Search results for: navier-stokes equations in a rotating frame of refence

Authors: Lian Song, Shao-Bo Kang, Bo Yang

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Concrete filled steel tubular (CFST) structure has been widely used in construction practices due to its superior performances under various loading conditions. However, limited studies are available when this type of structure is subjected to impact or explosive loads. Current methods in relevant design codes are not specific for preventing progressive collapse of CFST structures. Therefore, it is necessary to carry out numerical simulations on CFST structure under impact loads. In this study, finite element analyses are conducted on the mechanical behaviour of composite frames which composed of CFST columns and steel beams subject to impact loading. In the model, CFST columns are simulated using finite element software ABAQUS. The model is verified by test results of solid and hollow CFST columns under lateral impacts, and reasonably good agreement is obtained through comparisons. Thereafter, a multi-scale finite element modelling technique is developed to evaluate the behaviour of a five-storey three-span planar composite frame. Alternate path method and direct simulation method are adopted to perform the dynamic response of the frame when a supporting column is removed suddenly. In the former method, the reason for column removal is not considered and only the remaining frame is simulated, whereas in the latter, a specific impact load is applied to the frame to take account of the column failure induced by vehicle impact. Comparisons are made between these two methods in terms of displacement history and internal force redistribution, and design recommendations are provided for the design of CFST structures under impact loads.

Keywords: planar composite frame, collapse analysis, impact loading, direct simulation method, alternate path method

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Authors: Shahrokh Barati

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In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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Authors: Bijit Kalita, K. V. N. Surendra

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Rotating disk is one of the most indispensable parts of a rotating machine. Rotating disk has found many applications in the diverging field of science and technology. In this paper, we have taken into consideration the problem of a heavy spinning disk mounted on a rotor system acted upon by boundary traction. Finite element modelling is used at various loading condition to determine the mixed mode stress intensity factors. The effect of combined shear and normal traction on the boundary is incorporated in the analysis under the action of gravity. The variation near the crack tip is characterized in terms of the stress intensity factor (SIF) with an aim to find the SIF for a wide range of parameters. The results of the finite element analyses carried out on the compressed disk of a belt pulley arrangement using fracture mechanics concepts are shown. A total of hundred cases of the problem are solved for each of the variations in loading arc parameter and crack orientation using finite element models of the disc under compression. All models were prepared and analyzed for the uncracked disk, disk with a single crack at different orientation emanating from shaft hole as well as for a disc with pair of cracks emerging from the same center hole. Curves are plotted for various loading conditions. Finally, crack propagation paths are determined using kink angle concepts.

Keywords: crack-tip deformations, static loading, stress concentration, stress intensity factor

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Muhammad Rizwan, Naveed Ahmad, Akhtar Naeem Khan

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Seismic behavior factors are evaluated for the performance assessment of low rise reinforced concrete RC frame structures based on experimental study of unidirectional dynamic shake table testing of two 1/3rd reduced scaled two storey frames, with a code confirming special moment resisting frame (SMRF) model and a noncompliant model of similar characteristics but built in low strength concrete .The models were subjected to a scaled accelerogram record of 1994 Northridge earthquake to deformed the test models to final collapse stage in order to obtain the structural response parameters. The fully compliant model was observed with more stable beam-sway response, experiencing beam flexure yielding and ground-storey column base yielding upon subjecting to 100% of the record. The response modification factor - R factor obtained for the code complaint and deficient prototype structures were 7.5 and 4.5 respectively, which is about 10% and 40% less than the UBC-97 specified value for special moment resisting reinforced concrete frame structures.

Keywords: Northridge 1994 earthquake, reinforced concrete frame, response modification factor, shake table testing

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Authors: Ramzi Suleiman

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Recently, the author proposed an observationally-based relativity theory termed information relativity theory (IRT). The theory is simple and is based only on basic principles, with no prior axioms and no free parameters. For the case of a body of mass in uniform rectilinear motion relative to an observer, the theory transformations uncovered a matter-dark matter duality, which prescribes that the sum of the densities of the body's baryonic matter and dark matter, as measured by the observer, is equal to the body's matter density at rest. It was shown that the theory transformations were successful in predicting several important phenomena in small particle physics, quantum physics, and cosmology. This paper extends the theory transformations to the cases of rotating disks and spheres. The resulting transformations for a rotating disk are utilized to derive predictions of the radial distributions of matter and dark matter densities in rotationally supported galaxies based solely on their observed rotation curves. It is also shown that for galaxies with flattening curves, good approximations of the radial distributions of matter and dark matter and of the dark matter fraction could be obtained from one measurable scale radius. Test of the model on five galaxies, chosen randomly from the SPARC database, yielded impressive predictions. The rotation curves of all the investigated galaxies emerged as accurate traces of the predicted radial density distributions of their dark matter. This striking result raises an intriguing physical explanation of gravity in galaxies, according to which it is the proximal drag of the stars and gas in the galaxy by its rotating dark matter web. We conclude by alluding briefly to the application of the proposed model to stellar systems and black holes. This study also hints at the potential of the discovered matter-dark matter duality in fixing the standard model of elementary particles in a natural manner without the need for hypothesizing about supersymmetric particles.

Keywords: dark matter, galaxies rotation curves, SPARC, rotating disk

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Authors: Hamid Nikzad, Shinta Yoshitomi

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In this paper, nonlinear static pushover analysis is performed on 15 storied RC building structure with a shear wall to evaluate the seismic performance of the building. Section sizes of the members are obtained based on structural optimization method utilizing MATLAB frame optimizer, then the structure is simulated and designed in ETABS program conforming ACI 318-14 design code. The pushover curve has been generated by pushing the top node of the structure to the limited target displacement. Members failure due to the formation of plastic hinges, considering shear wall-frame structure was observed and the result of this study is presented based on current regulation of FEMA356, ASCE7-10, and ACI 318-14 design criteria

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures

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Authors: Aboozar Aghaei

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In the present work, the dissimilar Monel400 and SS316 were joined by friction stir welding (FSW). The applied rotating speed was 400 rpm, whereas the traverse speed varied between 50 and 150 mm/min. At a constant rotating speed, the sound welds were obtained at the welding speeds of 50 and 100 mm/min. However, a groove-like defect was formed when the welding speed exceeded 100 mm/min. The mechanical properties of the joints were evaluated using tensile and fatigue tests. The fatigue strength of dissimilar FSWed specimens was higher than that of both Monel400 and SS316. To study the failure behavior of FSWed specimens, the fracture surfaces were analyzed using a scanning electron microscope (SEM). The failure analysis indicates that different mechanisms may contribute to the fracture of welds. This was attributed to the dissimilar characteristics of dissimilar materials exhibiting different failure behaviors.

Keywords: frictions stir welding (FSW), stainless steel, mechanical properties, Monel400

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Aboozar Aghaei, Kamran Dehghani

Abstract:

In the present work, the dissimilar Monel400 and SS316 were joined by friction stir welding (FSW). The applied rotating speed was 400 rpm, whereas the traverse speed varied between 50 and 150 mm/min. At a constant rotating speed, the sound welds were obtained at the welding speeds of 50 and 100 mm/min. However, a groove-like defect was formed when the welding speed exceeded 100 mm/min. The mechanical properties of the joints were evaluated using tensile and fatigue tests. The fatigue strength of dissimilar FSWed specimens was higher than that of both Monel400 and SS316. To study the failure behavior of FSWed specimens, the fracture surfaces were analyzed using a scanning electron microscope (SEM). The failure analysis indicates that different mechanisms may contribute to the fracture of welds. This was attributed to the dissimilar characteristics of dissimilar materials exhibiting different failure behaviors.

Keywords: frictions stir welding, stainless steel, Monel400, mechanical properties

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Authors: Ali Kadir, S. R. Mishra, M. Shamshuddin, O. Anwar Beg

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Motivation- Rotating disk bio-reactors are fundamental to numerous medical/biochemical engineering processes including oxygen transfer, chromatography, purification and swirl-assisted pumping. The modern upsurge in biologically-enhanced engineering devices has embraced new phenomena including bioconvection of micro-organisms (photo-tactic, oxy-tactic, gyrotactic etc). The proven thermal performance superiority of nanofluids i.e. base fluids doped with engineered nanoparticles has also stimulated immense implementation in biomedical designs. Motivated by these emerging applications, we present a numerical thermofluid dynamic simulation of the transport phenomena in bioconvection nanofluid rotating disk bioreactor flow. Methodology- We study analytically and computationally the time-dependent three-dimensional viscous gyrotactic bioconvection in swirling nanofluid flow from a rotating disk configuration. The disk is also deformable i.e. able to extend (stretch) in the radial direction. Stefan blowing is included. The Buongiorno dilute nanofluid model is adopted wherein Brownian motion and thermophoresis are the dominant nanoscale effects. The primitive conservation equations for mass, radial, tangential and axial momentum, heat (energy), nanoparticle concentration and micro-organism density function are formulated in a cylindrical polar coordinate system with appropriate wall and free stream boundary conditions. A mass convective condition is also incorporated at the disk surface. Forced convection is considered i.e. buoyancy forces are neglected. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Karman and other transformations to render the boundary value problem (BVP) into an ordinary differential system which is solved with the efficient Adomian decomposition method (ADM). Validation with earlier Runge-Kutta shooting computations in the literature is also conducted. Extensive computations are presented (with the aid of MATLAB symbolic software) for radial and circumferential velocity components, temperature, nanoparticle concentration, micro-organism density number and gradients of these functions at the disk surface (radial local skin friction, local circumferential skin friction, Local Nusselt number, Local Sherwood number, motile microorganism mass transfer rate). Main Findings- Increasing radial stretching parameter decreases radial velocity and radial skin friction, reduces azimuthal velocity and skin friction, decreases local Nusselt number and motile micro-organism mass wall flux whereas it increases nano-particle local Sherwood number. Disk deceleration accelerates the radial flow, damps the azimuthal flow, decreases temperatures and thermal boundary layer thickness, depletes the nano-particle concentration magnitudes (and associated nano-particle species boundary layer thickness) and furthermore decreases the micro-organism density number and gyrotactic micro-organism species boundary layer thickness. Increasing Stefan blowing accelerates the radial flow and azimuthal (circumferential flow), elevates temperatures of the nanofluid, boosts nano-particle concentration (volume fraction) and gyrotactic micro-organism density number magnitudes whereas suction generates the reverse effects. Increasing suction effect reduces radial skin friction and azimuthal skin friction, local Nusselt number, and motile micro-organism wall mass flux whereas it enhances the nano-particle species local Sherwood number. Conclusions - Important transport characteristics are identified of relevance to real bioreactor nanotechnological systems not discussed in previous works. ADM is shown to achieve very rapid convergence and highly accurate solutions and shows excellent promise in simulating swirling multi-physical nano-bioconvection fluid dynamics problems. Furthermore, it provides an excellent complement to more general commercial computational fluid dynamics simulations.

Keywords: bio-nanofluids, rotating disk bioreactors, Von Karman swirling flow, numerical solutions

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Authors: Byung Il You, Ryun Oh, Gyo Woo Lee

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Manhole refers to facilities that are accessible to the people cleaning and inspection of sewer, and its covering is called manhole lid. Manhole lid is typically made of a cast iron material. Due to the heavy weight of the cast iron manhole lids their installation and maintenance are not easy, and an electrical shock and corrosion aging of them can cause critical problems. The manhole body and the lid manufacturing using the fiber-reinforced composite material can reduce the weight considerably compared to the cast iron manhole. But only the fiber reinforcing is hard to maintain the heavy load, and the method of the iron frame with double injection molding of the composite material has been proposed widely. In this study reflecting the situation of this market, the structural design of the iron frame for the composite manhole lid was carried out. Structural analysis with the computer simulation for the effectively distributed load on the iron frame was conducted. In addition, we want to assess manufacturing costs through the comparing of weights and number of welding spots of the frames. Despite the cross-sectional area is up to 38% compared with the basic solid form the maximum von Mises stress is increased at least about 7 times locally near the rim and the maximum strain in the central part of the lid is about 5.5 times. The number of welding points related to the manufacturing cost was increased gradually with the more complicated shape. Also, the higher the height of the arch in the center of the lid the better result might be obtained. But considering the economic aspect of the composite fabrication we determined the same thickness as the frame for the height of the arch at the center of the lid. Additionally in consideration of the number of the welding points we selected the hexagonal as the optimal shape. Acknowledgment: These are results of a study on the 'Leaders Industry-university Cooperation' Project, supported by the Ministry of Education (MOE).

Keywords: manhole lid, iron frame, structural design, computer simulation

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Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li

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Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.

Keywords: coupling theory, stiffness matrix, e-bike, finite element model

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Authors: Draoui Belkacem, Rahmani Lakhdar, Benachour Elhadj, Seghier Oussama

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Rheology is known to have a strong impact on the flow behavior and the power consumption of mechanically agitated vessels. The laminar 2D agitation flow and power consumption of viscoplastic fluids with an anchor impeller in a stirring tank is studied by using computational fluid dynamics (CFD). In this work the objective of this paper is: to evaluate the power consumption for yield stress fluids in standard mixing system. The power consumption is calculated for the different types of anchor impeller configurations and an optimum configuration is proposed.The hydrodynamic fields of incompressible yield stress fluid with model of Bingham in a cylindrical vessel not chicaned equipped with anchor stirrer was undertaken by means of numerical simulation. The flow structures, and especially the effect of inertia, the plasticity and the yield stress, are discussed.

Keywords: rheology, 2D, numerical, anchor, rotating vissel, non-Newtonien fluid

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Vera Wilden, Benno Hoffmeister, Georgios Balaskas, Lukas Rauber, Burkhard Walter

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Light-weight timber frame elements represent an efficient structural solution for wooden multistory buildings. The wall elements of such buildings – which act as shear diaphragms- provide lateral stiffness and resistance to wind and seismic loads. The tendency towards multi-story structures leads to challenges regarding the prediction of stiffness, strength and ductility of the buildings. Lightweight timber frame elements are built up of several structural parts (sheeting, fasteners, frame, support and anchorages); each of them contributing to the dynamic response of the structure. This contribution describes the experimental and numerical investigation and development of enhanced lightweight timber frame buildings. These developments comprise high-performance timber frame walls with the variable arrangements of sheathing planes and dissipative anchors at the base of the timber buildings, which reduce damages to the timber structure and can be exchanged after significant earthquakes. In order to prove the performance of the developed elements in the context of a real building a full-scale two-story building core was designed and erected in the laboratory and tested experimentally for its seismic performance. The results of the tests and a comparison of the test results to the predicted behavior are presented. Observation during the test also reveals some aspects of the design and details which need to consider in the application of the timber walls in the context of the complete building.

Keywords: dissipative anchoring, full scale test, push-over-test, wood shear walls

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Authors: D. S. Naumann, B. J. Evans, O. Hassan

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This paper outlines the development of an automated aerodynamic optimisation algorithm using a novel method of parameterising a computational mesh by employing user–defined control nodes. The shape boundary movement is coupled to the movement of the novel concept of the control nodes via a quasi-1D-linear deformation. Additionally, a second order smoothing step has been integrated to act on the boundary during the mesh movement based on the change in its second derivative. This allows for both linear and non-linear shape transformations dependent on the preference of the user. The domain mesh movement is then coupled to the shape boundary movement via a Delaunay graph mapping. A Modified Cuckoo Search (MCS) algorithm is used for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible NavierStokes solver is used for aerodynamic modelling to predict aerodynamic design fitness. The resulting coupled algorithm is applied to a range of test cases in two dimensions including the design of a subsonic, transonic and supersonic intake and the optimisation approach is compared with more conventional optimisation strategies. Ultimately, the algorithm is tested on a three dimensional wing optimisation case.

Keywords: mesh movement, aerodynamic shape optimization, cuckoo search, shape parameterisation

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Authors: Xijun Yu, Zhenzhen Li, Zupeng Jia

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This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.

Keywords: cell-centered Lagrangian scheme, compressible Euler equations, RKDG method

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Authors: Michele Sinico

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In the Giovanelli illusion, some collinear dots appear misaligned, when each dot lies within a circle and the circles are not collinear. In this illusion, the role of the frame of reference, determined by the circles, is considered a crucial factor. Three experiments were carried out to study the influence of directionality of the circles on the misalignment. The adjustment method was used. Participants changed the orthogonal position of each dot, from the left to the right of the sequence, until a collinear sequence of dots was achieved. The first experiment verified the illusory effect of the misalignment. In the second experiment, the influence of two different directionalities of the circles (-0.58° and +0.58°) on the misalignment was tested. The results show an over-normalization on the sequences of the dots. The third experiment tested the misalignment of the dots without any inclination of the sequence of circles (0°). Only a local illusory effect was found. These results demonstrate that the directionality of the circles, as a global factor, can increase the misalignment. The findings also indicate that directionality and the frame of reference are independent factors in explaining the Giovanelli illusion.

Keywords: Giovannelli illusion, visual illusion, directionality, misalignment, the frame of reference

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Authors: Navid Daryasafar, Nima Farshidfar

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In this article, we make attempt to hide error in video with an emphasis on the time-wise use of autoregressive (AR) models. To resolve this problem, we assume that all information in one or more video frames is lost. Then, lost frames are estimated using analogous Pixels time information in successive frames. Accordingly, after presenting autoregressive models and how they are applied to estimate lost frames, two general methods are presented for using these models. The first method which is the same standard method of autoregressive models estimates lost frame in unidirectional form. Usually, in such condition, previous frames information is used for estimating lost frame. Yet, in the second method, information from the previous and next frames is used for estimating the lost frame. As a result, this method is known as bidirectional estimation. Then, carrying out a series of tests, performance of each method is assessed in different modes. And, results are compared.

Keywords: error steganography, unidirectional estimation, bidirectional estimation, AR linear estimation

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Authors: B. Mahfoud, R. Harouz

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The present work examine numerically the effect of axial magnetic field on mixed convection through a cylindrical cavity, filled with a liquid metal and having a rotating top and bottom disks. Effects of Richardson number (Ri = 0, 0.5, 1, and 2) and Hartman number (Ha = 0, 5, 10, and 20) on temperature and flow fields were analyzed. The basic state of this system is steady and axisymmetric, when the counter-rotation is sufficiently large, producing a free shear layer. This shear layer is unstable and different complex flows appear successively: steady states with an azimuthal wavenumber of 1; travelling waves and steady states with an azimuthal wavenumber of 2. Mixed modes and azimuthal wavenumber of 3 are also found with increasing Hartmann number. The stability diagram (Recr-Ha) corresponding to the axisymmetric-three-dimensional transition for increasing values of the axial magnetic field is obtained.

Keywords: axisymmetric, counter-rotating, instabilities, magnetohydrodynamic, magnetic field, wavenumber

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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Authors: Payel Das, Gnaneshwar Nelakanti

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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

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Authors: Augusto P. Andrade, Pedro L. Guedes, Pedro T. Da Silva, Liliane Ventura

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The present study evaluates the contribution of sunglasses frames as additional eye safety for ultraviolet backscatter light. Current sunglasses standards establish safe limits regarding lens transmittance in the 280 nm to 380 nm range. However, frames are additionally relevant in protecting the eyes from ultraviolet exposure. This study involves the use of a prototype that simulates backscattered light environments and quantifies the contribution of the frame as a function of the light that reaches the eye when wearing sunglasses. The prototype consists of an LED illuminated sphere, a mannequin head with optical sensors, and baseline and measurements are performed. A set of 29 samples was tested, and results show the variation of light blocking presented by different types of frames, ranging from 68% to 80%. This is still ongoing research. Prototype improvements for allowing albedo simulation, as well as the six types of sky simulation, are being implemented to show the intensity of UV light reaching the eye for several environments worldwide.

Keywords: sunglasses standards, sunglasses frame, ultraviolet protection, albedo

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Hua Li, Hongwu Deng

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The turbine blade's leading edge is usually cooled by jet impingement cooling technology due to the heaviest heat load. For a rotating turbine blade, however, the channel orientation (β, the angle between the jet direction and the rotating plane) could play an important role in influencing the flow field and heat transfer. Therefore, in this work, the effects of channel orientation (from 90° to 180°) on heat transfer in a jet impingement cooling channel are experimentally investigated. Furthermore, the investigations are conducted under an isothermal boundary condition. Both the jet-to-target surface distance and jet-to-jet spacing are three times the jet hole diameter. The jet Reynolds number is 5,000, and the maximum jet rotation number reaches 0.24. The results show that the rotation-induced variations of heat transfer are different in each channel orientation. In the cases of 90°≤β≤135°, a vortex generated in the low-radius region of the supply channel changes the mass-flowrate distribution in each jet hole. Therefore, the heat transfer in the low-radius region decreases with the rotation number, whereas the heat transfer in the high-radius region increases, indicating that a larger temperature gradient in the radial direction could appear in the turbine blade's leading edge. When 135°<β≤180°; however, the heat transfer of the entire stagnant zone decreases with the rotation number. The rotation-induced jet deflection is the primary factor that weakens the heat transfer, and jets cannot reach the target surface at high rotation numbers. For the downstream regions, however, the heat transfer is enhanced by 50%-80% in every channel orientation because the dead zone is broken by the rotation-induced secondary flow in the impingement channel.

Keywords: heat transfer, jet impingement cooling, channel orientation, high rotation number, isothermal boundary

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

Abstract:

In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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