Search results for: Volterra integral equations

Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: A. Chillali, M. Sahmoudi

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In this paper we will give a method for encoding the elements of the ring of integers of sextic extension, namely L = Q(a,b) which is a rational quadratic over cubic field K =Q(a) where a^{2} is a rational square free integer and b is a root of irreducible polynomiale of degree 3.

Keywords: coding, integral bases, sextic, quadratic

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Radoslaw Pytlak, Damian Suski

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The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

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Authors: Mateusz Janas

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Innovative implementations in the micro, small, and medium-sized enterprises (MSME) sector are among the essential activities considering the current market realities, technological advancements, and digitization trends. MSMEs play a crucial role and significantly influence the economic conditions of countries, as their competitiveness directly impacts the global economy. Business development and investment in innovation and technology are integral parts of every modern enterprise's strategy, seeking to maintain and achieve a desired competitive position. The instability of the socio-economic environment, along with contemporary changes in artificial intelligence implementation and digitization, requires businesses to adopt increasingly newer solutions and actions. Enterprises must strive to survive in the global market and build competitive positions, especially in uncertain conditions. Being aware of the significance of innovative actions is crucial for MSMEs as it enables them to enhance their operations and expand their scope. It is essential for managers and executives of MSMEs to be focused on development and innovation, as their approach will also impact their employees, emphasizing results and maximizing the company's value. Managers of MSMEs must be aware of various threats, costs, opportunities, and gains that can arise from implementing new technical and organizational solutions. Businesses must view development as an integral part of their strategy and continuously strive for improvement.

Keywords: innovation, SME, develop, management

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: axisymmetric problem, compressible Navier-Stokes equations, continuous finite elements, swirling flow

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Authors: Amor Jnifene, Cedric Cocaud

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One of the most constraining problems facing the development of autonomous vehicles is the limitations of current technologies. Guidance and navigation controllers need to be faster and more robust. Communication data links need to be more reliable and secure. For an Unmanned Aerial Vehicles (UAV) to be useful, and fully autonomous, one important feature that needs to be an integral part of the navigation system is autonomous trajectory planning. The work discussed in this paper presents a method for on-line trajectory planning for UAV’s. This method takes into account various constraints of different types including specific vectors of approach close to target points, multiple objectives, and other constraints related to speed, altitude, and obstacle avoidance. The trajectory produced by the proposed method ensures a smooth transition between different segments, satisfies the minimum curvature imposed by the dynamics of the UAV, and finds the optimum velocity based on available atmospheric conditions. Given a set of objective points and waypoints a skeleton of the trajectory is constructed first by linking all waypoints with straight segments based on the order in which they are encountered in the path. Secondly, vectors of approach (VoA) are assigned to objective waypoints and their preceding transitional waypoint if any. Thirdly, the straight segments are replaced by 3D curvilinear trajectories taking into account the aircraft dynamics. In summary, this work presents a method for on-line 3D trajectory generation (TG) of Unmanned Aerial Vehicles (UAVs). The method takes as inputs a series of waypoints and an optional vector of approach for each of the waypoints. Using a dynamic model based on the performance equations of fixed wing aircrafts, the TG computes a set of 3D parametric curves establishing a course between every pair of waypoints, and assembling these sets of curves to construct a complete trajectory. The algorithm ensures geometric continuity at each connection point between two sets of curves. The geometry of the trajectory is optimized according to the dynamic characteristics of the aircraft such that the result translates into a series of dynamically feasible maneuvers. In summary, this work presents a method for on-line 3D trajectory generation (TG) of Unmanned Aerial Vehicles (UAVs). The method takes as inputs a series of waypoints and an optional vector of approach for each of the waypoints. Using a dynamic model based on the performance equations of fixed wing aircraft, the TG computes a set of 3D parametric curves establishing a course between every pair of waypoints, and assembling these sets of curves to construct a complete trajectory. The algorithm ensures geometric continuity at each connection point between two sets of curves. The geometry of the trajectory is optimized according to the dynamic characteristics of the aircraft such that the result translates into a series of dynamically feasible maneuvers.

Keywords: trajectory planning, unmanned autonomous air vehicle, vector of approach, waypoints

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Authors: D. Pradeep Mitra, Prafulla

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Looking to the word propellant-less system it makes us to believe that it is an impossible one, but this paper demonstrates the use of microwaves to create a system which makes impossible to be possible, it means a propellant-less propulsion system using microwaves. In these thrusters, microwaves are radiated into a sealed parabolic cavity through a waveguide, which act on the surface of the cavity and follow the axis of the thrusters to produce thrust. The advantages of these thrusters are: (1) Producing thrust without propellant; without erosion, wear, and thermal stress from the hot exhaust gas; and at the same time increasing quality. (2) If the microwave output power is stable, the performance of thrusters is not affected by its working environment. This paper is demonstrated from general maxwell equations. These equations are used to create the mathematical model of the thrusters. These mathematical model helps us to calculate the Q factor and calculate the approximate thrust which would be generated in the system.

Keywords: propellant less, microwaves, parabolic wave guide, propulsion system

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Authors: Shyh Ming Chern

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Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Morteza Faghfouri

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In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.

Keywords: integral submanifolds, S-space forms, doubly warped product, inequality

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Authors: Luis F. Bianchessi, Gustavo G. Shimamoto, Matthieu Tubino

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The use of biodiesel has been diffused in Brazil and all over the world by the trading of biodiesel (B100). In Brazil, the diesel oil currently being sold is a blend, containing 7% biodiesel (B7). In this context, it is necessary to develop methods capable of identifying this blend composition, especially regarding the biodiesel quality used for making these blends. In this study, hydrogen nuclear magnetic resonance spectra (1H-NMR) are proposed as a form of identifying and confirming the quality of type B10 blends (10% of biodiesel and 90% of diesel). Furthermore, the presence of vegetable oils, which may be from fuel adulteration or as an evidence of low degree of transesterification conversion during the synthesis of B100, may also be identified. Mixtures of diesel, vegetable oils and their respective biodiesel were prepared. Soybean oil and macauba kernel oil were used as raw material. The diesel proportion remained fixed at 90%. The other proportion (10%) was varied in terms of vegetable oil and biodiesel. The 1H-NMR spectra were obtained for each one of the mixtures, in order to find a correlation between the spectra and the amount of biodiesel, as well as the amount of residual vegetable oil. The ratio of the integral of the methylenic hydrogen H-2 of glycerol (exclusive of vegetable oil) with respect to the integral of the olefinic hydrogens (present in vegetable oil and biodiesel) was obtained. These ratios were correlated with the percentage of vegetable oil in each mixture, from 0% to 10%. The obtained correlation could be described by linear relationships with R2 of 0.9929 for soybean biodiesel and 0.9982 for macauba kernel biodiesel. Preliminary results show that the technique can be used to monitor the biodiesel quality in commercial diesel-biodiesel blends, besides indicating possible adulteration.

Keywords: biodiesel, diesel, biodiesel quality, adulteration

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: exponentially shrinking sheet, magnetic field, mixed convection, suction

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Authors: Chuang-Hung Lin, Cheng-Yuan Hsu, Jia-Yan Lin

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It is an indispensible strategy to adopt greenery approach on architectural bases so as to improve ecological habitats, decrease heat-island effect, purify air quality, and relieve surface runoff as well as noise pollution, all of which are done in an attempt to achieve sustainable environment. How we can do with plant design to attain the best visual quality and ideal carbon dioxide fixation depends on whether or not we can appropriately make use of greenery according to the nature of architectural bases. To achieve the goal, it is a need that architects and landscape architects should be provided with sufficient local references. Current greenery studies focus mainly on the heat-island effect of urban with large scale. Most of the architects still rely on people with years of expertise regarding the adoption and disposition of plantation in connection with microclimate scale. Therefore, environmental design, which integrates science and aesthetics, requires fundamental research on landscape environment technology divided from building environment technology. By doing so, we can create mutual benefits between green building and the environment. This issue is extremely important for the greening design of the bases of green buildings in cities and various open spaces. The purpose of this study is to establish plant selection and allocation strategies under different building sunshade levels. Initially, with the shading of sunshine on the greening bases as the starting point, the effects of the shades produced by different building types on the greening strategies were analyzed. Then, by measuring the PAR( photosynthetic active radiation), the relative DLI( daily light integral) was calculated, while the DLI Map was established in order to evaluate the effects of the building shading on the established environmental greening, thereby serving as a reference for plant selection and allocation. The discussion results were to be applied in the evaluation of environment greening of greening buildings and establish the “right plant, right place” design strategy of multi-level ecological greening for application in urban design and landscape design development, as well as the greening criteria to feedback to the eco-city greening buildings.

Keywords: daily light integral, plant design, urban open space

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Authors: Alex Fedoseyev

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This study investigates a generalized hydrodynamic equation (GHE) simplified model for the simulation of turbulent flow over a two-dimensional backward-facing step (BFS) at Reynolds number Re=132000. The GHE were derived from the generalized Boltzmann equation (GBE). GBE was obtained by first principles from the chain of Bogolubov kinetic equations and considers particles of finite dimensions. The GHE has additional terms, temporal and spatial fluctuations, compared to the Navier-Stokes equations (NSE). These terms have a timescale multiplier τ, and the GHE becomes the NSE when $\tau$ is zero. The nondimensional τ is a product of the Reynolds number and the squared length scale ratio, τ=Re*(l/L)², where l is the apparent Kolmogorov length scale, and L is a hydrodynamic length scale. The BFS flow modeling results obtained by 2D calculations cannot match the experimental data for Re>450. One or two additional equations are required for the turbulence model to be added to the NSE, which typically has two to five parameters to be tuned for specific problems. It is shown that the GHE does not require an additional turbulence model, whereas the turbulent velocity results are in good agreement with the experimental results. A review of several studies on the simulation of flow over the BFS from 1980 to 2023 is provided. Most of these studies used different turbulence models when Re>1000. In this study, the 2D turbulent flow over a BFS with height H=L/3 (where L is the channel height) at Reynolds number Re=132000 was investigated using numerical solutions of the GHE (by a finite-element method) and compared to the solutions from the Navier-Stokes equations, k–ε turbulence model, and experimental results. The comparison included the velocity profiles at X/L=5.33 (near the end of the recirculation zone, available from the experiment), recirculation zone length, and velocity flow field. The mean velocity of NSE was obtained by averaging the solution over the number of time steps. The solution with a standard k −ε model shows a velocity profile at X/L=5.33, which has no backward flow. A standard k−ε model underpredicts the experimental recirculation zone length X/L=7.0∓0.5 by a substantial amount of 20-25%, and a more sophisticated turbulence model is needed for this problem. The obtained data confirm that the GHE results are in good agreement with the experimental results for turbulent flow over two-dimensional BFS. A turbulence model was not required in this case. The computations were stable. The solution time for the GHE is the same or less than that for the NSE and significantly less than that for the NSE with the turbulence model. The proposed approach was limited to 2D and only one Reynolds number. Further work will extend this approach to 3D flow and a higher Re.

Keywords: backward-facing step, comparison with experimental data, generalized hydrodynamic equations, separation, reattachment, turbulent flow

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Authors: Andrey V. Malyshev, Anna B. Petrova, Anatoly P. Surzhikov

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The article presents the results of the influence of diamagnetic additives on the defects level of ferrite ceramics. For this purpose, we use a previously developed method based on the mathematical analysis of experimental temperature dependences of the initial permeability. A phenomenological expression for the description of such dependence was suggested and an interpretation of its main parameters was given. It was shown, that the main criterion of the integral defects level of ferrite ceramics is the relation of two parameters correlating with elastic stress value in a material. Model samples containing a controlled number of intergranular phase inclusions served to prove the validity of the proposed method, as well as to assess its sensitivity in comparison with the traditional XRD (X-ray diffraction) analysis. The broadening data of diffraction reflexes of model samples have served for such comparison. The defects level data obtained by the proposed method are in good agreement with the X-ray data. The method showed high sensitivity. Therefore, the legitimacy of the selection relationship β/α parameters of phenomenological expression as a characteristic of the elastic state of the ferrite ceramics confirmed. In addition, the obtained data can be used in the detection of non-magnetic phases and testing the optimal sintering production technology of soft magnetic ferrites.

Keywords: cure point, initial permeability, integral defects level, homogeneity

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Madhu Aneja, Sapna Sharma

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The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: bioconvection, finite element method, gyrotactic micro-organisms, inclined stretching sheet, nanofluid

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Krzysztof Pomorski

Abstract:

In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

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Authors: Suguru Miyauchi, Toshiyuki Hayase

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Biological membranes have selective permeability, and the capsules or cells enclosed by the membrane show the deformation by the osmotic flow. This mass transport phenomenon is observed everywhere in a living body. For the understanding of the mass transfer in a body, it is necessary to consider the mass transfer phenomenon across the membrane as well as the deformation of the membrane by a flow. To our knowledge, in the numerical analysis, the method for mass transfer across the moving membrane has not been established due to the difficulty of the treating of the mass flux permeating through the moving membrane with selective permeability. In the existing methods for the mass transfer across the membrane, the approximate delta function is used to communicate the quantities on the interface. The methods can reproduce the permeation of the solute, but cannot reproduce the non-permeation. Moreover, the computational accuracy decreases with decreasing of the permeable coefficient of the membrane. This study aims to develop the numerical method capable of treating three-dimensional problems of mass transfer across the moving flexible membrane. One of the authors developed the numerical method with high accuracy based on the finite element method. This method can capture the discontinuity on the membrane sharply due to the consideration of the jumps in concentration and concentration gradient in the finite element discretization. The formulation of the method takes into account the membrane movement, and both permeable and non-permeable membranes can be treated. However, searching the cross points of the membrane and fluid element boundaries and splitting the fluid element into sub-elements are needed for the numerical integral. Therefore, cumbersome operation is required for a three-dimensional problem. In this paper, we proposed an improved method to avoid the search and split operations, and confirmed its effectiveness. The membrane shape was treated implicitly by introducing the level set function. As the construction of the level set function, the membrane shape in one fluid element was expressed by the shape function of the finite element method. By the numerical experiment, it was found that the shape function with third order appropriately reproduces the membrane shapes. The same level of accuracy compared with the previous method using search and split operations was achieved by using a number of sampling points of the numerical integral. The effectiveness of the method was confirmed by solving several model problems.

Keywords: finite element method, level set method, mass transfer, membrane permeability

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: Vikas Teotia, Sanjay Malhotra, Elina Mishra, Prashant Kumar, R. R. Singh, Priti Ukarde, P. P. Marathe, Y. S. Mayya

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Bhabha Atomic Research Centre, Trombay is developing low energy high intensity Proton Accelerator (LEHIPA) as pre-injector for 1 GeV proton accelerator for accelerator driven sub-critical reactor system (ADSS). LEHIPA consists of RFQ (Radio Frequency Quadrupole) and DTL (Drift Tube Linac) as major accelerating structures. DTL is RF resonator operating in TM010 mode and provides longitudinal E-field for acceleration of charged particles. The RF design of drift tubes of DTL was carried out to maximize the shunt impedance; this demands the diameter of drift tubes (DTs) to be as low as possible. The width of the DT is however determined by the particle β and trade-off between a transit time factor and effective accelerating voltage in the DT gap. The array of Drift Tubes inside DTL shields the accelerating particle from decelerating RF phase and provides transverse focusing to the charged particles which otherwise tends to diverge due to Columbic repulsions and due to transverse e-field at entry of DTs. The magnetic lenses housed inside DTS controls the transverse emittance of the beam. Quadrupole magnets are preferred over solenoid magnets due to relative high focusing strength of former over later. The availability of small volume inside DTs for housing magnetic quadrupoles has motivated the usage of permanent magnet quadrupoles rather than Electromagnetic Quadrupoles (EMQ). This provides another advantage as joule heating is avoided which would have added thermal loaded in the continuous cycle accelerator. The beam dynamics requires uniformity of integral magnetic gradient to be better than ±0.5% with the nominal value of 2.05 tesla. The paper describes the magnetic design of the PMQ using Sm2Co17 rare earth permanent magnets. The paper discusses the results of five pre-series prototype fabrications and qualification of their prototype permanent magnet quadrupoles and a full scale DT developed with embedded PMQs. The paper discusses the magnetic pole design for optimizing integral Gdl uniformity and the value of higher order multipoles. A novel but simple method of tuning the integral Gdl is discussed.

Keywords: DTL, focusing, PMQ, proton, rate earth magnets

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Authors: Elsayed M. A. Elbashbeshy, T. G. Emam, M. S. El-Azab, K. M. Abdelgaber

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The effect of thermal radiation on flow, heat and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder embedded in a porous medium with suction/injection is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.

Keywords: laminar flow, boundary layer, stretching horizontal cylinder, thermal radiation, suction/injection, nanofluid

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: Niloufar Ghoreishi, Ali Nekouzadeh

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The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: flight stability, phugoid mode, short period mode, climb phase, damping coefficient

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Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

Abstract:

This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: Emmanuel Ophel Gilbert, Williams Speret

Abstract:

The control for fluid flow behaviours of viscous fluids and heat transfer occurrences within heated mini-channel is considered. Heat transfer and flow characteristics of different viscous liquids, such as engine oil, automatic transmission fluid, one-half ethylene glycol, and deionized water were numerically analyzed. Some mathematical applications such as Fourier series and Laplace Z-Transforms were employed to ascertain the behaviour-wave like structure of these each viscous fluids. The steady, laminar flow and heat transfer equations are reckoned by the aid of numerical simulation technique. Further, this numerical simulation technique is endorsed by using the accessible practical values in comparison with the anticipated local thermal resistances. However, the roughness of this mini-channel that is one of the physical limitations was also predicted in this study. This affects the frictional factor. When an additive such as tetracycline was introduced in the fluid, the heat input was lowered, and this caused pro rata effect on the minor and major frictional losses, mostly at a very minute Reynolds number circa 60-80. At this ascertained lower value of Reynolds numbers, there exists decrease in the viscosity and minute frictional losses as a result of the temperature of these viscous liquids been increased. It is inferred that the three equations and models are identified which supported the numerical simulation via interpolation and integration of the variables extended to the walls of the mini-channel, yields the utmost reliance for engineering and technology calculations for turbulence impacting jets in the near imminent age. Out of reasoning with a true equation that could support this control for the fluid flow, Navier-stokes equations were found to tangential to this finding. Though, other physical factors with respect to these Navier-stokes equations are required to be checkmated to avoid uncertain turbulence of the fluid flow. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme via numerical simulation method that takes into account certain terms in the full Navier-Stokes equations. However, this resulted in dropping out in the approximation of certain assumptions. Concrete questions raised in the main body of the work are sightseen further in the appendices.

Keywords: frictional losses, heat transfer, laminar flow, mini-channel, number simulation, Reynolds number, turbulence, viscous fluids

Procedia PDF Downloads 177