Search results for: Volterra integro-differential equations

Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was anticipated using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient energy equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: participating media, finite volume method, radiation coupled with conduction, heat transfer

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Authors: Amin Noor, Roslinda Nazar, Norihan Md. Arifin

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In this paper, a numerical and theoretical study has been performed for the stagnation-point boundary layer flow and heat transfer towards a shrinking sheet in a nanofluid. The mathematical nanofluid 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. Numerical results are obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction Φ, the shrinking parameter λ and the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that solutions do not exist for larger shrinking rates and dual (upper and lower branch) solutions exist when λ < -1.0. A stability analysis has been performed to show which branch solutions are stable and physically realizable. It is also found that the upper branch solutions are stable while the lower branch solutions are unstable.

Keywords: heat transfer, nanofluid, shrinking sheet, stability analysis, stagnation-point flow

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Authors: Mostefa Hamrat, Bensaid Boulekbache, Mohamed Chemrouk, Sofiane Amziane

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The paper presents the results of an experimental work on the flexural behaviour of two types of concrete in terms of the progressive cracking process until failure and the crack opening, and beam deflection, using Digital Image Correlation (DIC) technique. At serviceability limit states, comparisons of the building code equations and the equations developed by some researchers for the short-term deflections and crack widths have been made using the reinforced concrete test beams. The experimental results show that the addition of steel fibers increases the first cracking load and amplify the number of cracks that conducts to a remarkable decreasing in the crack width with an increasing in ductility. This study also shows that there is a good agreement between the deflection values for RC beams predicted by the major codes (Eurocode2, ACI 318, and the CAN/CSA-S806) and the experimental results for beams with steel fibers at service load. The most important added benefit of the DIC technique is that it allows detecting the first crack with a high precision easily measures the crack opening and follows the progressive cracking process until failure of reinforced concrete members.

Keywords: beams, digital image correlation (DIC), deflection, crack width, serviceability, codes provisions

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Authors: Fatma Mohamed Magdy Badr El Dine, Amr Mohamed Abd Allah

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Introduction: Age estimation of individuals is one of the crucial steps in forensic practice. Different traditional methods rely on the length of the diaphysis of long bones of limbs, epiphyseal-diaphyseal union, fusion of the primary ossification centers as well as dental eruption. However, there is a growing need for the development of precise and reliable methods to estimate age, especially in cases where dismembered corpses, burnt bodies, purified or fragmented parts are recovered. Teeth are the hardest and indestructible structure in the human body. In recent years, assessment of pulp/tooth area ratio, as an indirect quantification of secondary dentine deposition has received a considerable attention. However, scanty work has been done in Egypt in terms of applicability of pulp/tooth ratio for age estimation. Aim of the Work: The present work was designed to assess the Cameriere’s method for age estimation from pulp/tooth ratio of maxillary canines, central and lateral incisors among a sample from Egyptian population. In addition, to formulate regression equations to be used as population-based standards for age determination. Material and Methods: The present study was conducted on 270 peri-apical X-rays of maxillary canines, central and lateral incisors (collected from 131 males and 139 females aged between 19 and 52 years). The pulp and tooth areas were measured using the Adobe Photoshop software program and the pulp/tooth area ratio was computed. Linear regression equations were determined separately for canines, central and lateral incisors. Results: A significant correlation was recorded between the pulp/tooth area ratio and the chronological age. The linear regression analysis revealed a coefficient of determination (R² = 0.824 for canine, 0.588 for central incisor and 0.737 for lateral incisor teeth). Three regression equations were derived. Conclusion: As a conclusion, the pulp/tooth ratio is a useful technique for estimating age among Egyptians. Additionally, the regression equation derived from canines gave better result than the incisors.

Keywords: age determination, canines, central incisors, Egypt, lateral incisors, pulp/tooth ratio

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Authors: C. Yin, B. Zhang, Y. Liu, J. Cai

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Airborne EM (AEM) is an effective geophysical exploration tool, especially suitable for ridged mountain areas. In these areas, topography will have serious effects on AEM system responses. However, until now little study has been reported on topographic effect on airborne EM systems. In this paper, an edge-based unstructured finite-element (FE) method is developed for 3D topographic modeling for both frequency and time-domain airborne EM systems. Starting from the frequency-domain Maxwell equations, a vector Helmholtz equation is derived to obtain a stable and accurate solution. Considering that the AEM transmitter and receiver are both located in the air, the scattered field method is used in our modeling. The Galerkin method is applied to discretize the Helmholtz equation for the final FE equations. Solving the FE equations, the frequency-domain AEM responses are obtained. To accelerate the calculation speed, the response of source in free-space is used as the primary field and the PARDISO direct solver is used to deal with the problem with multiple transmitting sources. After calculating the frequency-domain AEM responses, a Hankel’s transform is applied to obtain the time-domain AEM responses. To check the accuracy of present algorithm and to analyze the characteristic of topographic effect on airborne EM systems, both the frequency- and time-domain AEM responses for 3 model groups are simulated: 1) a flat half-space model that has a semi-analytical solution of EM response; 2) a valley or hill earth model; 3) a valley or hill earth with an abnormal body embedded. Numerical experiments show that close to the node points of the topography, AEM responses demonstrate sharp changes. Special attentions need to be paid to the topographic effects when interpreting AEM survey data over rugged topographic areas. Besides, the profile of the AEM responses presents a mirror relation with the topographic earth surface. In comparison to the topographic effect that mainly occurs at the high-frequency end and early time channels, the EM responses of underground conductors mainly occur at low frequencies and later time channels. For the signal of the same time channel, the dB/dt field reflects the change of conductivity better than the B-field. The research of this paper will serve airborne EM in the identification and correction of the topographic effects.

Keywords: 3D, Airborne EM, forward modeling, topographic effect

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Authors: R. Gharari, N. Kojouri, R. Hosseini Aghdam, E. Alibeigi, B. Salmasian

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In this research, the WWER1000/V446 (a PWR Russian type reactor) is chosen as the case study. It is assumed that radioactive materials that release into the environment are more than allowable limit due to a complete failure of the ventilation system (reactor stack). In the following, the HOTSPOT and the RASCAL computational codes have been used and coupled with a developed program using MATLAB software to evaluate Total effective dose equivalent (TEDE) and cancer risk according to the BEIR equations for various human organs. In addition, effects of the containment spray system and climate conditions on the TEDE have been investigated. According to the obtained results, there is an inverse correlation between the received dose and the wind speed; the amount of the TEDE for wind speed 2 m/s and is more than wind speed for 14 m/s during the class A of the climate (2.168 and 0.444 mSv, respectively). Also, containment spray system can effect and reduce the amount of the fission products and TEDE. Furthermore, the probability of the cancer risk for women is more than men, and for children is more than adults. In addition, a specific emergency zonal planning is proposed. Results are promising in which the site selection of the WWER1000/V446 were considered safe for the public in this situation.

Keywords: TEDE, total effective dose equivalent, RASCAL and HOTSPOT codes, BEIR equations, cancer risk

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Authors: K. Jagannath, Akhilesh Kotian, S. S. Sharma, Achutha Kini U., P. R. Prabhu

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Boiling process is characterized by the rapid formation of vapour bubbles at the solid–liquid interface (nucleate boiling) with pre-existing vapour or gas pockets. Computational fluid dynamics (CFD) is an important tool to study bubble dynamics. In the present study, CFD simulation has been carried out to determine the bubble detachment diameter and its terminal velocity. Volume of fluid method is used to model the bubble and the surrounding by solving single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. In the simulation, bubble is generated by allowing water-vapour to enter a cylinder filled with liquid water through an inlet at the bottom. After the bubble is fully formed, the bubble detaches from the surface and rises up during which the bubble accelerates due to the net balance between buoyancy force and viscous drag. Finally when these forces exactly balance each other, it attains a constant terminal velocity. The bubble detachment diameter and the terminal velocity of the bubble are captured by the monitor function provided in FLUENT. The detachment diameter and the terminal velocity obtained is compared with the established results based on the shape of the bubble. A good agreement is obtained between the results obtained from simulation and the equations in comparison with the established results.

Keywords: bubble growth, computational fluid dynamics, detachment diameter, terminal velocity

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Authors: Fateme Nokhodchi Bonab

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Studies related to magnetic resonance imaging (MRI) and drug delivery are reviewed in this study to demonstrate the role of transport theory in porous media in facilitating advances in biomedical applications. Diffusion processes are believed to be important in many therapeutic modalities such as: B. Delivery of drugs to the brain. We analyse the progress in the development of diffusion equations using the local volume average method and the evaluation of applications related to diffusion equations. Torsion and porosity have significant effects on diffusive transport. In this study, various relevant models of torsion are presented and mathematical modeling of drug release from biodegradable delivery systems is analysed. In this study, a new model of drug release kinetics from porous biodegradable polymeric microspheres under bulk and surface erosion of the polymer matrix is presented. Solute drug diffusion, drug dissolution from the solid phase, and polymer matrix erosion have been found to play a central role in controlling the overall drug release process. This work paves the way for MRI and drug delivery researchers to develop comprehensive models based on porous media theory that use fewer assumptions compared to other approaches.

Keywords: MRI, porous media, drug delivery, biomedical applications

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: Adam L. Yanagihara, Yong Seok Park

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The goal of this paper is to converge upon a design of a brake system that could be used for a roller coaster found at an amusement park. It was necessary to find what could be deemed as a “comfortable” deceleration so that passengers do not feel as if they are suddenly jerked and pressed against the restraining harnesses. A human factors engineering approach was taken in order to determine this deceleration. Using a previous study that tested the deceleration of transit vehicles, it was found that a -0.45 G deceleration would be used as a design requirement to build this system around. An adjustable linear eddy current brake using permanent magnets would be the ideal system to use in order to meet this design requirement. Anthropometric data were then used to determine a realistic weight and length of the roller coaster that the brake was being designed for. The weight and length data were then factored into magnetic brake force equations. These equations were used to determine how the brake system and the brake run layout would be designed. A final design for the brake was determined and it was found that a total of 12 brakes would be needed with a maximum braking distance of 53.6 m in order to stop a roller coaster travelling at its top speed and loaded to maximum capacity. This design is derived from theoretical calculations, but is within the realm of feasibility.

Keywords: eddy current brake, engineering design, design synthesis, human factors engineering

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Authors: J. Sharon Mano Pappu, Sathyanarayana N. Gummadi

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Growth of Debaryomyces nepalensis on mixed substrates in batch culture follows diauxic pattern of completely utilizing glucose during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming xylose. The present study deals with the development of cybernetic mathematical model for prediction of xylitol production and yield. Production of xylitol from xylose in batch fermentation is investigated in the presence of glucose as the co-substrate. Different ratios of glucose and xylose concentrations are assessed to study the impact of multi substrate on production of xylitol in batch reactors. The parameters in the model equations were estimated from experimental observations using integral method. The model equations were solved simultaneously by numerical technique using MATLAB. The developed cybernetic model of xylose fermentation in the presence of a co-substrate can provide answers about how the ratio of glucose to xylose influences the yield and rate of production of xylitol. This model is expected to accurately predict the growth of microorganism on mixed substrate, duration of intermediate lag phase, consumption of substrate, production of xylitol. The model developed based on cybernetic modelling framework can be helpful to simulate the dynamic competition between the metabolic pathways.

Keywords: co-substrate, cybernetic model, diauxic growth, xylose, xylitol

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Authors: Nur Dayana Khairunnisa Rosli, Seripah Awang Kechil

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Swirling flows with velocity slip are important in nature and industrial processes. The present work considers the effects of velocity slip, temperature jump and suction/injection on the flow and heat transfer of power-law fluids due to a rotating disk in the presence of magnetic field. The system of the partial differential equations is highly non-linear. The number of independent variables is reduced by transforming the system into a system of coupled non-linear ordinary differential equations using similarity transformations. The effects of suction/injection, velocity slip and temperature jump on the flow rates are investigated for various cases of shear thinning and shear thickening power law fluids. The thermal and velocity jump strongly reduce the heat transfer rate and skin friction coefficient. Suction decreases the radial and tangential skin friction coefficient and the rate of heat transfer. It is also observed that the effects are more pronounced in the case of shear thinning fluids as compared to shear thickening fluids.

Keywords: heat transfer, power-law fluids, rotating disk, suction or injection, temperature jump, velocity slip

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Authors: Rangoli Goyal, Rama Bhargava

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The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, diffusiophoresis, Brownian motion

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Authors: Mahdad M’hamed, Belaidi Idir

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This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

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Authors: Man Young Kim

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Catalytic combustion is generally accepted as an environmentally preferred alternative for the generation of heat and power from fossil fuels mainly due to its advantages related to the stable combustion under very lean conditions with low emissions of NOx, CO, and UHC at temperatures lower than those occurred in conventional flame combustion. Despite these advantages, the commercial application of catalytic combustion has been delayed because of complicated reaction processes and the difficulty in developing appropriate catalysts with the required stability and durability. To develop the catalytic combustors, detailed studies on the combustion characteristics of catalytic combustion should be conducted. To the end, in current research, quantitative studies on the combustion characteristics of the catalytic combustors, with a Pd-based catalyst for MCFC power generation systems, relying on numerical simulations have been conducted. In addition, data from experimental studies of variations in outlet temperatures and fuel conversion, taken after operating conditions have been used to validate the present numerical approach. After introducing the governing equations for mass, momentum, and energy equations as well as a description of catalytic combustion kinetics, the effects of the excess air ratio, space velocity, and inlet gas temperature on the catalytic combustion characteristics are extensively investigated. Quantitative comparisons are also conducted with previous experimental data. Finally, some concluding remarks are presented.

Keywords: catalytic combustion, methane, BOP, MCFC power generation system, inlet temperature, excess air ratio, space velocity

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Authors: Dávid Kovács, Bálint Csanády, Dániel Boros, Iván Ivkovic, Lóránt Nagy, Dalma Tóth-Lakits, László Márkus, András Lukács

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The modeling practice of financial instruments has seen significant change over the last decade due to the recognition of time-dependent and stochastically changing correlations among the market prices or the prices and market characteristics. To represent this phenomenon, the Stochastic Correlation Process (SCP) has come to the fore in the joint modeling of prices, offering a more nuanced description of their interdependence. This approach has allowed for the attainment of realistic tail dependencies, highlighting that prices tend to synchronize more during intense or volatile trading periods, resulting in stronger correlations. Evidence in statistical literature suggests that, similarly to the volatility, the SCP of certain stock prices follows rough paths, which can be described using fractional differential equations. However, estimating parameters for these equations often involves complex and computation-intensive algorithms, creating a necessity for alternative solutions. In this regard, the Fractional Ornstein-Uhlenbeck (fOU) process from the family of fractional processes offers a promising path. We can effectively describe the rough SCP by utilizing certain transformations of the fOU. We employed neural networks to understand the behavior of these processes. We had to develop a fast algorithm to generate a valid and suitably large sample from the appropriate process to train the network. With an extensive training set, the neural network can estimate the process parameters accurately and efficiently. Although the initial focus was the fOU, the resulting model displayed broader applicability, thus paving the way for further investigation of other processes in the realm of financial mathematics. The utility of SCP extends beyond its immediate application. It also serves as a springboard for a deeper exploration of fractional processes and for extending existing models that use ordinary Wiener processes to fractional scenarios. In essence, deploying both SCP and fractional processes in financial models provides new, more accurate ways to depict market dynamics.

Keywords: fractional Ornstein-Uhlenbeck process, fractional stochastic processes, Heston model, neural networks, stochastic correlation, stochastic differential equations, stochastic volatility

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Authors: Mohsen Torabi, Nader Karimi, Kaili Zhang

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This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.

Keywords: entropy generation, exothermicity or endothermicity, forced convection, local thermal non-equilibrium, analytical modelling

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Authors: Hammad Majeed, Hanna Knuutila, Magne Hillestad, Hallvard F. Svendsen

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Formation of aerosols can cause serious complications in industrial exhaust gas CO2 capture processes. SO3 present in the flue gas can cause aerosol formation in an absorption based capture process. Small mist droplets and fog formed can normally not be removed in conventional demisting equipment because their submicron size allows the particles or droplets to follow the gas flow. As a consequence of this aerosol based emissions in the order of grams per Nm3 have been identified from PCCC plants. In absorption processes aerosols are generated by spontaneous condensation or desublimation processes in supersaturated gas phases. Undesired aerosol development may lead to amine emissions many times larger than what would be encountered in a mist free gas phase in PCCC development. It is thus of crucial importance to understand the formation and build-up of these aerosols in order to mitigate the problem. Rigorous modelling of aerosol dynamics leads to a system of partial differential equations. In order to understand mechanics of a particle entering an absorber an implementation of the model is created in Matlab. The model predicts the droplet size, the droplet internal variable profiles and the mass transfer fluxes as function of position in the absorber. The Matlab model is based on a subclass method of weighted residuals for boundary value problems named, orthogonal collocation method. The model comprises a set of mass transfer equations for transferring components and the essential diffusion reaction equations to describe the droplet internal profiles for all relevant constituents. Also included is heat transfer across the interface and inside the droplet. This paper presents results describing the basic simulation tool for the characterization of aerosols formed in CO2 absorption columns and gives examples as to how various entering droplets grow or shrink through an absorber and how their composition changes with respect to time. Below are given some preliminary simulation results for an aerosol droplet composition and temperature profiles.

Keywords: absorption columns, aerosol formation, amine emissions, internal droplet profiles, monoethanolamine (MEA), post combustion CO2 capture, simulation

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Gaoyang Meng, Philip Harrison

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When manufacturing composite laminates, the fibre directions within the laminate are never perfectly straight and inevitably contain some degree of stochastic in-plane waviness or ‘meandering’. In this work we aim to understand the relationship between the degree of meandering of the fibre paths, and the resulting uncertainty in the laminate’s final mechanical properties. To do this, a numerical tool is developed to automatically generate meandering fibre paths in each of the laminate's 8 plies (using Matlab) and after mapping this information into finite element simulations (using Abaqus), the statistical variability of the tensile mechanical properties of a [45°/90°/-45°/0°]s carbon/epoxy (IM7/8552) laminate is predicted. The stiffness, first ply failure strength and ultimate failure strength are obtained. Results are generated by inputting the degree of variability in the fibre paths and the laminate is then examined in all directions (from 0° to 359° in increments of 1°). The resulting predictions are output as flower (polar) plots for convenient analysis. The average fibre orientation of each ply in a given laminate is determined by the laminate layup code [45°/90°/-45°/0°]s. However, in each case, the plies contain increasingly large amounts of in-plane waviness (quantified by the standard deviation of the fibre direction in each ply across the laminate. Four different amounts of variability in the fibre direction are tested (2°, 4°, 6° and 8°). Results show that both the average tensile stiffness and the average tensile strength decrease, while the standard deviations increase, with an increasing degree of fibre meander. The variability in stiffness is found to be relatively insensitive to the rotation angle, but the variability in strength is sensitive. Specifically, the uncertainty in laminate strength is relatively low at orientations centred around multiples of 45° rotation angle, and relatively high between these rotation angles. To concisely represent all the information contained in the various polar plots, rotation-angle dependent Weibull distribution equations are fitted to the data. The resulting equations can be used to quickly estimate the size of the errors bars for the different mechanical properties, resulting from the amount of fibre directional variability contained within the laminate. A longer term goal is to use these equations to quickly introduce realistic variability at the component level.

Keywords: advanced composite laminates, FE simulation, in-plane waviness, tensile properties, uncertainty quantification

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Authors: Dorota Miroslaw-Swiatek, Mateusz Grygoruk, Sylwia Szporak

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We applied a two-dimensional surface water flow model with irregular wet boundaries. In this model, flow equations are in the form of a 2-D, non-linear diffusion equations which allows to account spatial variations in flow resistance and topography. Calculation domain to simulate the flow pattern in the floodplain is congruent with a Digital Elevation Model (DEM) grid. The rate and direction of sheet flow in wetlands is affected by vegetation type and density, therefore the developed model take into account spatial distribution vegetation resistance to the water flow. The model was tested in a part of the Biebrza Valley, of an outstanding heterogeneity in the elevation and flow resistance distributions due to various ecohydrological conditions and management measures. In our approach we used the highest-possible quality of the DEM in order to obtain hydraulic slopes and vegetation distribution parameters for the modelling. The DEM was created from the cloud of points measured in the LiDAR technology. The LiDAR reflects both the land surface as well as all objects on top of it such as vegetation. Depending on the density of vegetation cover the ability of laser penetration is variable. Therefore to obtain accurate land surface model the “vegetation effect” was corrected using data collected in the field (mostly the vegetation height) and satellite imagery such as Ikonos (to distinguish different vegetation types of the floodplain and represent them spatially). Model simulation was performed for the spring thaw flood in 2009.

Keywords: floodplain flow, Biebrza valley, model simulation, 2D surface flow model

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Authors: Hiba Akrout, Khaoula Hidouri, Béchir Chaouachi, Romdhane Ben Slama

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A simple solar distiller has been constructed in order to desalt water via the solar distillation process. An experimental study has been conducted in June. The aim of this work is to study the effect of the distance between the cold condensing surface and the hot steam generation surface in order to optimize the geometric characteristics of a simple solar still. To do this, we have developed a mathematical model based on thermal and mass equations system. Subsequently, the equations system resolution has been made through a program developed on MATLAB software, which allowed us to evaluate the production of this system as a function of the distance separating the two surfaces. In addition, this model allowed us to determine the evolution of the humid air temperature inside the solar still as well as the humidity ratio profile all over the day. Simulations results show that the solar distiller production, as well as the humid air temperature, are proportional to the global solar radiation. It was also found that the air humidity ratio inside the solar still has a similar evolution of that of solar radiation. Moreover, the solar distiller average height augmentation, for constant water depth, induces the diminution of the production. However, increasing the water depth for a fixed average height of solar distiller reduces the production.

Keywords: distillation, solar energy, heat transfer, mass transfer, average height

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Meng-Yu Lin, Wan-Ju Lee

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Pore-water pressure, which mediates effective stress and shear strength at grain contacts, has a great influence on the motion of debris flow. The factors that control the diffusion of excess pore-water pressure play very important roles in the debris-flow motion. This research investigates these effects by solving the distribution of pore-water pressure numerically in an unsteady, surging motion of debris flow. The governing equations are the depth-averaged equations for the motion of debris-flow surges coupled with the one-dimensional diffusion equation for excess pore-water pressures. The pore-pressure diffusion equation is solved using a Fourier series, which may improve the accuracy of the solution. The motion of debris-flow surge is modelled using a Lagrangian particle method. From the computational results, the effects of pore-pressure diffusivities and the initial excess pore pressure on the formations of debris-flow surges are investigated. Computational results show that the presence of pore water can increase surge velocities and then changes the profiles of depth distribution. Due to the linear distribution of the vertical component of pore-water velocity, pore pressure dissipates rapidly near the bottom and forms a parabolic distribution in the vertical direction. Increases in the diffusivity of pore-water pressure cause the pore pressures decay more rapidly and then decrease the mobility of the surge.

Keywords: debris flow, diffusion, Lagrangian particle method, pore-pressure diffusivity, pore-water pressure

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

Abstract:

In this research, the free vibration of a rectangular sandwich nano-plate (SNP) made of three smart layers in the visco Pasternak foundation is studied. The core of the sandwich is a piezo magnetic nano-plate integrated with two layers of piezoelectric materials. First-order shear deformation plate theory is utilized to derive the motion equations by using Hamilton’s principle, piezoelectricity, and modified couple stress theory. Elastic medium is modeled by visco Pasternak foundation, where the damping coefficient effect is investigated on the stability of sandwich nano-plate. These equations are solved by the differential quadrature method (DQM), considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, shear correction factor, damping coefficient, and boundary conditions on the dimensionless frequency of sandwich nano-plate. The results are also compared by those available in the literature, and these findings can be used for automotive industry, communications equipment, active noise, stability, and vibration cancellation systems and utilized for designing the magnetostrictive actuator, motor, transducer and sensors in nano and micro smart structures.

Keywords: free vibration, modified couple stress theory, sandwich nano-plate, visco Pasternak foundation

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Authors: Evln Ranga Charyulu, S. P. Venu Madhavarao, S. Udaya kumar, S. V. S. S. N. V. G. Krishna Murthy

Abstract:

With the advent of new nanometer process technologies, it is possible to integrate billion transistors on a single substrate. When more and more functionality included there is the possibility of multi-million transistors switching simultaneously consuming more power and dissipating more power along with more leakage of current into the substrate of porous silicon or germanium material. These results in substrate heating and thermal noise generation coupled to signals of interest. The heating process is represented by coupled nonlinear partial differential equations in porous silicon and germanium. By identifying heat sources and heat fluxes may results in designing of ultra-low power circuits. The PDEs are solved by finite difference scheme assuming that boundary layer equations in porous silicon and germanium. Local heat fluxes along the vertical isothermal surface immersed in porous SI/Ge are considered. The parameters considered for optimization are thermal diffusivity, thermal expansion coefficient, thermal diffusion ratio, permeability, specific heat at constant temperatures, Rayleigh number, amplitude of wavy surface, mass expansion coefficient. The diffusion of heat was caused by the concentration gradient. Thermal physical properties are homogeneous and isotropic. By using L8, TAGUCHI method the parameters are optimized.

Keywords: heat transfer, pde, taguchi optimization, SI/Ge

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Authors: Ibrahim Yakubu Seini, Oluwole Daniel Makinde

Abstract:

MHD chemically reacting viscous fluid flow towards a vertical surface with slip and convective boundary conditions has been conducted. The temperature and the chemical species concentration of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the vertical surface. The governing differential equations are modeled and transformed into systems of ordinary differential equations, which are then solved numerically by a shooting method. The effects of various parameters on the heat and mass transfer characteristics are discussed. Graphical results are presented for the velocity, temperature, and concentration profiles whilst the skin-friction coefficient and the rate of heat and mass transfers near the surface are presented in tables and discussed. The results revealed that increasing the strength of the magnetic field increases the skin-friction coefficient and the rate of heat and mass transfers toward the surface. The velocity profiles are increased towards the surface due to the presence of the Lorenz force, which attracts the fluid particles near the surface. The rate of chemical reaction is seen to decrease the concentration boundary layer near the surface due to the destructive chemical reaction occurring near the surface.

Keywords: boundary layer, surface slip, MHD flow, chemical reaction, heat transfer, mass transfer

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Authors: Emmanuel Agunloye, Asterios Gavriilidis, Luca Mazzei

Abstract:

Gold nanoparticles are commonly synthesized by reducing chloroauric acid with sodium citrate. This method, referred to as the citrate method, can produce spherical gold nanoparticles (NPs) in the size range 10-150 nm. Gold NPs of this size are useful in many applications. However, the NPs are usually polydisperse and irreproducible. A better understanding of the synthesis mechanisms is thus required. This work thoroughly investigated the only model that describes the synthesis. This model combines mass and population balance equations, describing the NPs synthesis through a sequence of chemical reactions. Chloroauric acid reacts with sodium citrate to form aurous chloride and dicarboxy acetone. The latter organizes aurous chloride in a nucleation step and concurrently degrades into acetone. The unconsumed precursor then grows the formed nuclei. However, depending on the pH, both the precursor and the reducing agent react differently thus affecting the synthesis. In this work, we investigated the model for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used Parsival, a commercial numerical code, whilst to test it, we considered various conditions studied experimentally by different researchers, for which results are available in the literature. The model poorly predicted the experimental data. We believe that this is because the model does not account for the acid-base properties of both chloroauric acid and sodium citrate.

Keywords: citrate method, gold nanoparticles, Parsival, population balance equations, Turkevich organizer theory

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Authors: Ranjith Maniyeri, Ahamed C. Saleel

Abstract:

Two-dimensional fluid flow over a stationary circular cylinder is one of the bench mark problem in the field of fluid-structure interaction in computational fluid dynamics (CFD). Motivated by this, in the present work, a two-dimensional computational model is developed using an improved version of immersed boundary method which combines the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Lagrangian coordinates are used to represent the cylinder and Eulerian coordinates are used to describe the fluid flow. A two-dimensional Dirac delta function is used to transfer the quantities between the sold to fluid domain. Further, continuity and momentum equations governing the fluid flow are solved using fractional step based finite volume method on a staggered Cartesian grid system. The developed code is validated by comparing the values of drag coefficient obtained for different Reynolds numbers with that of other researcher’s results. Also, through numerical simulations for different Reynolds numbers flow behavior is well captured. The stability analysis of the improved version of immersed boundary method is tested for different values of feedback forcing coefficients.

Keywords: Feedback Forcing Scheme, Finite Volume Method, Immersed Boundary Method, Navier-Stokes Equations

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Authors: H. Ozbasaran

Abstract:

Lateral torsional buckling is a global stability loss which should be considered in the design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice. Such equations can be obtained by using energy method. Unfortunately, this method has a vital drawback. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. The accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties, and loading case, the hardest step is to determine a proper mode function. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for the concentrated load at the free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: buckling mode, cantilever, lateral-torsional buckling, I-beam

Procedia PDF Downloads 349