Search results for: stokes equations

Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

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The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: entropy generation, hybrid nano fluid, heat transfer, porous disks

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: curved stretching sheet, finite difference method, MHD, variable thermal conductivity

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Authors: Pradeepa Teegala, Ramreddy Chitteti

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This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

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Authors: Atilla Bayram

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This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: computed force method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss

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Authors: Eda Gök

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Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: non-local continuum mechanics, peridynamic theory, solid structures, tensile loading, flexural loading

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Authors: Raj Nandkeolyar, Precious Sibanda

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The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

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Authors: Isadora Bugarin, Taygoara F. de Oliveira

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Binary fluids and emulsions, in general, are present in a vast range of industrial, medical, and scientific applications, showing complex behaviors responsible for defining the flow dynamics and the system operation. However, the literature describing those highlighted fluids in non-isothermal models is currently still limited. The present work brings a detailed investigation on droplet migration due to natural convection in square enclosure, aiming to clarify the effects of drop viscosity on the flow dynamics by showing how distinct viscosity ratios (droplet/ambient fluid) influence the drop motion and the final movement pattern kept on stationary regimes. The analysis was taken by observing distinct combinations of Rayleigh number, drop initial position, and viscosity ratios. The Navier-Stokes and Energy equations were solved considering the Boussinesq approximation in a laminar flow using the finite differences method combined with the Level Set method for binary flow solution. Previous results collected by the authors showed that the Rayleigh number and the drop initial position affect drastically the motion pattern of the droplet. For Ra ≥ 10⁴, two very marked behaviors were observed accordingly with the initial position: the drop can travel either a helical path towards the center or a cyclic circular path resulting in a closed cycle on the stationary regime. The variation of viscosity ratio showed a significant alteration of pattern, exposing a large influence on the droplet path, capable of modifying the flow’s behavior. Analyses on viscosity effects on the flow’s unsteady Nusselt number were also performed. Among the relevant contributions proposed in this work is the potential use of the flow initial conditions as a mechanism to control the droplet migration inside the enclosure.

Keywords: binary fluids, droplet motion, level set method, natural convection, viscosity

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Authors: G. Khamooshian

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One of the main points of application of the mechanisms of the series and parallel is the subject of managing them. The control of this mechanism and similar mechanisms is one that has always been the intention of the scholars. On the other hand, modeling the behavior of the system is difficult due to the large number of its parameters, and it leads to complex equations that are difficult to solve and eventually difficult to control. In this paper, a six-linkage robot has been presented that could be used in different areas such as medical robots. Using these robots needs a robust control. In this paper, the system equations are first found, and then the system conversion function is written. A new controller has been designed for this robot which could be used in other parallel robots and could be very useful. Parallel robots are so important in robotics because of their stability, so methods for control of them are important and the robust controller, especially in parallel robots, makes a sense.

Keywords: 3-RRS, 6 linkage, parallel robot, control

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Authors: Masato Sasaki, Masayoshi Yamamoto

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The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: wireless power transfer, omni-directional, orthogonal, efficiency

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Authors: M. Y. Malika, Farzana, Abdul Rehman

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The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs.

Keywords: boundary layer flow, exponentially stretched surface, Maxwell fluid, numerical solution

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Authors: Lina Wu, Jia Liu, Ye Li

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The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: Muhammad Omer Farooq Saeed

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The purpose of the proposal is to find out what time actually is! And to understand the natural phenomenon of the behavior of time and light corresponding to the motion of the bodies at relatively high speeds. The utmost concern of the paper is to deal with the possible demerits in the equations of relativity, thereby providing some valuable extensions in those equations and concepts. The idea used develops the most basic conception of the relative motion of the body with respect to space and a real understanding of time and the variation of energy of the body in different frames of reference. The results show the development of a completely new understanding of time, relative motion and energy, along with some extensions in the equations of special relativity most importantly the time dilation and the mass-energy relationship that will explain all frames of a body, all in one go. The proposal also raises serious questions on the validity of the “Principle of Equivalence” on which the General Relativity is based, most importantly a serious case of the bending light that eventually goes against its own governing concepts of space-time being proposed in the theory. The results also predict the existence of a completely new field that explains the fact just how and why bodies acquire energy in space-time. This field explains the production of gravitational waves based on time. All in all, this proposal challenges the formulas and conceptions of Special and General Relativity, respectively.

Keywords: time, relative motion, energy, speed, frame of reference, photon, curvature, space-time, time –differentials

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: H. Daaou Nedjari, O. Guerri, M. Saighi

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A numerical study was conducted to optimize the positioning of wind turbines over complex terrains. Thus, a two-dimensional disk model was used to calculate the flow velocity deficit in wind farms for both flat and complex configurations. The wind turbine wake was assessed using the hybrid methods that combine CFD (Computational Fluid Dynamics) with the actuator disc model. The wind turbine rotor has been defined with a thrust force, coupled with the Navier-Stokes equations that were resolved by an open source computational code (Code_Saturne V3.0 developed by EDF) The simulations were conducted in atmospheric boundary layer condition considering a two-dimensional region located at the north of Algeria at 36.74°N longitude, 02.97°E latitude. The topography elevation values were collected according to a longitudinal direction of 1km downwind. The wind turbine sited over topography was simulated for different elevation variations. The main of this study is to determine the topography effect on the behavior of wind farm wake flow. For this, the wake model applied in complex terrain needs to selects the singularity effects of topography on the vertical wind flow without rotor disc first. This step allows to determine the existence of mixing scales and friction forces zone near the ground. So, according to the ground relief the wind flow waS disturbed by turbulence and a significant speed variation. Thus, the singularities of the velocity field were thoroughly collected and thrust coefficient Ct was calculated using the specific speed. In addition, to evaluate the land effect on the wake shape, the flow field was also simulated considering different rotor hub heights. Indeed, the distance between the ground and the hub height of turbine (Hhub) was tested in a flat terrain for different locations as Hhub=1.125D, Hhub = 1.5D and Hhub=2D (D is rotor diameter) considering a roughness value of z0=0.01m. This study has demonstrated that topographical farm induce a significant effect on wind turbines wakes, compared to that on flat terrain.

Keywords: CFD, wind turbine wake, k-epsilon model, turbulence, complex topography

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Authors: Pranitha Janapatla, Venkata Suman Gontla

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The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Yang Zhong, Heng Liu

Abstract:

The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Roudane Mohamed

Abstract:

In this study we are interested in improving the efficiency of a steam boiler to 4.5T/h and minimize fume discharge temperature by the addition of a heat exchanger against the current in the energy system, the output of the boiler. The mathematical approach to the problem is based on the use of heat transfer by convection and conduction equations. These equations have been chosen because of their extensive use in a wide range of application. A software and developed for solving the equations governing these phenomena and the estimation of the thermal characteristics of boiler through the study of the thermal characteristics of the heat exchanger by both LMTD and NUT methods. Subsequently, an analysis of the thermal performance of the steam boiler by studying the influence of different operating parameters on heat flux densities, temperatures, exchanged power and performance was carried out. The study showed that the behavior of the boiler is largely influenced. In the first regime (P = 3.5 bar), the boiler efficiency has improved significantly from 93.03 to 99.43 at the rate of 6.47% and 4.5%. For maximum speed, the change is less important, it is of the order of 1.06%. The results obtained in this study of great interest to industrial utilities equipped with smoke tube boilers for the preheating air temperature intervene to calculate the actual temperature of the gas so the heat exchanged will be increased and minimize temperature smoke discharge. On the other hand, this work could be used as a model of computation in the design process.

Keywords: numerical simulation, efficiency, fire tube, heat exchanger, convection and conduction

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Authors: Igor Filikhin, Vladimir M. Suslov, Roman Ya. Kezerashvili, Branislav Vlahivic

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The mass-polarization term of the three-body kinetic energy operator is evaluated for different systems which include two identical particles: A+A+B. The term has to be taken into account for the analysis of AB- and AA-interactions based on experimental data for two- and three-body ground state energies. In this study, we present three-body calculations within the framework of a potential model for the kaonic clusters K−K−p and ppK−, nucleus 3H and hypernucleus 6 ΛΛHe. The systems are well clustering as A+ (A+B) with a ground state energy E2 for the pair A+B. The calculations are performed using the method of the Faddeev equations in configuration space. The phenomenological pair potentials were used. We show a correlation between the mass ratio mA/mB and the value δB of the mass-polarization term. For bosonic-like systems, this value is defined as δB = 2E2 − E3, where E3 is three-body energy when VAA = 0. For the systems including three particles with spin(isospin), the models with average AB-potentials are used. In this case, the Faddeev equations become a scalar one like for the bosonic-like system αΛΛ. We show that the additional energy conected with the mass-polarization term can be decomposite to a sum of the two parts: exchenge related and reduced mass related. The state of the system can be described as the following: the particle A1 is bound within the A + B pair with the energy E2, and the second particle A2 is bound with the pair with the energy E3 − E2. Due to the identity of A particles, the particles A1 and A2 are interchangeable in the pair A + B. We shown that the mass polarization δB correlates with a type of AB potential using the system αΛΛ as an example.

Keywords: three-body systems, mass polarization, Faddeev equations, nuclear interactions

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Ahmad Almajid

Abstract:

The idea of unifying quantum mechanics with general relativity is still a dream for many researchers, as physics has only two paths, no more. Einstein's path, which is mainly based on particle mechanics, and the path of Paul Dirac and others, which is based on wave mechanics, the incompatibility of the two approaches is due to the radical difference in the initial assumptions and the mathematical nature of each approach. Logical thinking in modern physics leads us to two problems: - In quantum mechanics, despite its success, the problem of measurement and the problem of wave function interpretation is still obscure. - In special relativity, despite the success of the equivalence of rest-mass and energy, but at the speed of light, the fact that the energy becomes infinite is contrary to logic because the speed of light is not infinite, and the mass of the particle is not infinite too. These contradictions arise from the overlap of relativistic and quantum mechanics in the neighborhood of the speed of light, and in order to solve these problems, one must understand well how to move from relativistic mechanics to quantum mechanics, or rather, to unify them in a way different from Dirac's method, in order to go along with God or Nature, since, as Einstein said, "God doesn't play dice." From De Broglie's hypothesis about wave-particle duality, Léon Brillouin's definition of the new proper time was deduced, and thus the quantum Lorentz factor was obtained. Finally, using the Euler-Lagrange equation, we come up with new equations in quantum mechanics. In this paper, the two problems in modern physics mentioned above are solved; it can be said that this new approach to quantum mechanics will enable us to unify it with general relativity quite simply. If the experiments prove the validity of the results of this research, we will be able in the future to transport the matter at speed close to the speed of light. Finally, this research yielded three important results: 1- Lorentz quantum factor. 2- Planck energy is a limited case of Einstein energy. 3- Real quantum mechanics, in which new equations for quantum mechanics match and exceed Dirac's equations, these equations have been reached in a completely different way from Dirac's method. These equations show that quantum mechanics is a limited case of relativistic mechanics. At the Solvay Conference in 1927, the debate about quantum mechanics between Bohr, Einstein, and others reached its climax, while Bohr suggested that if particles are not observed, they are in a probabilistic state, then Einstein said his famous claim ("God does not play dice"). Thus, Einstein was right, especially when he didn't accept the principle of indeterminacy in quantum theory, although experiments support quantum mechanics. However, the results of our research indicate that God really does not play dice; when the electron disappears, it turns into amicable particles or an elastic medium, according to the above obvious equations. Likewise, Bohr was right also, when he indicated that there must be a science like quantum mechanics to monitor and study the motion of subatomic particles, but the picture in front of him was blurry and not clear, so he resorted to the probabilistic interpretation.

Keywords: lorentz quantum factor, new, planck’s energy as a limiting case of einstein’s energy, real quantum mechanics, new equations for quantum mechanics

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

Abstract:

Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers' equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile

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Authors: M. Ghanbari, S. Hossainpour, G. Rezazadeh

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In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

Keywords: micro-polar theory, Galerkin method, MEMS, micro-fluid

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Authors: Rachid Fermous, Rima Mebrek

Abstract:

Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamic multi-fluid equations, we investigated the expansion of dense plasma. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. It is shown that dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

Keywords: plasma expansion, quantum degeneracy, weakly relativistic, under-dense plasma

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Authors: Adamu S. Salawu, Ibrahim O. Isah

Abstract:

Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: A. Terfous, Y. Liu, A. Ghenaim, P. A. Garambois

Abstract:

With increasing urbanization worldwide, it is crucial to sustainably manage sediment flows in urban networks and especially in stormwater detention basins. One key aspect is to propose optimized designs for detention tanks in order to best reduce flood peak flows and in the meantime settle particles. It is, therefore, necessary to understand complex flows patterns and sediment deposition conditions in stormwater detention basins. The aim of this paper is to study flow structure and particle deposition pattern for a given tank geometry in view to control and maximize sediment deposition. Both numerical simulation and experimental works were done to investigate the flow and sediment distribution in a storm tank with a cavity. As it can be indicated, the settle distribution of the particle in a rectangular tank is mainly determined by the flow patterns and the bed shear stress. The flow patterns in a rectangular tank differ with different geometry, entrance flow rate and the water depth. With the changing of flow patterns, the bed shear stress will change respectively, which also play an influence on the particle settling. The accumulation of the particle in the bed changes the conditions at the bottom, which is ignored in the investigations, however it worth much more attention, the influence of the accumulation of the particle on the sedimentation should be important. The approach presented here is based on the resolution of the Reynolds averaged Navier-Stokes equations to account for turbulent effects and also a passive particle transport model. An analysis of particle deposition conditions is presented in this paper in terms of flow velocities and turbulence patterns. Then sediment deposition zones are presented thanks to the modeling with particle tracking method. It is shown that two recirculation zones seem to significantly influence sediment deposition. Due to the possible overestimation of particle trap efficiency with standard wall functions and stick conditions, further investigations seem required for basal boundary conditions based on turbulent kinetic energy and shear stress. These observations are confirmed by experimental investigations processed in the laboratory.

Keywords: storm sewers, sediment deposition, numerical simulation, experimental investigation

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Authors: Minoo Ghasemzadeh, Rouzbeh Riazi, Shidvash Vakilipour, Alireza Ramezani

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In this study, thermo acoustic oscillations of a lean premixed combustor has been investigated, and a mono-dimensional code was developed in this regard. The linearized equations of motion are solved for perturbations with time dependence〖 e〗^iwt. Two flame models were considered in this paper and the effect of mean flow and boundary conditions were also investigated. After manipulation of flame heat release equation together with the equations of flow perturbation within the main components of the combustor model (i.e., plenum/ premixed duct/ and combustion chamber) and by considering proper boundary conditions between the components of model, a system of eight homogeneous equations can be obtained. This simplification, for the main components of the combustor model, is convenient since low frequency acoustic waves are not affected by bends. Moreover, some elements in the combustor are smaller than the wavelength of propagated acoustic perturbations. A convection time is also assumed to characterize the required time for the acoustic velocity fluctuations to travel from the point of injection to the location of flame front in the combustion chamber. The influence of an extended flame model on the acoustic frequencies of combustor was also investigated, assuming the effect of flame speed as a function of equivalence ratio perturbation, on the rate of flame heat release. The abovementioned system of equations has a related eigenvalue equation which has complex roots. The sign of imaginary part of these roots determines whether the disturbances grow or decay and the real part of these roots would give the frequency of the modes. The results show a reasonable agreement between the predicted values of dominant frequencies in the present model and those calculated in previous related studies.

Keywords: combustion instability, dominant frequencies, flame speed, premixed combustor

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Authors: Oscar Bautista, Jose Arcos

Abstract:

In this work, we conduct a theoretical analysis of an oscillatory electroosmotic flow in a parallel-plate microchannel taking into account slippage at the microchannel walls. The governing equations given by the Poisson-Boltzmann (with the Debye-Huckel approximation) and momentum equations are nondimensionalized from which four dimensionless parameters appear; a Reynolds angular number, the ratio between the zeta potentials of the microchannel walls, the electrokinetic parameter and the dimensionless slip length which measures the competition between the Navier slip length and the half height microchannel. The principal results indicate that the slippage has a strong influence on the magnitude of the oscillatory electroosmotic flow increasing the velocity magnitude up to 50% for the numerical values used in this work.

Keywords: electroosmotic flows, oscillatory flow, slippage, microchannel

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