Search results for: Volterra integro-differential equations
1041 Stability Analysis of Three-Dimensional Flow and Heat Transfer over a Permeable Shrinking Surface in a Cu-Water Nanofluid
Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop
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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.
Keywords: Heat Transfer, Nanofluid, Shrinking Surface, Stability Analysis, Three-Dimensional Flow.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21851040 Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations
Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman
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In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.Keywords: Backward Differentiation Formula, block, secondorder.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20141039 Effect of Delay on Supply Side on Market Behavior: A System Dynamic Approach
Authors: M. Khoshab, M. J. Sedigh
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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.Keywords: Dynamic System, Lag on Supply Demand, Market Stability, Supply Demand Model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15411038 Solution of First kind Fredholm Integral Equation by Sinc Function
Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,
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Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27421037 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra
Authors: Ali Shojaei-Fard
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In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14301036 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation
Authors: Aziz Sezgin
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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.Keywords: Backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16631035 Rational Chebyshev Tau Method for Solving Natural Convection of Darcian Fluid About a Vertical Full Cone Embedded in Porous Media Whit a Prescribed Wall Temperature
Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard
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The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.
Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19281034 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method
Authors: Changqing Yang, Jianhua Hou, Beibo Qin
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A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25751033 Laminar Free Convection of Nanofluid Flow in Horizontal Porous Annulus
Authors: Manal H. Saleh
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A numerical study has been carried out to investigate the heat transfer by natural convection of nanofluid taking Cu as nanoparticles and the water as based fluid in a three dimensional annulus enclosure filled with porous media (silica sand) between two horizontal concentric cylinders with 12 annular fins of 2.4mm thickness attached to the inner cylinder under steady state conditions. The governing equations which used are continuity, momentum and energy equations under an assumptions used Darcy law and Boussinesq-s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7. The parameters affected on the system are modified Rayleigh number (10 ≤Ra*≤ 1000), fin length Hf (3, 7 and 11mm), radius ratio Rr (0.293, 0.365 and 0.435) and the volume fraction(0 ≤ ¤ò ≤ 0 .35). It was found that the average Nusselt number depends on (Ra*, Hf, Rr and φ). The results show that, increasing of fin length decreases the heat transfer rate and for low values of Ra*, decreasing Rr cause to decrease Nu while for Ra* greater than 100, decreasing Rr cause to increase Nu and adding Cu nanoparticles with 0.35 volume fraction cause 27.9% enhancement in heat transfer. A correlation for Nu in terms of Ra*, Hf and φ, has been developed for inner hot cylinder.Keywords: Annular fins, laminar free convection, nanofluid, porous media, three dimensions horizontal annulus.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24781032 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease
Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly
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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Keywords: Parkinson's disease, Step method, delay differential equation, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7231031 Investigation of Tearing in Hydroforming Process with Analytical Equations and Finite Element Method
Authors: H.Seidi, M.Jalali Azizpour, S.A.Zahedi
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Today, Hydroforming technology provides an attractive alternative to conventional matched die forming, especially for cost-sensitive, lower volume production, and for parts with irregular contours. In this study the critical fluid pressures which lead to rupture in the workpiece has been investigated by theoretical and finite element methods. The axisymmetric analysis was developed to investigate the tearing phenomenon in cylindrical Hydroforming Deep Drawing (HDD). By use of obtained equations the effect of anisotropy, drawing ratio, sheet thickness and strain hardening exponent on tearing diagram were investigated.Keywords: Hydroforming deep drawing, Pressure path, Axisymmetric analysis, Finite element simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16641030 Universal Kinetic Modeling of RAFT Polymerization using Moment Equations
Authors: Mehdi Salami-Kalajahi, Pejman Ganjeh-Anzabi, Vahid Haddadi-Asl, Mohammad Najafi
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In the following text, we show that by introducing universal kinetic scheme, the origin of rate retardation and inhibition period which observed in dithiobenzoate-mediated RAFT polymerization can be described properly. We develop our model by utilizing the method of moments, then we apply our model to different monomer/RAFT agent systems, both homo- and copolymerization. The modeling results are in an excellent agreement with experiments and imply the validity of universal kinetic scheme, not only for dithiobenzoate-mediated systems, but also for different types of monomer/RAFT agent ones.Keywords: RAFT Polymerization, Mechanism, Kinetics, Moment Equations, Modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19871029 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method
Authors: Nisha Goyal, R.K. Gupta
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This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.
Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16071028 Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder
Authors: T. V. S. Sekhar, B. Hema Sundar Raju
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Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16531027 Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
Authors: Gilbert Makanda, Roelf Sypkens
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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9021026 Spectral Investigation for Boundary Layer Flow over a Permeable Wall in the Presence of Transverse Magnetic Field
Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand
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The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11581025 A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation
Authors: Vikas Tewari, K.R. Pardasani
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Calcium is very important for communication among the neurons. It is vital in a number of cell processes such as secretion, cell movement, cell differentiation. To reduce the system of reactiondiffusion equations of [Ca2+] into a single equation, two theories have been proposed one is excess buffer approximation (EBA) other is rapid buffer approximation (RBA). The RBA is more realistic than the EBA as it considers both the mobile and stationary endogenous buffers. It is valid near the mouth of the channel. In this work we have studied the effects of different types of buffers on calcium diffusion under RBA. The novel thing studied is the effect of sodium ions on calcium diffusion. The model has been made realistic by considering factors such as variable [Ca2+], [Na+] sources, sodium-calcium exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The proposed mathematical leads to a system of partial differential equations which has been solved numerically to study the relationships between different parameters such as buffer concentration, buffer disassociation rate, calcium permeability. We have used Forward Time Centred Space (FTCS) approach to solve the system of partial differential equations.Keywords: rapid buffer approximation, sodium-calcium exchangeprotein, Sarcolemmal Calcium ATPase pump, buffer disassociationrate, forward time centred space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15041024 A Quick Prediction for Shear Behaviour of RC Membrane Elements by Fixed-Angle Softened Truss Model with Tension-Stiffening
Authors: X. Wang, J. S. Kuang
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The Fixed-angle Softened Truss Model with Tension-stiffening (FASTMT) has a superior performance in predicting the shear behaviour of reinforced concrete (RC) membrane elements, especially for the post-cracking behaviour. Nevertheless, massive computational work is inevitable due to the multiple transcendental equations involved in the stress-strain relationship. In this paper, an iterative root-finding technique is introduced to FASTMT for solving quickly the transcendental equations of the tension-stiffening effect of RC membrane elements. This fast FASTMT, which performs in MATLAB, uses the bisection method to calculate the tensile stress of the membranes. By adopting the simplification, the elapsed time of each loop is reduced significantly and the transcendental equations can be solved accurately. Owing to the high efficiency and good accuracy as compared with FASTMT, the fast FASTMT can be further applied in quick prediction of shear behaviour of complex large-scale RC structures.
Keywords: Bisection method, fixed-angle softened truss model with tension-stiffening, iterative root-finding technique, reinforced concrete membrane.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8171023 Application of Computational Intelligence Techniques for Economic Load Dispatch
Authors: S.C. Swain, S. Panda, A.K. Mohanty, C. Ardil
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This paper presents the applications of computational intelligence techniques to economic load dispatch problems. The fuel cost equation of a thermal plant is generally expressed as continuous quadratic equation. In real situations the fuel cost equations can be discontinuous. In view of the above, both continuous and discontinuous fuel cost equations are considered in the present paper. First, genetic algorithm optimization technique is applied to a 6- generator 26-bus test system having continuous fuel cost equations. Results are compared to conventional quadratic programming method to show the superiority of the proposed computational intelligence technique. Further, a 10-generator system each with three fuel options distributed in three areas is considered and particle swarm optimization algorithm is employed to minimize the cost of generation. To show the superiority of the proposed approach, the results are compared with other published methods.
Keywords: Economic Load Dispatch, Continuous Fuel Cost, Quadratic Programming, Real-Coded Genetic Algorithm, Discontinuous Fuel Cost, Particle Swarm Optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22621022 RBF- based Meshless Method for Free Vibration Analysis of Laminated Composite Plates
Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla
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The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21151021 Unconventional Calculus Spreadsheet Functions
Authors: Chahid K. Ghaddar
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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24431020 Pulsating Flow of an Incompressible Couple Stress Fluid Between Permeable Beds
Authors: T. K. V. Iyengar, Punnamchandar Bitla
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The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.
Keywords: Pulsating flow, couple stress fluid, permeable beds, mass flux, shear stress.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21161019 Stability Analysis for an Extended Model of the Hypothalamus-Pituitary-Thyroid Axis
Authors: Beata Jackowska-Zduniak
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We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14741018 Free Flapping Vibration of Rotating Inclined Euler Beams
Authors: Chih-Ling Huang, Wen-Yi Lin, Kuo-Mo Hsiao
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A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.Keywords: Flapping vibration, Inclination angle, Natural frequency, Rotating beam.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21761017 Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis
Authors: Anuar Ishak
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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. 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 mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24701016 Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach
Authors: R. Bhargava, Sonam Singh
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In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18831015 Assessment of the Effect of Feed Plate Location on Interactions for a Binary Distillation Column
Authors: A. Khelassi, R. Bendib
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The paper considers the effect of feed plate location on the interactions in a seven plate binary distillation column. The mathematical model of the distillation column is deduced based on the equations of mass and energy balances for each stage, detailed model for both reboiler and condenser, and heat transfer equations. The Dynamic Relative Magnitude Criterion, DRMC is used to assess the interactions in different feed plate locations for a seven plate (Benzene-Toluene) binary distillation column ( the feed plate is originally at stage 4). The results show that whenever we go far from the optimum feed plate position, the level of interaction augments.Keywords: Distillation column, assessment of interactions, feedplate location, DRMC.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23891014 Implicit Two Step Continuous Hybrid Block Methods with Four Off-Steps Points for Solving Stiff Ordinary Differential Equation
Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator
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In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20911013 Parallel-Distributed Software Implementation of Buchberger Algorithm
Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury
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Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18231012 New Coordinate System for Countries with Big Territories
Authors: Mohammed Sabri Ali Akresh
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The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM.
Keywords: Harmonic equations, coordinate system, projections, algorithms and parallels.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1834