Search results for: kinetic equation

Authors: H. Sütçü, C. Efe

Abstract:

In this study, pyrolysis characteristics of Dursunbey-Balıkesir lignite and its pyrolysis kinetics are examined. The pyrolysis experiments carried out at three different heating rates are performed by using thermogravimetric method. Kinetic parameters are calculated by Coats & Redfern kinetic model and the degree of pyrolysis process is determined for each of the heating rate.

Keywords: lignite, thermogravimetric analysis, pyrolysis, kinetics

Procedia PDF Downloads 367

Authors: Kebede Gamo Sebehanie, Olu Emmanuel Femi, Alberto Velázquez Del Rosario, Abubeker Yimam Ali, Gudeta Jafo Muleta

Abstract:

Water pollution is one of the most serious worldwide issues today. Among water pollution, heavy metals are becoming a concern to the environment and human health due to their non-biodegradability and bioaccumulation. In this study, a magnetite-cellulose nanocomposite derived from renewable resources is employed for hexavalent chromium elimination by adsorption. Magnetite nanoparticles were synthesized directly from iron ore using solvent extraction and co-precipitation technique. Cellulose nanofiber was extracted from sugarcane bagasse using the alkaline treatment and acid hydrolysis method. Before and after the adsorption process, the MNPs-CNF composites were evaluated using X-ray diffraction (XRD), Scanning electron microscope (SEM), Fourier transform infrared (FTIR), and Vibrator sample magnetometer (VSM), and Thermogravimetric analysis (TGA). The impacts of several parameters such as pH, contact time, initial pollutant concentration, and adsorbent dose on adsorption efficiency and capacity were examined. The kinetic and isotherm adsorption of Cr (VI) was also studied. The highest removal was obtained at pH 3, and it took 80 minutes to establish adsorption equilibrium. The Langmuir and Freundlich isotherm models were used, and the experimental data fit well with the Langmuir model, which has a maximum adsorption capacity of 8.27 mg/g. The kinetic study of the adsorption process using pseudo-first-order and pseudo-second-order equations revealed that the pseudo-second-order equation was more suited for representing the adsorption kinetic data. Based on the findings, pure MNPs and MNPs-CNF nanocomposites could be used as effective adsorbents for the removal of Cr (VI) from wastewater.

Keywords: magnetite-cellulose nanocomposite, hexavalent chromium, adsorption, sugarcane bagasse

Procedia PDF Downloads 129

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

Procedia PDF Downloads 201

Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

Abstract:

In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

Procedia PDF Downloads 306

Authors: Anju Kumari, R. P. Sharma

Abstract:

The localization of Kinetic Alfvén Wave (KAW) caused by finite amplitude background density fluctuations has been studied in intermediate beta plasma. KAW breaks up into localized large amplitude structures when perturbed by MHD fluctuations of the medium which are in the form of magnetosonic waves. Numerical simulation has been performed to analyse the localized structures and resulting turbulent spectrum of KAW applicable to magnetopause. Simulation results reveal that power spectrum deviates from Kolmogorov scaling at the transverse size of KAW, equal to ion gyroradius. Steepening of power spectrum at shorter wavelengths may be accountable for heating and acceleration of the plasma particles. The obtained results are compared with observations collected from the THEMIS spacecraft in magnetopause.

Keywords: Kinetic Alfvén Wave (KAW), localization, turbulence, turbulent spectrum

Procedia PDF Downloads 493

Authors: Marina Borgert Moraes, Gilmar Patrocinio Thim

Abstract:

It is still unknown how the presence of nanoparticles such as graphene oxide (GO) or carbon nanotubes (CNT) influence the curing process and the final mechanical properties as well. In this work, kinetic and mechanical properties of the nanocomposites were analyzed, where the kinetic process was followed by DSC and the mechanical properties by DMA as well as mechanical tests. Initially, CNT was annealed at high temperature (1800 °C) under vacuum atmosphere, followed by a chemical treatment using acids and ethylenediamine. GO was synthesized through chemical route, washed clean, dried and ground to #200. The presence of functional groups on CNT and GO surface was confirmed by XPS spectra and FT-IR. Then, nanoparticles and acetone were mixed by sonication in order to obtain the composites. DSC analyses were performed on samples with different curing cycles (1h 80 °C + 2h 120 °C; 3h 80 °C + 2h 120 °C; 5h 80 °C) and samples with different times at constant temperature (120 °C). Mechanical tests were performed according to ASTM D638 and D790. Results showed that the kinetic process and the mechanical strength are very dependent on the presence of graphene and functionalized-CNT in the nanocomposites, and the GO reinforced samples had a slightly bigger improvement compared to functionalized CNT.

Keywords: carbon nanotube, epoxy resin, graphene oxide, nanocomposite

Procedia PDF Downloads 262

Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

Procedia PDF Downloads 187

Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

Abstract:

D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

Procedia PDF Downloads 344

Authors: Weiping Liu

Abstract:

This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

Procedia PDF Downloads 406

Authors: Saeed Moarrefi, Shou-Han Zhou, Liyuan Fan

Abstract:

Coupling with solid oxide fuel cells, methane dry reforming is a promising pathway for energy production while mitigating carbon emissions. However, the influence of carbon dioxide and electrochemical reactions on the internal dry reforming reaction within the fuel cells remains debatable, requiring accurate kinetic models to describe the internal reforming behaviors. We employed the Power-Law and Langmuir Hinshelwood–Hougen Watson models in an electrolyte-supported solid oxide fuel cell with a NiO-GDC-YSZ anode. The current density used in this study ranges from 0 to 1000 A/m2 at 973 K to 1173 K to estimate various kinetic parameters. The influence of the electrochemical reactions on the adsorption terms, the equilibrium of the reactions, the activation energy, the pre-exponential factor of the rate constant, and the adsorption equilibrium constant were studied. This study provides essential parameters for future simulations and highlights the need for a more detailed examination of reforming kinetic models.

Keywords: dry reforming kinetics, Langmuir Hinshelwood–Hougen Watson, power-law, SOFC

Procedia PDF Downloads 22

Authors: Benedict Ita, Peter Okoi

Abstract:

In this work, the concept of the extended Nikiforov-Uvarov technique is discussed and employed to obtain the exact bound state energy eigenvalues and the corresponding normalized eigenfunctions of the inverse square root potential. With expressions for the exact energy eigenvalues and corresponding eigenfunctions, the expressions for the expectation values of the inverse separation-squared, kinetic energy, and the momentum-squared of the potential are presented using the Hellmann Feynman theorem. For visualization, algorithms written and implemented in Python language are used to generate tables and plots for l-states of the energy eigenvalues and some expectation values. The results obtained here may find suitable applications in areas like atomic and molecular physics, chemical physics, nuclear physics, and solid-state physics.

Keywords: Schrodinger equation, Nikoforov-Uvarov method, inverse square root potential, diatomic molecules, Python programming, Hellmann-Feynman theorem, second order differential equation, matrix algebra

Procedia PDF Downloads 19

Authors: Abhishek Soni, A. Kumaraswamy, M. S. Mahesh

Abstract:

Bullet penetration in steel plate is investigated with the help of three-dimensional, non-linear, transient, dynamic, finite elements analysis using explicit time integration code LSDYNA. The effect of large strain, strain-rate and temperature at very high velocity regime was studied from number of simulations of semi-spherical nose shape bullet penetration through single layered circular plate with 2 mm thickness at impact velocities of 500, 1000, and 1500 m/s with the help of Johnson Cook material model. Mie-Gruneisen equation of state is used in conjunction with Johnson Cook material model to determine pressure-volume relationship at various points of interests. Two material models viz. Plastic-Kinematic and Johnson- Cook resulted in different deformation patterns in steel plate. It is observed from the simulation results that the velocity drop and loss of kinetic energy occurred very quickly up to perforation of plate, after that the change in velocity and changes in kinetic energy are negligibly small. The physics behind this kind of behaviour is presented in the paper.

Keywords: AISI 4340 steel, ballistic impact simulation, bullet penetration, non-linear FEM

Procedia PDF Downloads 208

Authors: Imene Atek, Abed M. Affoune, Hubert Girault, Pekka Peljo

Abstract:

Due to the need for a rigorous mathematical model that can help to estimate kinetic properties for soluble-insoluble systems, through voltammetric experiments, a Nicholson Semi Analytical Approach was used in this work for modeling and prediction of theoretical linear sweep voltammetry responses for reversible, quasi reversible or irreversible electron transfer reactions. The redox system of interest is a one-step metal electrodeposition process. A rigorous analysis of simulated linear scan voltammetric responses following variation of dimensionless factors, the rate constant and charge transfer coefficients in a broad range was studied and presented in the form of the so called kinetic zones diagrams. These kinetic diagrams were divided into three kinetics zones. Interpreting these zones leads to empirical mathematical models which can allow the experimenter to determine electrodeposition reactions kinetics whatever the degree of reversibility. The validity of the obtained results was tested and an excellent experiment–theory agreement has been showed.

Keywords: electrodeposition, kinetics diagrams, modeling, voltammetry

Procedia PDF Downloads 141

Authors: Zh. Saffari, A. Naeimi, M. S. Ekrami-Kakhki, Kh. Khandan-Barani

Abstract:

The textile industries are becoming a major source of environmental contamination because an alarming amount of dye pollutants are generated during the dyeing processes. Organic dyes are one of the largest pollutants released into wastewater from textile and other industrial processes, which have shown severe impacts on human physiology. Nano-structure compounds have gained importance in this category due their anticipated high surface area and improved reactive sites. In recent years several novel adsorbents have been reported to possess great adsorption potential due to their enhanced adsorptive capacity. Nano-MnO2 has great potential applications in environment protection field and has gained importance in this category because it has a wide variety of structure with large surface area. The diverse structures, chemical properties of manganese oxides are taken advantage of in potential applications such as adsorbents, sensor catalysis and it is also used for wide catalytic applications, such as degradation of dyes. In this study, adsorption of Methyl Violet (MV) dye from aqueous solutions onto MnO2 nanoparticles (MNP) has been investigated. The surface characterization of these nano particles was examined by Particle size analysis, Scanning Electron Microscopy (SEM), Fourier Transform Infrared (FTIR) spectroscopy and X-Ray Diffraction (XRD). The effects of process parameters such as initial concentration, pH, temperature and contact duration on the adsorption capacities have been evaluated, in which pH has been found to be most effective parameter among all. The data were analyzed using the Langmuir and Freundlich for explaining the equilibrium characteristics of adsorption. And kinetic models like pseudo first- order, second-order model and Elovich equation were utilized to describe the kinetic data. The experimental data were well fitted with Langmuir adsorption isotherm model and pseudo second order kinetic model. The thermodynamic parameters, such as Free energy of adsorption (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°) were also determined and evaluated.

Keywords: MnO2 nanoparticles, adsorption, methyl violet, isotherm models, kinetic models, surface chemistry

Procedia PDF Downloads 258

Authors: Jean C. G. Silva, Kaline N. Ferreira, Rennio F. Sena, Flavio L. H. Silva

Abstract:

The Prosopis juliflora (called algaroba in Northeastern Region of Brazil) is a species of medium to large size that can reach 18 meters high, being typical of arid and semi-arid regions by to requirement less water to survive; this is a fundamental attribute from its adaptation. It's considered of multiple uses, because the trunk, the fruit, and the algaroba pods are utilized for several purposes, among them, the production of wood from lumber mill, charcoal, alcohol, animal and human consumption, being hence, a culture of economic and social value. The use of waste Prosopis juliflora can be carried out for like pyrolysis and gasification processes, in order to energy production in those regions where it is grown. Thus this study aims to characterize the residue of the algaroba pods and evaluate the kinetic parameters, activation energy (Ea) and pre-exponential factor (k0), the devolatilization process through the data obtained from TG/DTG curves with different levels of heating rates. At work was used the heating rates of 5 K.min-1, 10 K.min-1, 15 K.min-1, 20 K.min-1 and 30 K.min-1, in inert nitrogen atmosphere (99.997%) under a flow of 40 ml.min-1. The kinetic parameters were obtained using the methods of Friedman and Ozawa-Flynn-Wall.

Keywords: activation energy, devolatilization, kinetic parameters, waste

Procedia PDF Downloads 388

Authors: Ozan Kahraman, Hao Feng

Abstract:

Several models such as Weibull, Modified Gompertz, Biphasic linear, and Log-logistic models have been proposed in order to describe non-linear inactivation kinetics and used to fit non-linear inactivation data of several microorganisms for inactivation by heat, high pressure processing or pulsed electric field. First-order kinetic parameters (D-values and z-values) have often been used in order to identify microbial inactivation by non-thermal processing methods such as ultrasound. Most ultrasonic inactivation studies employed first-order kinetic parameters (D-values and z-values) in order to describe the reduction on microbial survival count. This study was conducted to analyze the E. coli O157:H7 inactivation data by using five microbial survival models (First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic). First-order, Weibull, Modified Gompertz, Biphasic linear and Log-logistic kinetic models were used for fitting inactivation curves of Escherichia coli O157:H7. The residual sum of squares and the total sum of squares criteria were used to evaluate the models. The statistical indices of the kinetic models were used to fit inactivation data for E. coli O157:H7 by MTS at three temperatures (40, 50, and 60 0C) and three pressures (100, 200, and 300 kPa). Based on the statistical indices and visual observations, the Weibull and Biphasic models were best fitting of the data for MTS treatment as shown by high R2 values. The non-linear kinetic models, including the Modified Gompertz, First-order, and Log-logistic models did not provide any better fit to data from MTS compared the Weibull and Biphasic models. It was observed that the data found in this study did not follow the first-order kinetics. It is possibly because of the cells which are sensitive to ultrasound treatment were inactivated first, resulting in a fast inactivation period, while those resistant to ultrasound were killed slowly. The Weibull and biphasic models were found as more flexible in order to determine the survival curves of E. coli O157:H7 treated by MTS on apple-carrot juice.

Keywords: Weibull, Biphasic, MTS, kinetic models, E.coli O157:H7

Procedia PDF Downloads 366

Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

Procedia PDF Downloads 221

Authors: Joy Marie Mora, Mark Daniel De Luna, Tsair-Wang Chung

Abstract:

Transesterification reaction of soybean oil with methanol was carried out to produce fatty acid methyl esters (FAME) using calcined alkali metal (Na and Li) supported by pumice silica as the solid base catalyst. Pumice silica catalyst was activated by loading alkali metal ions to its surface via an ion-exchange method. Response surface methodology (RSM) in combination with Box-Behnken design (BBD) was used to optimize the operating parameters in biodiesel production, namely: reaction temperature, methanol to oil molar ratio, reaction time, and catalyst concentration. Using the optimized sets of parameters, FAME yields using sodium and lithium silicate catalysts were 98.80% and 98.77%, respectively. A pseudo-first order kinetic equation was applied to evaluate the kinetic parameters of the reaction. The prepared catalysts were characterized by several techniques such as X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Brunauer-Emmett-Teller (BET) sorptometer, and scanning electron microscopy (SEM). In addition, the reusability of the catalysts was successfully tested in two subsequent cycles.

Keywords: alkali metal, biodiesel, Box-Behnken design, heterogeneous catalyst, kinetics, optimization, pumice, transesterification

Procedia PDF Downloads 306

Authors: M. Rajabi, O. Moradi

Abstract:

In this study, removal of Nickel and Zinc by graphene oxide and functionalized graphene oxide–gelaycin surfaces was examined. Amino group was added to surface of graphene oxide to produced functionalized graphene oxide–gelaycin. Effect of contact time and initial concentration of Ni (II) and Zn(II) ions were studied. Results showed that with increase of initial concentration of Ni (II) and Zn(II) adsorption capacity was increased. After 50 min has not a large change at adsorption capacity therefore, 50 min was selected as optimaze time. Scanning electron microscope (SEM) and fourier transform infrared (FT-IR) spectroscopy spectra used for the analysis confirmed the successful fictionalization of the Graphene oxide surface. Adsorption experiments of Ni (II) and Zn(II) ions graphene oxide and functionalized graphene oxide–gelaycin surfaces fixed at 298 K and pH=6. The Pseudo Firs-order and the Pseudo Second-order (types I, II, III and IV) kinetic models were tested for adsorption process and results showed that the kinetic parameters best fits with to type (I) of pseudo-second-order model because presented low X2 values and also high R2 values.

Keywords: graphene oxide, gelaycin, nickel, zinc, adsorption, kinetic, graphene oxide, gelaycin, nickel, zinc, adsorption, kinetic

Procedia PDF Downloads 307

Authors: A. Zerarka, W. Djoudi

Abstract:

We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

Procedia PDF Downloads 657

Authors: Abimbola M. Enitan, J. Adeyemo

Abstract:

Anaerobic modeling is a useful tool to describe and simulate the condition and behaviour of anaerobic treatment units for better effluent quality and biogas generation. The present investigation deals with the anaerobic treatment of brewery wastewater with varying organic loads. The chemical oxygen demand (COD) and total suspended solids (TSS) of the influent and effluent of the bioreactor were determined at various retention times to generate data for kinetic coefficients. The bio-kinetic coefficients in the modified Stover–Kincannon kinetic and methane generation models were determined to study the performance of anaerobic digestion process. At steady-state, the determination of the kinetic coefficient (K), the endogenous decay coefficient (Kd), the maximum growth rate of microorganisms (µmax), the growth yield coefficient (Y), ultimate methane yield (Bo), maximum utilization rate constant Umax and the saturation constant (KB) in the model were calculated to be 0.046 g/g COD, 0.083 (dˉ¹), 0.117 (d-¹), 0.357 g/g, 0.516 (L CH4/gCODadded), 18.51 (g/L/day) and 13.64 (g/L/day) respectively. The outcome of this study will help in simulation of anaerobic model to predict usable methane and good effluent quality during the treatment of industrial wastewater. Thus, this will protect the environment, conserve natural resources, saves time and reduce cost incur by the industries for the discharge of untreated or partially treated wastewater. It will also contribute to a sustainable long-term clean development mechanism for the optimization of the methane produced from anaerobic degradation of waste in a close system.

Keywords: brewery wastewater, methane generation model, environment, anaerobic modeling

Procedia PDF Downloads 270

Authors: Hebert Montegranario, Mauricio Londoño

Abstract:

Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

Procedia PDF Downloads 547

Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

Procedia PDF Downloads 497

Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

Abstract:

Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

Procedia PDF Downloads 517

Authors: Seyed Sadegh Naseralavi

Abstract:

This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

Procedia PDF Downloads 283

Authors: Johnson Oladele Fatokun, I. P. Akpan

Abstract:

In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

Procedia PDF Downloads 418

Authors: Y. S. Shen, B. H. Liao

Abstract:

This study aimed to develop the design equation of a laminar-falling-film-slurry (LFFS) type photoreactor for the treatment of organic wastewaters containing isopropyl alcohol (IPA) by VUV-based advanced oxidation processes (AOPs). The photoreactor design equations were established by combining with the chemical kinetics of the photocatalytic system, light absorption model within the photoreactor, and was used to predict the decomposition of IPA in aqueous solutions in the photoreactors of different geometries at various operating conditions (volumetric flow rate, oxidants, catalysts, solution pH values, UV light intensities, and initial concentration of pollutants) to verify its rationality and feasibility. By the treatment of the LFFS-VUV only process, it was found that the decomposition rates of IPA in aqueous solutions increased with the increase of volumetric flow rate, VUV light intensity, dosages of TiO2 and H2O2. The removal efficiencies of IPA by photooxidation processes were in the order: VUV/H2O2>VUV/TiO2/H2O2>VUV/TiO2>VUV only. In VUV, VUV/H2O2, VUV/TiO2/H2O2 processes, integrating with the reaction kinetic equations of IPA, the mass conservation equation and the linear light source model, the photoreactor design equation can reasonably to predict reaction behaviors of IPA at various operating conditions and to describe the concentration distribution profiles of IPA within photoreactors.The results of this research can be useful basis for the future application of the homogeneous and heterogeneous VUV-based advanced oxidation processes.

Keywords: isopropyl alcohol, photoreactor design, VUV, AOPs

Procedia PDF Downloads 377

Authors: Kirti Singh, Kesheo Prasad

Abstract:

A 3D Acoustic Doppler velocimeter was used in the current investigation to quantify the mean and turbulence characteristics in non-uniform open-channel flows. Results are obtained from studies done in the laboratory, analysing the behavior of sand particles under turbulent open channel flow conditions flowing through rough, porous beds. Data obtained from ADV is used to calculate turbulent flow characteristics, Reynolds stresses and turbulent kinetic energy. Theoretical formulations for the distribution of Reynolds stress and the vertical velocity have been constructed using the Reynolds equation and the continuity equation of 2D open-channel flow. The measured Reynolds stress profile and the vertical velocity are comparable with the derived expressions. This study uses the Navier-Stokes equations for analysing the behavior of the vertical velocity profile in the dominant region of full-fledged turbulent flows in open channels, and it gives a new origination of the profile. For both wide and narrow open channels, this origination can estimate the time-averaged primary velocity in the turbulent boundary layer's outer region.

Keywords: turbulence, bed roughness, logarithmic law, shear stress correlations, ADV, Reynolds shear stress

Procedia PDF Downloads 107

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

Procedia PDF Downloads 153

Authors: Narumol Chintaganun

Abstract:

In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

Procedia PDF Downloads 557