Search results for: Einstein's equations

Authors: S. Ali, M. Baccar

Abstract:

In this work, numerical simulations were carried out using a specific CFD code in order to study the performance of an innovative Scraped Surface Heat Exchanger (SSHE) with helical ribbons for Bingham fluids (threshold fluids). The resolution of three-dimensional form of the conservation equations (continuity, momentum and energy equations) was carried out basing on the finite volume method (FVM). After studying the effect of dimensionless numbers (axial Reynolds, rotational Reynolds and Oldroyd numbers) on the hydrodynamic and thermal behaviors within SSHE, a parametric study was developed, by varying the width of the helical ribbon, the clearance between the stator wall and the tip of the ribbon and the number of turns of the helical ribbon, in order to improve the heat transfer inside the exchanger. The effect of these geometrical numbers on the hydrodynamic and thermal behaviors was discussed.

Keywords: Heat transfer, helical ribbons, hydrodynamic behavior, parametric study, scraped surface heat exchanger, thermal behavior.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

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This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: W. Lai, A. A. Khan

Abstract:

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Keywords: Discontinuous finite element, TVD Runge-Kuttascheme, slope limiters, Riemann solvers, shallow water flow.

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Authors: Avinash Chandra, R. P. Chhabra

Abstract:

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number, . The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of the streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the constant wall temperature is prescribed on the surface of the cylinder. The heat transfer characteristics are analyzed in terms of the local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is found to be minimum at the rear stagnation point on the flat surface. Overall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling considerations. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the interpolation of the present numerical results for the intermediate values of the Prandtl or Grashof numbers for both thermal boundary conditions.

Keywords: Constant heat flux, Constant surface temperature, Grashof number, natural convection, Prandtl number, Semi-circular cylinder

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Authors: Hanan Rizk

Abstract:

Heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques, and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed the proportional–integral–derivative (PID) controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: S. S. Nafee, A. K. Al-Ramady, S. A. Shaheen

Abstract:

The mixed oxide nuclear fuel (MOX) of U and Pu contains several percent of fission products and minor actinides, such as neptunium, americium and curium. It is important to determine accurately the decay heat from Curium isotopes as they contribute significantly in the MOX fuel. This heat generation can cause samples to melt very quickly if excessive quantities of curium are present. In the present paper, we introduce a new approach that can predict the decay heat from curium isotopes. This work is a part of the project funded by King Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, and take place in King Abdulaziz University (KAU), Saudi Arabia. The approach is based on the numerical solution of coupled linear differential equations that describe decays and buildups of many nuclides to calculate the decay heat produced after shutdown. Results show the consistency and reliability of the approach applied.

Keywords: Decay heat, Mixed oxide nuclear fuel, Numerical Solution of Linear Differential Equations, and Curium isotopes

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Authors: Hamidreza Bagheri, Alireza Shariati

Abstract:

There are many difficulties in the purification of raw components and products. However, researchers are seeking better ways for purification. One of the recent methods is extraction using supercritical fluids. In this study, the phase equilibria of benzoic acid -supercritical carbon dioxide system were investigated. Regarding the phase equilibria of this system, the modeling of solid-supercritical fluid behavior was performed using the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) and Peng-Robinson equations of state (PR EoS). For this purpose, five PC-SAFT EoS parameters for pure benzoic acid were obtained using its experimental vapor pressure. Benzoic acid has association sites and the behavior of the benzoic acid-supercritical fluid system was well predicted using both equations of state, while the binary interaction parameter values for PR EoS were negative. Genetic algorithm, which is one of the most accurate global optimization algorithms, was also used to optimize the pure benzoic acid parameters and the binary interaction parameters. The AAD% value for the PC-SAFT EoS, were 0.22 for the carbon dioxide-benzoic acid system.

Keywords: Supercritical fluids, Solubility, Solid, PC-SAFT EoS, Genetic algorithm.

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Authors: Zohreh Orshesh

Abstract:

In this study, a 3D combustion chamber was simulated using FLUENT 6.32. Aim to obtain detailed information on combustion characteristics and _ nitrogen oxides in the furnace and the effect of oxygen enrichment in a combustion process. Oxygenenriched combustion is an effective way to reduce emissions. This paper analyzes NO emission, including thermal NO and prompt NO. Flow rate ratio of air to fuel is varied as 1.3, 3.2 and 5.1 and the oxygen enriched flow rates are 28, 54 and 68 lit/min. The 3D Reynolds Averaged Navier Stokes (RANS) equations with standard k-ε turbulence model are solved together by Fluent 6.32 software. First order upwind scheme is used to model governing equations and the SIMPLE algorithm is used as pressure velocity coupling. Results show that for AF=1.3, increase the oxygen flow rate of oxygen reduction in NO emissions is Lance. Moreover, in a fixed oxygen enrichment condition, increasing the air to fuel ratio will increase the temperature peak, but not the NO emission rate. As a result, oxygen enrichment can reduce the NO emission at this kind of furnace in low air to fuel rates.

Keywords: Combustion chamber, Oxygen enrichment, Reynolds Averaged Navier- Stokes, NO emission

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Authors: M. Salmanpour, O. Nourani Zonouz

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In this research, a numerical simulation of an Electrohydrodynamic (EHD) actuator’s effects on the flow around a square cylinder by using a finite volume method has been investigated. This is one of the newest ways for controlling the fluid flows. Two plate electrodes are flush-mounted on the surface of the cylinder and one wire electrode is placed on the line with zero angle of attack relative to the stagnation point and excited with DC power supply. The discharge produces an electric force and changes the local momentum behaviors in the fluid layers. For this purpose, after selecting proper domain and boundary conditions, the electric field relating to the problem has been analyzed and then the results in the form of electrical body force have been entered in the governing equations of fluid field (Navier-Stokes equations). The effect of ionic wind resulted from the Electrohydrodynamic actuator, on the velocity, pressure and the wake behind cylinder has been considered. According to the results, it is observed that the fluid flow accelerates in the nearest wall of the frontal half of the cylinder and the pressure difference between frontal and hinder cylinder is increased.

Keywords: CFD, corona discharge, electro hydrodynamics, flow around square cylinders.

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Authors: Cheng-Ying Lo

Abstract:

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Keywords: Differential transform, hyperbolic heat transfer, thin film, ultrashort-pulsed laser.

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Authors: G.Ashwini, A.T.Eswara

Abstract:

This paper examines the forced convection flow of incompressible, electrically conducting viscous fluid past a sharp wedge in the presence of heat generation or absorption with an applied magnetic field. The system of partial differential equations governing Falkner - Skan wedge flow and heat transfer is first transformed into a system of ordinary differential equations using similarity transformations which is later solved using an implicit finite - difference scheme, along with quasilinearization technique. Numerical computations are performed for air (Pr = 0.7) and displayed graphically to illustrate the influence of pertinent physical parameters on local skin friction and heat transfer coefficients and, also on, velocity and temperature fields. It is observed that the magnetic field increases both the coefficients of skin friction and heat transfer. The effect of heat generation or absorption is found to be very significant on heat transfer, but its effect on the skin friction is negligible. Indeed, the occurrence of overshoot is noticed in the temperature profiles during heat generation process, causing the reversal in the direction of heat transfer.

Keywords: Heat generation / absorption, MHD Falkner- Skan flow, skin friction and heat transfer

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Authors: Yang Xiaoliang, Liu Wei, Wang Hongbo, Zhao Yunfei

Abstract:

Numerical investigation of the characteristics of an 80° delta wing in combined force-pitch and free-roll is presented. The implicit, upwind, flux-difference splitting, finite volume scheme and the second-order-accurate finite difference scheme are employed to solve the flow governing equations and Euler rigid-body dynamics equations, respectively. The characteristics of the delta wing in combined free-roll and large amplitude force-pitch is obtained numerically and shows a well agreement with experimental data qualitatively. The motion in combined force-pitch and free-roll significantly reduces the lift force and transverse stabilities of the delta wing, which is closely related to the flying safety. Investigations on sensitive factors indicate that the roll-axis moment of inertia and the structural damping have great influence on the frequency and amplitude, respectively. Moreover, the turbulence model is considered as an influencing factor in the investigation.

Keywords: combined force-pitch and free-roll, numericalsimulation, sensitive factors, slender delta wing, wing rock

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Authors: Rui Sun, Tamer M. Ismail, Xiaohan Ren, M. Abd El-Salam

Abstract:

Incineration of municipal solid waste (MSW) is one of the key scopes in the global clean energy strategy. A computational fluid dynamics (CFD) model was established in order to reveal these features of the combustion process in a fixed porous bed of MSW. Transporting equations and process rate equations of the waste bed were modeled and set up to describe the incineration process, according to the local thermal conditions and waste property characters. Gas phase turbulence was modeled using k-ε turbulent model and the particle phase was modeled using the kinetic theory of granular flow. The heterogeneous reaction rates were determined using Arrhenius eddy dissipation and the Arrhenius-diffusion reaction rates. The effects of primary air flow rate and temperature in the burning process of simulated MSW are investigated experimentally and numerically. The simulation results in bed are accordant with experimental data well. The model provides detailed information on burning processes in the fixed bed, which is otherwise very difficult to obtain by conventional experimental techniques.

Keywords: Computational Fluid Dynamics (CFD) model, Waste Incineration, Municipal Solid Waste (MSW), Fixed Bed, Primary air.

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Authors: Rama Bhargava, Mania Goyal

Abstract:

The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Keywords: Viscoelastic nanofluid, partial slip, stretching sheet, heat generation/absorption, MHD flow, FEM.

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Authors: M. M. Selim

Abstract:

The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.

Keywords: Dissipation medium, initial stress, longitudinal waves, reflection coefficients, reflection of plane waves, transverse waves.

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Authors: Gulshan Sachdeva, Ram Bilash

Abstract:

In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy-Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

Keywords: Exergy analysis, Gouy-Stodola, refrigeration, vapor absorption.

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Authors: Tejeet Singh, Ishavneet Singh

Abstract:

The present study focused on carrying out the creep analysis in an isotropic thick-walled composite cylindrical pressure vessel composed of aluminum matrix reinforced with silicon-carbide in particulate form. The creep behavior of the composite material has been described by the threshold stress based creep law. The values of stress exponent appearing in the creep law were selected as 3, 5 and 8. The constitutive equations were developed using well known von-Mises yield criteria. Models were developed to find out the distributions of creep stress and strain rate in thick-walled composite cylindrical pressure vessels under internal pressure. In order to obtain the stress distributions in the cylinder, the equilibrium equation of the continuum mechanics and the constitutive equations are solved together. It was observed that the radial stress, tangential stress and axial stress increases along with the radial distance. The cross-over was also obtained almost at the middle region of cylindrical vessel for tangential and axial stress for different values of stress exponent. The strain rates were also decreasing in nature along the entire radius.

Keywords: Steady state creep, composite, cylinder, pressure.

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Authors: T. H. Young, Y. S. Ciou

Abstract:

The free and forced in-plane vibrations of axially moving plates are investigated in this work. The plate possesses an internal damping of which the constitutive relation obeys the Kelvin-Voigt model, and the excitations are arbitrarily distributed on two opposite edges. First, the equations of motion and the boundary conditions of the axially moving plate are derived. Then, the extended Ritz method is used to obtain discretized system equations. Finally, numerical results for the natural frequencies and the mode shapes of the in-plane vibration and the in-plane response of the moving plate subjected to arbitrary edge excitations are presented. It is observed that the symmetry class of the mode shapes of the in-plane vibration disperses gradually as the moving speed gets higher, and the u- and v-components of the mode shapes belong to different symmetry class. In addition, large response amplitudes having shapes similar to the mode shapes of the plate can be excited by the edge excitations at the resonant frequencies and with the same symmetry class of distribution as the u-components.

Keywords: Arbitrary edge excitations, axially moving plates, in-plane vibration, extended Ritz method.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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Authors: O. Rahli, N. Mimouni, R. Bennacer, K. Bouhadef

Abstract:

This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.

Keywords: Heat and mass transfer, mixed convection, Poiseuille-Rayleigh-Benard flow, rectangular duct.

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Authors: Worachat Wannawong, Usa W. Humphries, Prungchan Wongwises, Suphat Vongvisessomjai, Wiriya Lueangaram

Abstract:

A numerical analysis of wave and hydrodynamic models is used to investigate the influence of WAve and Storm Surge (WASS) in the regional and coastal zones. The numerical analyzed system consists of the WAve Model Cycle 4 (WAMC4) and the Princeton Ocean Model (POM) which used to solve the energy balance and primitive equations respectively. The results of both models presented the incorporated surface wave in the regional zone affected the coastal storm surge zone. Specifically, the results indicated that the WASS generally under the approximation is not only the peak surge but also the coastal water level drop which can also cause substantial impact on the coastal environment. The wave–induced surface stress affected the storm surge can significantly improve storm surge prediction. Finally, the calibration of wave module according to the minimum error of the significant wave height (Hs) is not necessarily result in the optimum wave module in the WASS analyzed system for the WASS prediction.

Keywords: energy balance equation, numerical analysis, primitiveequation, storm surge, wave.

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Authors: Bandaris Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.

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Authors: Li Zong-Cheng

Abstract:

It is by reason of the unified measure of varieties of resources and the unified processing of the disposal of varieties of resources, that these closely related three of new basic models called the resources assembled node and the disposition integrated node as well as the intelligent organizing node are put forth in this paper; the three closely related quantities of integrative analytical mechanics including the disposal intensity and disposal- weighted intensity as well as the charge of resource charge are set; and then the resources assembled space and the disposition integrated space as well as the intelligent organizing space are put forth. The system of fundamental equations and model of complete factor synergetics is preliminarily approached for the general situation in this paper, to form the analytical base of complete factor synergetics. By the essential variables constituting this system of equations we should set twenty variables respectively with relation to the essential dynamical effect, external synergetic action and internal synergetic action of the system.

Keywords: complex system, disposal of resources, completefactor synergetics, fundamental equation.

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Authors: K. Soldatova, Y. Galerkin

Abstract:

A loading factor performance is necessary for the modeling of centrifugal compressor gas dynamic performance curve. Measured loading factors are linear function of a flow coefficient at an impeller exit. The performance does not depend on the compressibility criterion. To simulate loading factor performances, the authors present two parameters: a loading factor at zero flow rate and an angle between an ordinate and performance line. The calculated loading factor performances of non-viscous are linear too and close to experimental performances. Loading factor performances of several dozens of impellers with different blade exit angles, blade thickness and number, ratio of blade exit/inlet height, and two different type of blade mean line configuration. There are some trends of influence, which are evident – comparatively small blade thickness influence, and influence of geometry parameters is more for impellers with bigger blade exit angles, etc. Approximating equations for both parameters are suggested. The next phase of work will be simulating of experimental performances with the suggested approximation equations as a base.

Keywords: Centrifugal compressor stage, centrifugal compressor, loading factor, gas dynamic performance curve.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

Abstract:

A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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

Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: Biomagnetic fluid, FHD, nonlinear stretching sheet, slip parameter.

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

Abstract:

This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: Dynamic response, Nonlinear impact response, Finite Element analysis, Numerical analysis.

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

Abstract:

In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: Electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, Non-Newtonian power-law fluids, numerical simulation.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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