Search results for: elliptic equations

Authors: Gilbert Makanda

Abstract:

The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.

Keywords: free convection, suction/injection, partial slip, viscous dissipation

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Authors: R. Haoui

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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: finite volume, lunchers, nozzles, shock wave

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Authors: Humayun R. H. Kabir

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An analytical solution before used for static and free-vibration response has been extended for thermal buckling response on cylindrical panel with anti-symmetric laminations. The partial differential equations that govern kinematic behavior of shells produce five coupled differential equations. The basic displacement and rotational unknowns are similar to first order shear deformation theory---three displacement in spatial space, and two rotations about in-plane axes. No drilling degree of freedom is considered. Boundary conditions are considered as complete hinge in all edges so that the panel respond on thermal inductions. Two sets of double Fourier series are considered in the analytical solution process. The sets are selected that satisfy mixed type of natural boundary conditions. Numerical results are presented for the first 10 eigenvalues, and first 10 mode shapes for Ux, Uy, and Uz components. The numerical results are compared with a finite element based solution.

Keywords: higher order shear deformation, composite, thermal buckling, angle-ply laminations

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Authors: Mostafa Sefidgar, Kaamran Raahemifar, Hossein Bazmara, Madjid Soltani

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The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, and drug extravasation from microvascular. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to show how capillary network structure induced by tumor affects drug delivery. The effect of heterogeneous capillary network induced by tumor on interstitial fluid flow and drug delivery is investigated by this multi scale method. The sprouting angiogenesis model is used for generating capillary network induced by tumor. Fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network and fluid flow in normal and tumor tissues. The Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. Finally, convection-diffusion-reaction equation is used to simulate drug delivery. The dynamic approach which changes the capillary network structure based on signals sent by hemodynamic and metabolic stimuli is used in this study for more realistic assumption. The study indicates that drug delivery to solid tumors depends on the tumor induced capillary network structure. The dynamic approach generates the irregular capillary network around the tumor and predicts a higher interstitial pressure in the tumor region. This elevated interstitial pressure with irregular capillary network leads to a heterogeneous distribution of drug in the tumor region similar to in vivo observations. The investigation indicates that the drug transport properties have a significant role against the physiological barrier of drug delivery to a solid tumor.

Keywords: solid tumor, physiological barriers to drug delivery, angiogenesis, microvascular network, solute transport

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Authors: L. Rakesh, T. Y. Heblekar

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This study entails the development and optimization of a mathematical model for a floating drum biogas reactor from first principles using thermal and empirical considerations. The model was derived on the basis of mass conservation, lumped mass heat transfer formulations and empirical biogas formation laws. The treatment leads to a system of coupled nonlinear ordinary differential equations whose solution mapped four-time independent controllable parameters to five output variables which adequately serve to describe the reactor performance. These equations were solved numerically using fourth order Runge-Kutta method for a range of input parameter values. Using the data so obtained an Artificial Neural Network with a single hidden layer was trained using Levenberg-Marquardt Damped Least Squares (DLS) algorithm. This network was then fine-tuned for optimal mapping by varying hidden layer size. This fast forward model was then employed as a health score generator in the Bacterial Foraging Optimization code. The optimal operating state of the simplified Biogas reactor was thus obtained.

Keywords: biogas, floating drum reactor, neural network model, optimization

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Authors: Yuri V. Kim

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This article presents a new approach to the Functional Testing of Space Systems (SS). It can be considered as a generic test and used for a wide class of SS that from the point of view of System Dynamics and Control may be described by the ordinary differential equations. Suggested methodology is based on using semi-natural experiment- laboratory stand that doesn’t require complicated, precise and expensive technological control-verification equipment. However, it allows for testing system as a whole totally assembled unit during Assembling, Integration and Testing (AIT) activities, involving system hardware (HW) and software (SW). The test physically activates system input (sensors) and output (actuators) and requires recording their outputs in real time. The data is then inserted in laboratory PC where it is post-experiment processed by Matlab/Simulink Identification Toolbox. It allows for estimating system dynamics in form of estimation of system differential equations by the experimental way and comparing them with expected mathematical model prematurely verified by mathematical simulation during the design process.

Keywords: system dynamics, space system ground tests and space qualification, system dynamics identification, satellite attitude control, assembling, integration and testing

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Authors: M. Towhidur Rahman, Nasim Zaman Piyas, M. Sadiqul Baree, Shahnewaz Ahmed

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The design of high-speed craft has recently become one of the most active areas of naval architecture. Speed increase makes these vehicles more efficient and useful for military, economic or leisure purpose. The planing hull is designed specifically to achieve relatively high speed on the surface of the water. Speed on the water surface is closely related to the size of the vessel and the installed power. The Savitsky method was first presented in 1964 for application to non-monohedric hulls and for application to stepped hulls. This method is well known as a reliable comparative to CFD analysis of hull resistance. A computer program based on Savitsky’s method has been developed using MATLAB. The power of high-speed vessels has been computed in this research. At first, the program reads some principal parameters such as displacement, LCG, Speed, Deadrise angle, inclination of thrust line with respect to keel line etc. and calculates the resistance of the hull using empirical planning equations of Savitsky. However, some functions used in the empirical equations are available only in the graphical form, which is not suitable for the automatic computation. We use digital plotting system to extract data from nomogram. As a result, value of wetted length-beam ratio and trim angle can be determined directly from the input of initial variables, which makes the power calculation automated without manually plotting of secondary variables such as p/b and other coefficients and the regression equations of those functions are derived by using data from different charts. Finally, the trim angle, mean wetted length-beam ratio, frictional coefficient, resistance, and power are computed and compared with the results of Savitsky and good agreement has been observed.

Keywords: nomogram, planing hull, principal parameters, regression

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Authors: Tejeet Singh, Ishavneet Singh

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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: Romulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

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This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity of solutions to the Navier-Stokes equations, hypercomplex bifurcations, and turbulence. We offer a comprehensive analysis of Sobolev embedding theorems in fractional spaces and apply bifurcation theory within quaternionic dynamical systems to better understand the complex behaviors in fluid systems. Additionally, the research delves into energy dissipation mechanisms in turbulent flows through the framework of Besov spaces. Key mathematical tools, such as interpolation theory, Littlewood-Paley decomposition, and energy cascade models, are integrated to develop a robust theoretical approach to these problems. By addressing challenges related to the existence and smoothness of solutions, this work contributes to the ongoing exploration of the open Navier-Stokes problem, providing new insights into the intricate relationship between fluid dynamics and functional spaces.

Keywords: navier-stokes equations, hypercomplex bifurcations, turbulence, sobolev and besov space

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Authors: Xiao-Dong Wang, Wei-Mon Yan

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The flow field design in the bipolar plates affects the performance of the proton exchange membrane (PEM) fuel cell. This work adopted a combined optimization procedure, including a simplified conjugate-gradient method and a completely three-dimensional, two-phase, non-isothermal fuel cell model, to look for optimal flow field design for a single serpentine fuel cell of size 9×9 mm with five channels. For the direct solution, the two-fluid method was adopted to incorporate the heat effects using energy equations for entire cells. The model assumes that the system is steady; the inlet reactants are ideal gases; the flow is laminar; and the porous layers such as the diffusion layer, catalyst layer and PEM are isotropic. The model includes continuity, momentum and species equations for gaseous species, liquid water transport equations in the channels, gas diffusion layers, and catalyst layers, water transport equation in the membrane, electron and proton transport equations. The Bulter-Volumer equation was used to describe electrochemical reactions in the catalyst layers. The cell output power density Pcell is maximized subjected to an optimal set of channel heights, H1-H5, and channel widths, W2-W5. The basic case with all channel heights and widths set at 1 mm yields a Pcell=7260 Wm-2. The optimal design displays a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5, producing a Pcell=8894 Wm-2, about 22.5% increment. The reduced channel heights of channels 2-4 significantly increase the sub-rib convection and widths for effectively removing liquid water and oxygen transport in gas diffusion layer. The final diverging channel minimizes the leakage of fuel to outlet via sub-rib convection from channel 4 to channel 5. Near-optimal design without huge loss in cell performance but is easily manufactured is tested. The use of a straight, final channel of 0.1 mm height has led to 7.37% power loss, while the design with all channel widths to be 1 mm with optimal channel heights obtained above yields only 1.68% loss of current density. The presence of a final, diverging channel has greater impact on cell performance than the fine adjustment of channel width at the simulation conditions set herein studied.

Keywords: optimization, flow field design, simplified conjugate-gradient method, serpentine flow field, sub-rib convection

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Authors: Gulshan Sachdeva, Ram Bilash

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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: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Aarthi Sridhar, Henri Gavin, Karah Kelly

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Rolling Isolation Systems (RISs) are simple and effective means to mitigate earthquake hazards to equipment in critical and precious facilities, such as hospitals, network collocation facilities, supercomputer centers, and museums. The RIS works by isolating components acceleration the inertial forces felt by the subsystem. The RIS consists of two platforms with counter-facing concave surfaces (dishes) in each corner. Steel balls lie inside the dishes and allow the relative motion between the top and bottom platform. Formerly, a mathematical model for the dynamics of RISs was developed using Lagrange’s equations (LE) and experimentally validated. A new mathematical model was developed using Gauss’s Principle of Least Constraint (GPLC) and verified by comparing impulse response trajectories of the GPLC model and the LE model in terms of the peak displacements and accelerations of the top platform. Mathematical models for the RIS are tedious to derive because of the non-holonomic rolling constraints imposed on the system. However, using Gauss’s Principle of Least constraint to find the equations of motion removes some of the obscurity and yields a system that can be easily extended. Though the GPLC model requires more state variables, the equations of motion are far simpler. The non-holonomic constraint is enforced in terms of accelerations and therefore requires additional constraint stabilization methods in order to avoid the possibility that numerical integration methods can cause the system to go unstable. The GPLC model allows the incorporation of more physical aspects related to the RIS, such as contribution of the vertical velocity of the platform to the kinetic energy and the mass of the balls. This mathematical model for the RIS is a tool to predict the motion of the isolation platform. The ability to statistically quantify the expected responses of the RIS is critical in the implementation of earthquake hazard mitigation.

Keywords: earthquake hazard mitigation, earthquake isolation, Gauss’s Principle of Least Constraint, nonlinear dynamics, rolling isolation system

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Authors: Seyyed Feisal Asbaghian Namin, Reza Pilafkan, Mahmood Kaffash Irzarahimi

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TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.

Keywords: graphene sheets, molecular dynamics simulations, fundamental frequencies, nonlocal elasticity theory, nonlocal parameter

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

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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: G. Judakova, M. Bause

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The ability to model and simulate numerically natural gas flow in pipelines has become of high importance for the design of pipeline systems. The understanding of the formation of hydrate particles and their dynamical behavior is of particular interest, since these processes govern the operation properties of the systems and are responsible for system failures by clogging of the pipelines under certain conditions. Mathematically, natural gas flow can be described by multiphase flow models. Using the two-fluid modeling approach, the gas phase is modeled by the compressible Euler equations and the particle phase is modeled by the pressureless Euler equations. The numerical simulation of compressible multiphase flows is an important research topic. It is well known that for nonlinear fluxes, even for smooth initial data, discontinuities in the solution are likely to occur in finite time. They are called shock waves or contact discontinuities. For hyperbolic and singularly perturbed parabolic equations the standard application of the Galerkin finite element method (FEM) leads to spurious oscillations (e.g. Gibb's phenomenon). In our approach, we use stabilized FEM, the streamline upwind Petrov-Galerkin (SUPG) method, where artificial diffusion acting only in the direction of the streamlines and using a special treatment of the boundary conditions in inviscid convective terms, is added. Numerical experiments show that the numerical solution obtained and stabilized by SUPG captures discontinuities or steep gradients of the exact solution in layers. However, within this layer the approximate solution may still exhibit overshoots or undershoots. To suitably reduce these artifacts we add a discontinuity capturing or shock capturing term. The performance properties of our numerical scheme are illustrated for two-phase flow problem.

Keywords: two-phase flow, gas-particle mixture, inviscid two-fluid model, euler equation, finite element method, streamline upwind petrov-galerkin, shock capturing

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Authors: Hyun-Ho Lee, Kee-Won Kim

Abstract:

The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: Fuyuan Ma, Yuhan Wang, Junhe Zhang, Ying Wang

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Identifying the sources of information dissemination is a pivotal task in the study of collective behaviors in networks, enabling us to discern and intercept the critical pathways through which information propagates from its origins. This allows for the control of the information’s dissemination impact in its early stages. Numerous methods for source detection rely on pre-existing, underlying propagation models as prior knowledge. Current models that eschew prior knowledge attempt to harness label propagation algorithms to model the statistical characteristics of propagation states or employ Graph Neural Networks (GNNs) for deep reverse modeling of the diffusion process. These approaches are either deficient in modeling the propagation patterns of information or are constrained by the over-smoothing problem inherent in GNNs, which limits the stacking of sufficient model depth to excavate global propagation patterns. Consequently, we introduce the ODESI model. Initially, the model employs a label propagation algorithm to delineate the distribution density of infected states within a graph structure and extends the representation of infected states from integers to state vectors, which serve as the initial states of nodes. Subsequently, the model constructs a deep architecture based on GNNs-coupled Ordinary Differential Equations (ODEs) to model the global propagation patterns of continuous propagation processes. Addressing the challenges associated with solving ODEs on graphs, we approximate the analytical solutions to reduce computational costs. Finally, we conduct simulation experiments on two real-world social network datasets, and the results affirm the efficacy of our proposed ODESI model in source identification tasks.

Keywords: source identification, ordinary differential equations, label propagation, complex networks

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Authors: Yanyan Zhang, Ziyu Diao, Zhentao Liu, Ruidong Yan

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The wear character of the main bearing is one of the critical indicators for the overhaul of an internal combustion engine, and the aim of this paper is to reveal the dynamic wear mechanism of the main bearings. A numerical simulation model combined multi-body dynamic equations of the engine, the average Reynolds equations of the bearing lubricant, asperity contact and wear model of the joint surfaces were established under typical operating conditions. The wear results were verified by experimental data, and then the influence of operating conditions, bearing clearance and cylinder pressure on the wear character of selected main bearings were analyzed. The results show that the contribution degree of different working conditions on the wear profile and depth of each bearing is obviously different, and the increase of joint clearance or cylinder pressure will accelerate the wear. The numerical model presented can be used to wear prognosis for joints and provide guidance for optimization design of sliding bearings.

Keywords: dynamic simulation, multi-body dynamics, sliding bearing, surface wear

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Authors: Benselama Khadidja, El Meiche Noureddine

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This paper presents the effect of hybridization material on the variation of non-dimensional critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the Principle of Virtual Displacement; the formulation is based on a new function of shear deformation theory taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress-free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

Keywords: buckling, hybrid cross-ply laminates, Winkler and Pasternak, elastic foundation, two variables plate theory

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

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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, MHD, nonlinear stretching sheet

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Authors: Vimal Kumar Chouksey, S. P. Sharma

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This paper deals with theoretical analysis of performance of solar air collector having its duct packed with blackened wire screen matrices. The heat transfer equations for two-dimensional fully developed fluid flows under quasi-steady-state conditions have been developed in order to analyze the effect of bed depth on performance. A computer programme is developed in C++ language to estimate the temperature rise of entering air for evaluation of performance by solving the governing equations numerically using relevant correlations for heat transfer coefficient for packed bed systems. Results of air temperature rise and thermal efficiency obtained from the analysis have been compared with available experimental results and results have been found fairly in closed agreement. It has been found that there is considerable enhancement in performance with packed bed collector upto a certain total bed depth. Effect of total bed depth on efficiency show that there is an upper limiting value of total bed depth beyond which the thermal efficiency begins to fall again and this type of characteristics behavior is observed at all mass flow rate.

Keywords: plane collector, solar air heater, solar energy, wire screen packed bed

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Authors: Juan José Mesas, Luis Sainz

Abstract:

The motivation for the development of this paper lies in the need for energy networks to reduce losses, improve performance, optimize their operation and try to benefit from the interconnection capacity with other networks enabled for other energy carriers. These interconnections generate interdependencies between some energy networks and others, which requires suitable models and methods for their analysis. Traditionally, the modeling and study of energy networks have been carried out independently for each energy carrier. Thus, there are well-established models and methods for the steady-state analysis of electrical networks, gas networks, and thermal networks separately. What is intended is to extend and combine them adequately to be able to face in an integrated way the steady-state analysis of networks with multiple energy carriers. Firstly, the added value of multi-energy networks, their operation, and the basic principles that characterize them are explained. In addition, two current aspects of great relevance are exposed: the storage technologies and the coupling elements used to interconnect one energy network with another. Secondly, the characteristic equations of the different energy networks necessary to carry out the steady-state analysis are detailed. The electrical network, the natural gas network, and the thermal network of heat and cold are considered in this paper. After the presentation of the equations, a particular case of the steady-state analysis of a specific multi-energy network is studied. This network is represented graphically, the interconnections between the different energy carriers are described, their technical data are exposed and the equations that have previously been presented theoretically are formulated and developed. Finally, the two iterative numerical resolution methods considered in this paper are presented, as well as the resolution procedure and the results obtained. The pros and cons of the application of both methods are explained. It is verified that the results obtained for the electrical network (voltages in modulus and angle), the natural gas network (pressures), and the thermal network (mass flows and temperatures) are correct since they comply with the distribution, operation, consumption and technical characteristics of the multi-energy network under study.

Keywords: coupling elements, energy carriers, multi-energy networks, steady-state analysis

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

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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: A. Falavand Jozaei, A. Ghafouri

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Operation enhancement in an air cooler (heat exchanger) depends on the rate of heat transfer, and pressure drop. In this paper, for a given heat duty, study of the effects of FPI (fin per inch) and fin type (circular and hexagonal fins) on two parameters mentioned above is considered in an air cooler in Iran, Arvand petrochemical. A program in EES (Engineering Equations Solver) software moreover, Aspen B-JAC and HTFS+ software are used for this purpose to solve governing equations. At first the simulated results obtained from this program is compared to the experimental data for two cases of FPI. The effects of FPI from 3 to 15 over heat transfer (Q) to pressure drop ratio (Q/Δp ratio). This ratio is one of the main parameters in design, rating, and simulation heat exchangers. The results show that heat transfer (Q) and pressure drop increase with increasing FPI (fin per inch) steadily, and the Q/Δp ratio increases to FPI = 12 (for circular fins about 47% and for hexagonal fins about 69%) and then decreased gradually to FPI = 15 (for circular fins about 5% and for hexagonal fins about 8%), and Q/Δp ratio is maximum at FPI = 12. The FPI value selection between 8 and 12 obtained as a result to optimum heat transfer to pressure drop ratio. Also by contrast, between circular and hexagonal fins results, the Q/Δp ratio of hexagonal fins more than Q/Δp ratio of circular fins for FPI between 8 and 12 (optimum FPI).

Keywords: air cooler, circular and hexagonal fins, fin per inch, heat transfer and pressure drop

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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

Procedia PDF Downloads 435

Authors: Mohammed Ali Hjaji, A.K. El-Senussi, Said H. Eshtewi

Abstract:

The flexural dynamic response of symmetric laminated composite beams subjected to general transverse harmonic forces is investigated. The dynamic equations of motion and associated boundary conditions based on the first order shear deformation are derived through the use of Hamilton’s principle. The influences of shear deformation, rotary inertia, Poisson’s ratio and fibre orientation are incorporated in the present formulation. The resulting governing flexural equations for symmetric composite Timoshenko beams are exactly solved and the closed form solutions for steady state flexural response are then obtained for cantilever and simply supported boundary conditions. The applicability of the analytical closed-form solution is demonstrated via several examples with various transverse harmonic loads and symmetric cross-ply and angle-ply laminates. Results based on the present solution are assessed and validated against other well established finite element solutions and exact solutions available in the literature.

Keywords: analytical solution, flexural response, harmonic forces, symmetric laminated beams, steady state response

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Authors: Yuanhao Gao, Pin Lin, Kees Weijer

Abstract:

In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model.

Keywords: optimal control model, Stokes equation, finite element method, conjugate gradient method

Procedia PDF Downloads 407

Authors: Ayola D. N. Jayamaha, Gihan V. Dias, Surangika Ranathunga

Abstract:

Currently there are lot of educational tools designed for mathematics. Open source software such as GeoGebra and Octave are bulky in their architectural structure. In addition, there is MathLab software, which facilitates much more than what we ask for. Many of the computer aided online grading and assessment tools require integrating editors to their software. However, there are not exist suitable editors that cater for all their needs in editing equations and geometrical diagrams and graphs. Some of the existing software for editing equations is Alfred’s Equation Editor, Codecogs, DragMath, Maple, MathDox, MathJax, MathMagic, MathFlow, Math-o-mir, Microsoft Equation Editor, MiraiMath, OpenOffice, WIRIS Editor and MyScript. Some of them are commercial, open source, supports handwriting recognition, mobile apps, renders MathML/LaTeX, Flash / Web based and javascript display engines. Some of the diagram editors are GeoKone.NET, Tabulae, Cinderella 1.4, MyScript, Dia, Draw2D touch, Gliffy, GeoGebra, Flowchart, Jgraph, JointJS, J painter Online diagram editor and 2D sketcher. All these software are open source except for MyScript and can be used for editing mathematical diagrams. However, they do not fully cater the needs of a typical computer aided assessment tool or Educational Platform for Mathematics. This solution provides a Web based, lightweight, easy to implement and integrate solution of an html5 canvas that renders on all of the modern web browsers. The scope of the project is an editor that covers equations and mathematical diagrams and drawings on the O/L Mathematical Exam Papers in Sri Lanka. Using the tool the students can enter any equation to the system which can be on an online remote learning platform. The users can also create and edit geometrical drawings, graphs and do geometrical constructions that require only Compass and Ruler from the Editing Interface provided by the Software. The special feature of this software is the geometrical constructions. It allows the users to create geometrical constructions such as angle bisectors, perpendicular lines, angles of 600 and perpendicular bisectors. The tool correctly imitates the functioning of rulers and compasses to create the required geometrical construction. Therefore, the users are able to do geometrical drawings on the computer successfully and we have a digital format of the geometrical drawing for further processing. Secondly, we can create and edit Venn Diagrams, color them and label them. In addition, the students can draw probability tree diagrams and compound probability outcome grids. They can label and mark regions within the grids. Thirdly, students can draw graphs (1st order and 2nd order). They can mark points on a graph paper and the system connects the dots to draw the graph. Further students are able to draw standard shapes such as circles and rectangles by selecting points on a grid or entering the parametric values.

Keywords: geometrical drawings, html5 canvas, mathematical equations, toolbox

Procedia PDF Downloads 378

Authors: Medine Demir, Volker John

Abstract:

Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

Procedia PDF Downloads 67