothing) and prostate segmentation. The speckle reduction has been achieved by using stick filter and top-hat transform has been implemented for smoothing. A feed forward neural network and local binary pattern together have been use to find a point inside prostate object. Finally the boundary of prostate is extracted by the inside point and an active contour algorithm. A numbers of experiments are conducted to validate this method and results showed that this new algorithm extracted the prostate boundary with MSE less than 4.6% relative to boundary provided manually by physicians.

Keywords: Prostate segmentation, stick filter, neural network, active contour.

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Authors: Pakawhat Khumkhreung, Yottana Khunatorn

Abstract:

The flow pattern inside rectangular intake air duct of 300 MW lignite coal-fired power plant is investigated in order to analyze and reduce overall inlet system pressure drop. The system consists of the 45-degree inlet elbow, the flow instrument, the 90-degree mitered elbow and fans, respectively. The energy loss in each section can be determined by Bernoulli’s equation and ASHRAE standard table. Hence, computational fluid dynamics (CFD) is used in this study based on Navier-Stroke equation and the standard k-epsilon turbulence modeling. Input boundary condition is 175 kg/s mass flow rate inside the 11-m² cross sectional duct. According to the inlet air flow rate, the Reynolds number of airstream is 2.7x10⁶ (based on the hydraulic duct diameter), thus the flow behavior is turbulence. The numerical results are validated with the real operation data. It is found that the numerical result agrees well with the operating data, and dominant loss occurs at the flow rate measurement device. Normally, the air flow rate is measured by the airfoil and it gets high pressure drop inside the duct. To overcome this problem, the airfoil is planned to be replaced with the other type measuring instrument, such as the average pitot tube which generates low pressure drop of airstream. The numerical result in case of average pitot tube shows that the pressure drop inside the inlet airstream duct is decreased significantly. It should be noted that the energy consumption of inlet air system is reduced too.

Keywords: Airfoil, average pitot tube, combustion air, CFD, pressure drop, rectangular duct.

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Authors: Daniel Joseph Whittaker

Abstract:

This paper examines the broad array of historic sites from which Chicago common brick has emerged, and the methods this brick has been utilized within and around a new hybrid structure recently completed-and periodically opened to the public, as a private art, architecture, design, and social activism gallery space. Various technical aspects regarding the structural and aesthetic reuse methods of salvaged brick within the interior and exterior of this new Tadao Ando-designed building in Lincoln Park, Chicago, are explored. This paper expands specifically upon the multiple possible origins of Chicago common brick, as well as the extant brick currently composing the surrounding alley which is integral to demarcating the southern site boundary of the old apartment building now gallery. Themes encompassing Chicago’s archeological and architectural history, local resource extraction, and labor practices permeate this paper’s investigation into urban, social and architectural history and building construction technology advancements through time.

Keywords: Masonry construction, history brickmaking, private museums, Chicago Illinois, Tadao Ando.

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Authors: F. M. Hady, A. Mahdy, R. A. Mohamed, Omima A. Abo Zaid

Abstract:

A numerical approach of the effectiveness of numerous parameters on magnetohydrodynamic (MHD) natural convection heat and mass transfer problem of a dusty micropolar fluid in a non-Darcy porous regime is prepared in the current paper. In addition, a convective boundary condition is scrutinized into the micropolar dusty fluid model. The governing boundary layer equations are converted utilizing similarity transformations to a system of dimensionless equations to be convenient for numerical treatment. The resulting equations for fluid phase and dust phases of momentum, angular momentum, energy, and concentration with the appropriate boundary conditions are solved numerically applying the Runge-Kutta method of fourth-order. In accordance with the numerical study, it is obtained that the magnitude of the velocity of both fluid phase and particle phase reduces with an increasing magnetic parameter, the mass concentration of the dust particles, and Forchheimer number. While rises due to an increment in convective parameter and Darcy number. Also, the results refer that high values of the magnetic parameter, convective parameter, and Forchheimer number support the temperature distributions. However, deterioration occurs as the mass concentration of the dust particles and Darcy number increases. The angular velocity behavior is described by progress when studying the effect of the magnetic parameter and microrotation parameter.

Keywords: Micropolar dusty fluid, convective heating, natural convection, MHD, porous media.

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Authors: I. Otete, A. I. Ejere, I. S. Okunzuwa

Abstract:

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

Keywords: Schrödinger's equation, bound state, Hulthen-Yukawa potential, Nikiforov-Uvarov, D-dimensions

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Authors: Alexander Babin, Leonid Savin

Abstract:

In the present paper, increasing of energy efficiency of a thrust hybrid bearing with a central feeding chamber is considered. The mathematical model was developed to determine the pressure distribution and the reaction forces, based on the Reynolds equation and static characteristics’ equations. The boundary problem of pressure distribution calculation was solved using the method of finite differences. For various types of lubricants, geometry and operational characteristics, axial gaps can be determined, where the minimal friction coefficient is provided. The next part of the study considers the application of servovalves in order to maintain the desired position of the rotor. The report features the calculation results and the analysis of the influence of the operational and geometric parameters on the energy efficiency of mechatronic fluid-film bearings.

Keywords: Active bearings, energy efficiency, mathematical model, mechatronics, thrust multipad bearing.

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Authors: Delfim Soares Jr.

Abstract:

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically computed, taking into account the generalized-α method and subcycling techniques. As it is discussed and illustrated along the text, the proposed procedure is efficient and accurate, providing a very attractive time marching technique. 

Keywords: Dynamics, Time-Marching, Green’s Function, Generalized-α Method, Subcycling.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: Xi Gu, Guan Heng Yeoh, Victoria Timchenko

Abstract:

In the current work, a three-dimensional geometry of a 75% stenosed blood vessel is analyzed. Large eddy simulation (LES) with the help of a dynamic subgrid scale Smagorinsky model is applied to model the turbulent pulsatile flow. The geometry, the transmural pressure and the properties of the blood and the elastic boundary were based on clinical measurement data. For the flexible wall model, a thin solid region is constructed around the 75% stenosed blood vessel. The deformation of this solid region was modelled as a deforming boundary to reduce the computational cost of the solid model. Fluid-structure interaction is realized via a twoway coupling between the blood flow modelled via LES and the deforming vessel. The information of the flow pressure and the wall motion was exchanged continually during the cycle by an arbitrary Lagrangian-Eulerian method. The boundary condition of current time step depended on previous solutions. The fluctuation of the velocity in the post-stenotic region was analyzed in the study. The axial velocity at normalized position Z=0.5 shows a negative value near the vessel wall. The displacement of the elastic boundary was concerned in this study. In particular, the wall displacement at the systole and the diastole were compared. The negative displacement at the stenosis indicates a collapse at the maximum velocity and the deceleration phase.

Keywords: Large Eddy Simulation, Fluid Structural Interaction, Constricted Artery, Computational Fluid Dynamics.

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Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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Authors: Amrita Tripathi, Neeru Adlakha

Abstract:

Calcium [Ca2+] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involved. A mathematical model has been developed for cylindrical shaped neuron cell by incorporating physiological parameters like buffer, diffusion coefficient, and association rate. Appropriate initial and boundary conditions have been framed. The closed form solution has been developed in terms of modified Bessel function. A computer program has been developed in MATLAB 7.11 for the whole approach.

Keywords: Laplace Transform, Modified Bessel function, reaction diffusion equation, diffusion coefficient, excess buffer, calcium influx

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

Abstract:

Nowadays, there is little information, concerning the heat shield systems, and this information is not completely reliable to use in so many cases. for example, the precise calculation cannot be done for various materials. In addition, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test. Hence, using numerical modeling program that calculates the surface recession rate and interior temperature distribution is necessary. Also, numerical solution of governing equation for non-charring material ablation is presented in order to anticipate the recession rate and the heat response of non-charring heat shields. the governing equation is nonlinear and the Newton- Rafson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Rafson method for solving the governing equation is one of the advantages of the solving method because this method is simple and it can be easily generalized to more difficult problems. The obtained results compared with reliable sources in order to examine the accuracy of compiling code.

Keywords: Ablation rate, surface recession, interior temperaturedistribution, non charring material ablation, Newton Rafson method.

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Authors: Prashant Verma, K. K. Singh, Anjali Singh, Ujjaval Srivastava

Abstract:

Contraceptive policies have been derived to achieve desired reductions in the growth rate and also, applied to the data of Uttar-Pradesh, India for illustration. Using the Lotka’s integral equation for the stable population, expressions for the proportion of contraceptive users at different ages have been obtained. At the age of 20 years, 42% of contraceptive users is imperative to reduce the present annual growth rate of 0.036 to 0.02, assuming that 40% of the contraceptive users discontinue at the age of 25 years and 30% again continue contraceptive use at age 30 years. Further, presuming that 75% of women start using contraceptives at the age of 23 years, and 50% of the remaining women start using contraceptives at the age of 28 years, while the rest of them start using it at the age of 32 years. If we set a minimum age of marriage as 20 years, a reduction of 0.019 in growth rate will be obtained. This study describes how the level of contraceptive use at different age groups of women reduces the growth rate in the state of Uttar Pradesh. The article also promotes delayed marriage in the region.

Keywords: Child bearing, contraceptive devices, contraceptive policies, population growth, stable population.

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Authors: Ahmed M. Farag, Wael F. Mohamed, Atef A. Ata, Burhamy M. Burhamy

Abstract:

In the present paper, an improved initial value numerical technique is presented to analyze the free vibration of symmetrically laminated rectangular plate. A combination of the initial value method (IV) and the finite differences (FD) devices is utilized to develop the present (IVFD) technique. The achieved technique is applied to the equation of motion of vibrating laminated rectangular plate under various types of boundary conditions. Three common types of laminated symmetrically cross-ply, orthotropic and isotropic plates are analyzed here. The convergence and accuracy of the presented Initial Value-Finite Differences (IVFD) technique have been examined. Also, the merits and validity of improved technique are satisfied via comparing the obtained results with those available in literature indicating good agreements.

Keywords: Free Vibrations, Initial Value, Finite Differences, Laminated plates.

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Authors: Ekprasit Promtun, Sridhar Seshagiri

Abstract:

This paper considers the control of the longitudinal flight dynamics of an F-16 aircraft. The primary design objective is model-following of the pitch rate q, which is the preferred system for aircraft approach and landing. Regulation of the aircraft velocity V (or the Mach-hold autopilot) is also considered, but as a secondary objective. The problem is challenging because the system is nonlinear, and also non-affine in the input. A sliding mode controller is designed for the pitch rate, that exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with a steady-state response that is comparable to that of a conventional polynomial based gain-scheduled approach with integral control, but with improved transient performance. Integral action is introduced in the sliding mode design using the recently developed technique of “conditional integrators", and it is shown that robust regulation is achieved with asymptotically constant exogenous signals, without degrading the transient response. Through extensive simulation on the nonlinear multiple-input multiple-output (MIMO) longitudinal model of the F-16 aircraft, it is shown that the conditional integrator design outperforms the one based on the conventional linear control, without requiring any scheduling.

Keywords: Sliding-mode Control, Integral Control, Model Following, F-16 Longitudinal Dynamics, Pitch-Rate Control.

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

Abstract:

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

Abstract:

The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

Abstract:

The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: G. Revathi, P. Saikrishnan

Abstract:

An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.

Keywords: Boundary layer, suction, mass transfer, rotating sphere.

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Authors: M. Kidouche, H. Habbi, M. Zelmat, S. Grouni

Abstract:

In analyzing large scale nonlinear dynamical systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solutions properties of the large scale system are then deduced from the solution properties of the individual subsystems and the nature of the interconnections. In this paper a new approach is proposed for the stability analysis of large scale systems, which is based upon the concept of vector Lyapunov functions and the decomposition methods. The present results make use of graph theoretic decomposition techniques in which the overall system is partitioned into a hierarchy of strongly connected components. We show then, that under very reasonable assumptions, the overall system is stable once the strongly connected subsystems are stables. Finally an example is given to illustrate the constructive methodology proposed.

Keywords: Comparison principle, First integral, Large scale system, Lyapunov stability.

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