Search results for: kinetic equation method

Authors: Alireza Bahramian

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High-purity TiO₂ nanoparticles (NPs) with size ranging between 50 nm and 100 nm are synthesized from titanium slag through sulphate route under sonochemical procedure. The effect of dissolution parameters such as the sulfuric acid/slag weight ratio, caustic soda concentration, digestion temperature and time, and initial particle size of the dried slag on the extraction efficiency of TiO₂ and removal of iron are examined. By optimizing the digestion conditions, a rutile TiO₂ powder with surface area of 42 m²/g and mean pore diameter of 22.4 nm were prepared. A thermo-kinetic analysis showed that the digestion temperature has an important effect, while the acid/slag weight ratio and initial size of the slag has a moderate effect on the dissolution rate. The shrinking-core model including both chemical surface reaction and surface diffusion is used to describe the leaching process. A low value of activation energy, 38.12 kJ/mol, indicates the surface chemical reaction model is a rate-controlling step. The kinetic analysis suggested a first order reaction mechanism with respect to the acid concentrations.

Keywords: TiO₂ nanoparticles, titanium slag, dissolution rate, sonochemical method, thermo-kinetic study

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: Ude N. Callistus, Amulu F. Ndidi, Onukwuli D. Okechukwu, Amulu E. Patrick

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Power law approximation was used in this study to evaluate the reaction orders of calcium oxide, CaO catalyzed transesterification of refined cottonseed oil and methanol. The kinetics study was carried out at temperatures of 45, 55 and 65 ^oC. The kinetic parameters such as reaction order 2.02 and rate constant 2.8 hr^-1g^-1cat, obtained at the temperature of 65 ^oC best fitted the kinetic model. The activation energy, Ea obtained was 127.744 KJ/mol. The results indicate that the transesterification reaction of the refined cottonseed oil using calcium oxide catalyst is approximately second order reaction.

Keywords: refined cottonseed oil, transesterification, CaO, heterogeneous catalysts, kinetic model

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muhammad Younis

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In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: O. Abusaeeda, J. P. O. Evans, D. Downes

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We demonstrate the synthesis of intermediary views within a sequence of X-ray images that exhibit depth from motion or kinetic depth effect in a visual display. Each synthetic image replaces the requirement for a linear X-ray detector array during the image acquisition process. Scale invariant feature transform, SIFT, in combination with epipolar morphing is employed to produce synthetic imagery. Comparison between synthetic and ground truth images is reported to quantify the performance of the approach. Our work is a key aspect in the development of a 3D imaging modality for the screening of luggage at airport checkpoints. This programme of research is in collaboration with the UK Home Office and the US Dept. of Homeland Security.

Keywords: X-ray, kinetic depth, KDE, view synthesis

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Authors: Khushboo Bhavsar, Nisha K. Shah, Neha Parekh

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The status of wastewater treatment needs a novel and quick method for treating the wastewater containing ammoniacal nitrogen. Adsorption behavior of ammoniacal nitrogen from wastewater using the nanoparticles loaded coconut coir was investigated in the present work. Manganese Oxide (MnO2) and Zinc Oxide (ZnO) nanoparticles were prepared and used for the further adsorption study. Manganese nanoparticles loaded coconut coir (MNLCC) and Zinc nanoparticles loaded coconut coir (ZNLCC) were prepared via a simple method and was fully characterized. The properties of both MNLCC and ZNLCC were characterized by Scanning electron microscopy, Fourier Transform Infrared Spectroscopy and X-ray diffraction. Adsorption characteristics were studied using batch technique considering various parameters like pH, adsorbent dosage, time, temperature and agitation time. The NH3-N adsorption process for MNLCC and ZNLCC was thoroughly studied from both kinetic and equilibrium isotherm view-points. The results indicated that the adsorption efficiency of ZNLCC was better when compared to MNLCC. The adsorption kinetics at different experimental conditions showed that second order kinetic model best fits ensuring the monovalent binding sites existing in the present experimental system. The outcome of the entire study suggests that the ZNLCC can be a smart option for the treatment of the ammoniacal nitrogen containing wastewater.

Keywords: ammoniacal nitrogen, MnO2, Nanoparticles, ZnO

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Authors: Annarita Zarrillo

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This research is part of adaptive architecture, reflecting the evolution that the world of architectural design is going through. Today's architecture is no longer seen as a static system but, conversely, as a dynamic system that changes in response to the environment and the needs of users. One of the major forms of adaptivity is represented by kinetic structures. This study aims to underline the importance of experimentation on physical scale models for the study of dynamic structures and to present the case study of a modular kinetic structure designed through the use of parametric design software and created as a prototype in the laboratories of the Royal Danish Academy in Copenhagen.

Keywords: adaptive architecture, architectural application, kinetic structures, modular prototype

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Varvara Roubtsova, Mohamed Chekired

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Recent studies on the numerical simulation of geotechnical problems show the importance of considering the soil micro-structure. At this scale, soil is a discrete particle medium where the particles can interact with each other and with water flow under external forces, structure loads or natural events. This paper presents research conducted in a virtual laboratory named SiGran, developed at IREQ (Institut de recherche d’Hydro-Quebec) for the purpose of investigating a broad range of problems encountered in geotechnics. Using Discrete Element Method (DEM), SiGran simulated granular materials directly by applying Newton’s laws to each particle. The water flow was simulated by using Marker and Cell method (MAC) to solve the full form of Navier-Stokes’s equation for non-compressible viscous liquid. In this paper, examples of numerical simulation and their comparisons with real experiments have been selected to show the complexity of geotechnical research at the micro level. These examples describe transient flows into a porous medium, interaction of particles in a viscous flow, compacting of saturated and unsaturated soils and the phenomenon of liquefaction under seismic load. They also provide an opportunity to present SiGran’s capacity to compute the distribution and evolution of energy by type (particle kinetic energy, particle internal elastic energy, energy dissipated by friction or as a result of viscous interaction into flow, and so on). This work also includes the first attempts to apply micro discrete results on a macro continuum level where the Smoothed Particle Hydrodynamics (SPH) method was used to resolve the system of governing equations. The material behavior equation is based on the results of simulations carried out at a micro level. The possibility of combining three methods (DEM, MAC and SPH) is discussed.

Keywords: discrete element method, marker and cell method, numerical simulation, multi-scale simulations, smoothed particle hydrodynamics

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: BenedictI Ita, Etido P. Inyang

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In this work, the resolutions of the N-dimensional Schrödinger equation with the screened modified Kratzerplus inversely quadratic Yukawa potential (SMKIQYP) have been obtained with the Greene-Aldrich approximation scheme using the Nikiforov-Uvarov method. The eigenvalues and the normalized eigenfunctions are obtained. We then apply the energy spectrum to study four (HCl, N₂, NO, and CO) diatomic molecules. The results show that the energy spectra of these diatomic molecules increase as quantum numbers increase. The energy equation was also used to calculate the partition function and other thermodynamic properties. We predicted the partition function of CO and NO. To check the accuracy of our work, the special case (Modified Kratzer and screened Modified Kratzer potentials) of the collective potential energy eigenvalues agrees excellently with the existing literature.

Keywords: Schrödinger equation, Nikiforov-Uvarov method, modified screened Kratzer, inversely quadratic Yukawa potential, diatomic molecules

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Sirada Sripinun

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This work studied the isomerization of 1-butene over hydrotalcite catalyst. The experiments were conducted at various gas hourly space velocity (GHSV), reaction temperature, and feed concentration. No catalyst deactivation was observed over the reaction time of 16 hours. Two major reaction products were trans-2-butene and cis-2-butene. The reaction temperature played an important role on the reaction selectivity. At high operating temperatures, the selectivity of trans-2-butene was higher than the selectivity of cis-2-butene while it was opposite at a lower reaction temperature. In the range of operating conditions, the maximum conversion of 1-butene was found at 74% when T = 673 K and GHSV = 4 m3/h/kg-cat with trans- and cis-2-butene selectivities of 54% and 46% respectively. Finally, the kinetic parameters of the reaction were determined.

Keywords: hydrotalcite, isomerization, kinetic, 1-butene

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Authors: K. I. M. Guerra, L. A. P. Silva, J. C. Leal

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This study aims to understand with more amplitude and clarity the behavior of a porous medium where a pressure wave travels, translated into relative displacements inside the material, using mathematical tools derived from topology and symplectic geometry. The paper starts with a given partial differential equation based on the continuity and conservation theorems to describe the traveling wave through the porous body. A solution for this equation is proposed after all boundary, and initial conditions are fixed, and it’s accepted that the solution lies in a manifold U of purely spatial dimensions and that is embedded in the Real n-dimensional manifold, with spatial and kinetic dimensions. It’s shown that the U manifold of lower dimensions than IRna, where it is embedded, inherits properties of the vector spaces existing inside the topology it lies on. Then, a second manifold (U*), embedded in another space called IRnb of stress dimensions, is proposed and there’s a non-degenerative function that maps it into the U manifold. This relation is proved as a transformation in between two corresponding admissible solutions of the differential equation in distinct dimensions and properties, leading to a more visual and intuitive understanding of the whole dynamic process of a stress wave through a porous medium and also highlighting the dimensional invariance of Terzaghi’s theory for any coordinate system.

Keywords: poremechanics, soil dynamics, symplectic geometry, wave propagation

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Hamid Hamli Benzahar

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The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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Authors: Stephen Kirkup

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This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: Hakimeh Sharififard, Mansooreh Soleimani

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In this work, the magnetic activated carbon nanocomposite (Fe-CAC) has been synthesized by anchorage iron hydr(oxide) nanoparticles onto commercial activated carbon (CAC) surface and characterized using BET, XRF, SEM techniques. The influence of various removal parameters such as pH, contact time and initial concentration of vanadium on vanadium removal was evaluated using CAC and Fe-CAC in batch method. The sorption isotherms were studied using Langmuir, Freundlich and Dubinin–Radushkevich (D–R) isotherm models. These equilibrium data were well described by the Freundlich model. Results showed that CAC had the vanadium adsorption capacity of 37.87 mg/g, while the Fe-AC was able to adsorb 119.01 mg/g of vanadium. Kinetic data was found to confirm pseudo-second-order kinetic model for both adsorbents.

Keywords: magnetic activated carbon, remove, vanadium, nanocomposite, freundlich

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Authors: Warda Nasir, M. N. S. Qureshi

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Whistler waves are right handed circularly polarized waves and are frequently observed in space plasmas. The Low frequency branch of the Whistler waves having frequencies nearly around 100 Hz, known as Lion roars, are frequently observed in magnetosheath. Another feature of the magnetosheath is the observations of flat top electron distributions with single as well as two electron populations. In the past, lion roars were studied by employing kinetic model using classical bi-Maxwellian distribution function, however, could not be justified both on quantitatively as well as qualitatively grounds. We studied Whistler waves by employing kinetic model using non-Maxwellian distribution function such as the generalized (r,q) distribution function which is the generalized form of kappa and Maxwellian distribution functions by employing kinetic theory with single or two electron populations. We compare our results with the Cluster observations and found good quantitative and qualitative agreement between them. At times when lion roars are observed (not observed) in the data and bi-Maxwellian could not provide the sufficient growth (damping) rates, we showed that when generalized (r,q) distribution function is employed, the resulted growth (damping) rates exactly match the observations.

Keywords: kinetic model, whistler waves, non-maxwellian distribution function, space plasmas

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: L. Torchane

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This study is devoted to defining the optimal conditions for the nitriding of pure iron at atmospheric pressure by using NH3-Ar-C3H8 gas mixtures. After studying the mechanisms of phase formation and mass transfer at the gas-solid interface, a mathematical model is developed in order to predict the nitrogen transfer rate in the solid, the ε-carbonitride layer growth rate and the nitrogen and carbon concentration profiles. In order to validate the model and to show its possibilities, it is compared with thermogravimetric experiments, analyses and metallurgical observations (X-ray diffraction, optical microscopy and electron microprobe analysis). Results obtained allow us to demonstrate the sound correlation between the experimental results and the theoretical predictions.

Keywords: gaseous nitrocarburizing, kinetic model, diffusion, layer growth kinetic

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Authors: A. A. Khodadadi, S. C. Ravaj, B. D. Tavildari, M. B. Abdolahi

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The adsorption properties of local bentonite (Semnan Iran) and purified prepared from this bentonite towards Sr2+ adsorption, were investigated by batch equilibration. The influence of equilibration time, adsorption isotherms, kinetic adsorption, solution pH, and presence of EDTA and NaCl on these properties was studied and discussed. Kinetic data were found to be well fitted with a pseudo-second order kinetic model. Sr2+ is preferably adsorbed by bentonite and purified bentonite. The D-R isotherm model has the best fit with experimental data than other adsorption isotherm models. The maximum adsorption of Sr2+ representing the highest negative charge density on the surface of the adsorbent was seen at pH 12. Presence of EDTA and NaCl decreased the amount of Sr2+ adsorption.

Keywords: bentonite, purified bentonite, Sr2+, equilibrium isotherm, kinetics

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