Search results for: Quaternionic linear equations

Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: H. Aissa, L. Mouzai, M. Bouhadef

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The effects of down slope steepness on soil splash distribution under a water drop impact have been investigated in this study. The equipment used are the burette to simulate a water drop, a splash cup filled with sandy soil which forms the source area and a splash board to collect the ejected particles. The results found in this study have shown that the apparent mass increased with increasing downslope angle following a linear regression equation with high coefficient of determination. In the same way, the radial soil splash distribution over the distance has been analyzed statistically, and an exponential function was the best fit of the relationship for the different slope angles. The curves and the regressions equations validate the well known FSDF and extend the theory of Van Dijk.

Keywords: Splash distribution, water drop, slope steepness, soil detachment.

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Authors: Pelaez Verdet, Antonio, Loscertales Sanchez, Pilar

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One of the mayor problems of programming a cruise circuit is to decide which destinations to include and which don-t. Thus a decision problem emerges, that might be solved using a linear and goal programming approach. The problem becomes more complex if several boats in the fleet must be programmed in a limited schedule, trying their capacity matches best a seasonal demand and also attempting to minimize the operation costs. Moreover, the programmer of the company should consider the time of the passenger as a limited asset, and would like to maximize its usage. The aim of this work is to design a method in which, using linear and goal programming techniques, a model to design circuits for the cruise company decision maker can achieve an optimal solution within the fleet schedule.

Keywords: Itinerary design, cruise programming, goalprogramming, linear programming

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Authors: Jin Sun, Hongbin Gu

Abstract:

An important step in three-dimensional reconstruction and computer vision is camera calibration, whose objective is to estimate the intrinsic and extrinsic parameters of each camera. In this paper, two linear methods based on the different planes are given. In both methods, the general plane is used to replace the calibration object with very good precision. In the first method, after controlling the camera to undergo five times- translation movements and taking pictures of the orthogonal planes, a set of linear constraints of the camera intrinsic parameters is then derived by means of homography matrix. The second method is to get all camera parameters by taking only one picture of a given radius circle. experiments on simulated data and real images,indicate that our method is reasonable and is a good supplement to camera calibration.

Keywords: camera calibration, 3D reconstruction, computervision

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Authors: Mohammad Ali Lotfollahi-Yaghin, Hamid Ahmadi

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In the present paper, a set of parametric FE stress analyses is carried out for two-planar welded tubular DKT-joints under two different axial load cases. Analysis results are used to present general remarks on the effect of geometrical parameters on the stress concentration factors (SCFs) at the inner saddle, outer saddle, toe, and heel positions on the main (outer) brace. Then a new set of SCF parametric equations is developed through nonlinear regression analysis for the fatigue design of two-planar DKT-joints. An assessment study of these equations is conducted against the experimental data; and the satisfaction of the criteria regarding the acceptance of parametric equations is checked. Significant effort has been devoted by researchers to the study of SCFs in various uniplanar tubular connections. Nevertheless, for multi-planar joints covering the majority of practical applications, very few investigations have been reported due to the complexity and high cost involved.

Keywords: Offshore jacket structure, Parametric equation, Stress concentration factor (SCF), Two-planar tubular KT-joint

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Authors: M. J. Fadaee, H. Saffari, H. Khosravi

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Shear walls are used in most of the tall buildings for carrying the lateral load. When openings for doors or windows are necessary to be existed in the shear walls, a special type of the shear walls is used called "coupled shear walls" which in some cases is stiffened by specific beams and so, called "stiffened coupled shear walls". In this paper, a mathematical method for geometrically nonlinear analysis of the stiffened coupled shear walls has been presented. Then, a suitable formulation for determining the critical load of the stiffened coupled shear walls under gravity force has been proposed. The governing differential equations for equilibrium and deformation of the stiffened coupled shear walls have been obtained by setting up the equilibrium equations and the moment-curvature relationships for each wall. Because of the complexity of the differential equation, the energy method has been adopted for approximate solution of the equations.

Keywords: Buckling load, differential equation, energy method, geometrically nonlinear analysis, mathematical method, Stiffened coupled shear walls.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

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Recently, fast neural networks for object/face detection were presented in [1-3]. The speed up factor of these networks relies on performing cross correlation in the frequency domain between the input image and the weights of the hidden layer. But, these equations given in [1-3] for conventional and fast neural networks are not valid for many reasons presented here. In this paper, correct equations for cross correlation in the spatial and frequency domains are presented. Furthermore, correct formulas for the number of computation steps required by conventional and fast neural networks given in [1-3] are introduced. A new formula for the speed up ratio is established. Also, corrections for the equations of fast multi scale object/face detection are given. Moreover, commutative cross correlation is achieved. Simulation results show that sub-image detection based on cross correlation in the frequency domain is faster than classical neural networks.

Keywords: Conventional Neural Networks, Fast Neural Networks, Cross Correlation in the Frequency Domain.

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Authors: R .Lassoued, M. Guenfoud

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An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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Authors: Wen-Yuh Jywe, Bor-Jeng Lin, Jing-Chung Shen, Jeng-Dao Lee, Hsueh-Liang Huang, Tung-Hsien Hsieh

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In this study, a simple 2-D measurement system based on optical design was developed to measure the motion errors of the linear guideway. Compared with the transitional methods about the linear guideway for measuring the motion errors, our proposed 2-D optical measurement system can simultaneously measure horizontal and vertical running straightness errors for the linear guideway.

The performance of the 2-D optical measurement system is verified by experimental results. The standard deviation of the 2-D optical measurement system is about 0.4μm in the measurement range of 100 mm. The maximum measuring speed of the proposed automatic measurement instrument is 1 m/sec.

Keywords: 2-D measurement, linear guideway, motion errors, running straightness.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

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In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation

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Authors: V. Joshi Manohar, P. Sujatha, K. S. R. Anjaneyulu

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Nowadays Multilevel inverters are widely using in various applications. Modulation strategy at fundamental switching frequency like, SHEPWM is prominent technique to eliminate lower order of harmonics with less switching losses and better harmonic profile. The equations which are formed by SHE are highly nonlinear transcendental in nature, there may exist single, multiple or even no solutions for a particular MI. However, some loads such as electrical drives, it is required to operate in whole range of MI. In order to solve SHE equations for whole range of MI, intelligent techniques are well suited to solve equations so as to produce lest %THDV. Hence, this paper uses Continuous genetic algorithm for minimising harmonics. This paper also presents wavelet based analysis of harmonics. The developed algorithm is simulated and %THD from FFT analysis and Wavelet analysis are compared. MATLAB programming environment and SIMULINK models are used whenever necessary.

Keywords: Cascade H-Bridge Inverter (CHB), Continuous Genetic Algorithm (C-GA), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv), Wavelet Transform (WT).

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Authors: C. Ganesh Babu, P. T. Vanathi

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In this paper we present an enhanced noise reduction method for robust speech recognition using Adaptive Gain Equalizer with Non linear Spectral Subtraction. In Adaptive Gain Equalizer method (AGE), the input signal is divided into a number of subbands that are individually weighed in time domain, in accordance to the short time Signal-to-Noise Ratio (SNR) in each subband estimation at every time instant. Instead of focusing on suppression the noise on speech enhancement is focused. When analysis was done under various noise conditions for speech recognition, it was found that Adaptive Gain Equalizer method algorithm has an obvious failing point for a SNR of -5 dB, with inadequate levels of noise suppression for SNR less than this point. This work proposes the implementation of AGE when coupled with Non linear Spectral Subtraction (AGE-NSS) for robust speech recognition. The experimental result shows that out AGE-NSS performs the AGE when SNR drops below -5db level.

Keywords: Adaptive Gain Equalizer, Non Linear Spectral Subtraction, Speech Enhancement, and Speech Recognition.

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Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Leila Vafajoo, Farhad Khorasheh, Mehrnoosh Hamzezadeh Nakhjavani, Moslem Fattahi

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In the present study, a procedure was developed to determine the optimum reaction rate constants in generalized Arrhenius form and optimized through the Nelder-Mead method. For this purpose, a comprehensive mathematical model of a fixed bed reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3 catalyst was developed. Utilizing appropriate kinetic rate expressions for the main dehydrogenation reaction as well as side reactions and catalyst deactivation, a detailed model for the radial flow reactor was obtained. The reactor model composed of a set of partial differential equations (PDE), ordinary differential equations (ODE) as well as algebraic equations all of which were solved numerically to determine variations in components- concentrations in term of mole percents as a function of time and reactor radius. It was demonstrated that most significant variations observed at the entrance of the bed and the initial olefin production obtained was rather high. The aforementioned method utilized a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method was demonstrated by comparing the predicted values of the kinetic constants using the proposed method with a series of experimental values reported in the literature for different systems.

Keywords: Dehydrogenation, Pt-Sn/Al2O3 Catalyst, Modeling, Nelder-Mead, Optimization

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Authors: Z. Babic, I. Veza, A. Balic, M. Crnjac

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The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Keywords: De Novo Programming, production plan, stone souvenirs, variable prices.

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Authors: Aly Farag, Ayman El-Baz, Refaat Mohamed

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In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.

Keywords: Logistic regression model, Expectationmaximization, Segmentation.

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Authors: Jürgen Geiser, Robert Röhle

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In this paper we present modeling and simulation for physical vapor deposition for metallic bipolar plates. In the models we discuss the application of different models to simulate the transport of chemical reactions of the gas species in the gas chamber. The so called sputter process is an extremely sensitive process to deposit thin layers to metallic plates. We have taken into account lower order models to obtain first results with respect to the gas fluxes and the kinetics in the chamber. The model equations can be treated analytically in some circumstances and complicated multi-dimensional models are solved numerically with a software-package (UG unstructed grids, see [1]). Because of multi-scaling and multi-physical behavior of the models, we discuss adapted schemes to solve more accurate in the different domains and scales. The results are discussed with physical experiments to give a valid model for the assumed growth of thin layers.

Keywords: Convection-diffusion equations, multi-scale problem, physical vapor deposition, reaction equations, splitting methods.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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Authors: Ekaterina Artiukhina, Panagiotis Grammelis

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Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion, and co-firing applications. In the course of torrefaction, the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The nonstationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: Torrefaction, biomass pellets, model, heat and mass transfer.

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Authors: S. Deswal, M. Pal

Abstract:

The paper aims to compare the performance of vertical and inclined multiple plunging jets and to model and predict their mass transfer capacity by multi-linear regression based approach. The multiple vertical plunging jets have jet impact angle of θ = 90^O; whereas, multiple inclined plunging jets have jet impact angle of θ = 60^O. The results of the study suggests that mass transfer is higher for multiple jets, and inclined multiple plunging jets have up to 1.6 times higher mass transfer than vertical multiple plunging jets under similar conditions. The derived relationship, based on multi-linear regression approach, has successfully predicted the volumetric mass transfer coefficient (K_La) from operational parameters of multiple plunging jets with a correlation coefficient of 0.973, root mean square error of 0.002 and coefficient of determination of 0.946. The results suggests that predicted overall mass transfer coefficient is in good agreement with actual experimental values; thereby, suggesting the utility of derived relationship based on multi-linear regression based approach and can be successfully employed in modeling mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, multi-linear regression.

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

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Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty.

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Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

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Authors: Elias K. Maragos, Petros E. Maravelakis

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In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.

Keywords: Data envelopment analysis, Dynamic DEA, Piecewise linear inputs, Piecewise linear outputs.

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Authors: M. H. Kargarnovin, A. Mamandi

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This paper presents investigation effects of a sharp edged gust on aeroelastic behavior and time-domain response of a typical section model using Jones approximate aerodynamics for pure plunging motion. Flutter analysis has been done by using p and p-k methods developed for presented finite-state aerodynamic model for a typical section model (airfoil). Introduction of gust analysis as a linear set of ordinary differential equations in a simplified procedure has been carried out by using transformation into an eigenvalue problem.

Keywords: Aeroelastic response, jones approximation, pure plunging motion, sharp edged gust.

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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: C. Porkodi, R. Arumuganathan

Abstract:

In this paper a Public Key Cryptosystem is proposed using the number theoretic transforms (NTT) over a ring of integer modulo a composite number. The key agreement is similar to ElGamal public key algorithm. The security of the system is based on solution of multivariate linear congruence equations and discrete logarithm problem. In the proposed cryptosystem only fixed numbers of multiplications are carried out (constant complexity) and hence the encryption and decryption can be done easily. At the same time, it is very difficult to attack the cryptosystem, since the cipher text is a sequence of integers which are interrelated. The system provides authentication also. Using Mathematica version 5.0 the proposed algorithm is justified with a numerical example.

Keywords: Cryptography, decryption, discrete logarithm problem encryption, Integer Factorization problem, Key agreement, Number Theoretic Transform.

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Authors: Abdulhassan Abd. K, Sattar Al-Jabair, Khalid Sultan

Abstract:

We have measured the pressure drop and convective heat transfer coefficient of water – based AL(25nm),AL2O3(30nm) and CuO(50nm) Nanofluids flowing through a uniform heated circular tube in the fully developed laminar flow regime. The experimental results show that the data for Nanofluids friction factor show a good agreement with analytical prediction from the Darcy's equation for single-phase flow. After reducing the experimental results to the form of Reynolds, Rayleigh and Nusselt numbers. The results show the local Nusselt number and temperature have distribution with the non-dimensional axial distance from the tube entry. Study decided that thenNanofluid as Newtonian fluids through the design of the linear relationship between shear stress and the rate of stress has been the study of three chains of the Nanofluid with different concentrations and where the AL, AL2O3 and CuO – water ranging from (0.25 - 2.5 vol %). In addition to measuring the four properties of the Nanofluid in practice so as to ensure the validity of equations of properties developed by the researchers in this area and these properties is viscosity, specific heat, and density and found that the difference does not exceed 3.5% for the experimental equations between them and the practical. The study also demonstrated that the amount of the increase in heat transfer coefficient for three types of Nano fluid is AL, AL2O3, and CuO – Water and these ratios are respectively (45%, 32%, 25%) with insulation and without insulation (36%, 23%, 19%), and the statement of any of the cases the best increase in heat transfer has been proven that using insulation is better than not using it. I have been using three types of Nano particles and one metallic Nanoparticle and two oxide Nanoparticle and a statement, whichever gives the best increase in heat transfer.

Keywords: Newtonian, NUR factor, Brownian motion

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

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In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: Elastic foundation, impact, moving load, thick plate.

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Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. 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. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, shrinking sheet, stability analysis.

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