Search results for: Euler equations

Authors: Muskaan Sethi, Arnab Banerjee, Bappaditya Manna

Abstract:

The present paper aims to investigate a suitable contact between a wheel rolling over a flexible beam. A Linear Complementary (LCP) based approach has been adopted to simulate the contact dynamics for a rigid wheel traversing over a flexible Euler Bernoulli simply supported beam. The adopted methodology is suitable to incorporate the effect of frictional force acting at the wheel-beam interface. Moreover, the possibility of the generation of a gap between the two bodies has also been considered. The present method is based on a unilateral contact assumption which assumes that no penetration would occur when the two bodies come in contact. This assumption helps to predict the contact between wheels and beams in a more practical sense. The proposed methodology is validated with the previously published results and is found to be in good agreement. Further, this method is applied to simulate the contact between wheels and beams for various railway configurations. Moreover, different parametric studies are conducted to study the contact dynamics between the wheel and beam more thoroughly.

Keywords: contact dynamics, linear complementary problem, railway dynamics, unilateral contact

Procedia PDF Downloads 94

Authors: H. Shokouhmand, M. Tajerian

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At this paper velocity profile modeling and heat transfer in the micro heat pipes by using electrohydrodynamic (EHD) field at the transient regime have been studied. In the transient flow, one dimensional and two phase fluid flow and heat transfer for micro heat pipes with square cross section, have been studied. At this model Coulomb and dielectrophoretic forces are considered. Coupled, non-linear equations governed on the model (continuity, momentum, and energy equations) have been solved simultaneously by numerical methods. Transient behavior of affecting parameters e.g. substrate temperature, velocity of coolant liquid, radius of curvature and coolant liquid pressure, has been verified. By obtaining and plotting the mentioned parameters, it has been shown that the EHD field enhances the heat transfer process. So, the time required to reach the steady state regime decreases from 16 seconds to 2.4 seconds after applying EHD field. Another result has been observed implicitly that by increasing the heat input the effect of EHD field became more significant. The numerical results of model predict the experimental results available in the literature successfully, and it has been observed there is a good agreement between them.

Keywords: micro heat pipe, transient modeling, electrohydrodynamics, capillary, meniscus

Procedia PDF Downloads 256

Authors: Libena Cernohorska, Barbora Sutorova, Petr Teply

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There are pending discussions over an impact of global regulatory efforts on banks. In this paper we present a literature review on the profitability-risk-capital relationship in banking. Research papers dealing with this topic can be divided into two groups: the first group focusing on a capital-risk relationship and the second group analyzing a capital-profitability relationship. The first group investigates whether the imposition of stricter capital requirements reduces risk-taking incentives of banks based on a simultaneous equations model. Their model pioneered the idea that the changes in both capital and risk have endogenous and exogenous components. The results obtained by the authors indicate that changes in the capital level are positively related to the changes in asset risk. The second group of the literature concentrating solely on the relationship between the level of held capital and bank profitability is limited. Nevertheless, there are a lot of studies dealing with the banks’ profitability as such, where bank capital is very often included as an explanatory variable. Based on the literature review of dozens of relevant papers in this study, an empirical research on banks’ profitability and risk adjustment decisions under new banking rules Basel III rules can be easily undertaken.

Keywords: bank, Basel III, capital, decision making, profitability, risk, simultaneous equations model

Procedia PDF Downloads 486

Authors: Zintle Sikhunyana

Abstract:

Management of public finance in many countries such as South Africa is affected by political decisions and by policies around fiscal decentralization amongst the government spheres. Economic success is said to be determined by efficient management of public finance and by the policies or strategies that are implemented to support efficient public finance management. Policymakers focus on pay attention to how economic policies have been implemented and how they are directed into ensuring stable development. This will allow policymakers to address economic challenges through the usage of fiscal policy parameters that are linked to the achieved rate of economic growth and development. Efficient public finance management reduces the likelihood of corruption and corruption is said to have negative effects on economic growth and development. Corruption in public finance refers to an act of using funds for personal benefits. To achieve macroeconomic objectives, governments make use of government expenditure and government expenditure is financed through tax revenue. The main aim of this paper is to investigate the potential impact of public finance management on economic growth and development in South Africa. The secondary data obtained from the South African Reserve Bank (SARB) and World Bank for 1980- 2020 has been utilized to achieve the research objectives. To test the impact of public finance management on economic growth and development, the study will use Seeming Unrelated Regression Equation (SURE) Modelling that allows researchers to model multiple equations with interdependent variables. The advantages of using SUR are that it efficiently allows estimation of relationships between variables by combining information on different equations and SUR test restrictions that involve parameters in different equations. The findings have shown that there is a positive relationship between efficient public finance management and economic growth/development. The findings also show that efficient public finance management has an indirect positive impact on economic growth and development. Corruption has a negative impact on economic growth and development. It results in an efficient allocation of government resources and thereby improves economic growth and development. The study recommends that governments who aim to stimulate economic growth and development should target and strengthen public finance management policies or strategies.

Keywords: corruption, economic growth, economic development, public finance management, fiscal decentralization

Procedia PDF Downloads 193

Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

Procedia PDF Downloads 153

Authors: K. C. Kalam Aswathy, M. V. Anil Kumar

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The possible failure modes of cold-formed steel (CFS) lipped angle (LA) compression members are yielding, local, flexural-torsional, or flexural buckling, and any possible interaction between these buckling modes. In general, the strength estimated by current design guidelines is conservative for these members when flexural-torsional buckling (FTB) is the first global buckling mode, as the post-buckling strength of this mode is not accounted for in the global buckling strength equations. The initial part of this paper reports the results of an experimental and numerical study of CFS-LA members undergoing independent FTB. The modifications are suggested to global buckling strength equations based on these results. Subsequently, the reduction in the ultimate strength from strength corresponding to independent buckling modes for LA members undergoing interaction between buckling modes such as local-flexural torsional, flexural-flexural torsional, local-flexural, and local-flexural torsional-flexural are studied systematically using finite element analysis results. A simple and more accurate interaction equation that accounts for the above interactions between buckling modes in CFS-LA compression members is proposed.

Keywords: buckling interactions, cold-formed steel, flexural-torsional buckling, lipped angle

Procedia PDF Downloads 77

Authors: Daniel Y. Abebe, Jaehyouk Choi

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Link-to-column connection in eccentrically braced frames (EBF) has been a critical problem since the link flange connected to the column fractured prior to the required link rotation. Even though the problem in link-to-column connection still exist, the use of an eccentrically braced frame (EBF) is increasing day by day as EBF have high elastic stiffness, stable inelastic response under repeated lateral loading, and excellent ductility and energy dissipation capacity. In order to address this problem, a reduced web and flange link section is proposed and evaluated in this study. Reducing the web with holes makes the link to control the failure at the edge of holes introduced. Reducing the flange allows the link to control the location at which the plastic hinge is formed. Thus, the failure supposed to occur in the link flange connected at the connection move to the web and to the reduced link flange. Nonlinear FE analysis and experimental investigations have been done on the developed links, and the result shows that the link satisfies the plastic rotation limit recommended in AICS-360-10. Design equations that define the behavior of the proposed link have been recommended, and the equations were verified through the experimental and FE analysis results.

Keywords: EBFs, earthquake disaster, link-to-column connection, reduced link section

Procedia PDF Downloads 366

Authors: M. Seguini, D. Nedjar

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In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system.

Keywords: nonlinear analysis, soil-structure interaction, large deflection, Timoshenko beam, Euler-Bernoulli beam, Winkler foundation, Pasternak foundation, spatial variability

Procedia PDF Downloads 314

Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

Procedia PDF Downloads 141

Authors: Xiaodong Gao, Pingchuan Dong, Qichao Gao

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There has been lots of published work focused on asphaltene deposited on the smooth pipe under steady conditions, while particle deposition on the blockage wellbores under transient conditions has not been well elucidated. This work attempts to predict the deposition rate of asphaltene particles in blockage tube through CFD simulation. The Euler-Lagrange equation has been applied during the flow of crude oil and asphaltene particles. The net gravitational force, virtual mass, pressure gradient, saffman lift, and drag forces are incorporated in the simulations process. Validation of CFD simulation results is compared to the benchmark experiments from the previous literature. Furthermore, the effect of blockage location, blockage length, and blockage thickness on deposition rate are also analyzed. The simulation results indicate that the maximum deposition rate of asphaltene occurs in the blocked tube section, and the greater the deposition thickness, the greater the deposition rate. Moreover, the deposition amount and maximum deposition rate along the length of the tube have the same trend. Results of this study are in the ability to better understand the deposition of asphaltene particles in production and help achieve to deal with the asphaltene challenges.

Keywords: asphaltene deposition rate, blockage length, blockage thickness, blockage diameter, transient condition

Procedia PDF Downloads 188

Authors: Damir Latypov

Abstract:

A closed-form solution for 4-D double surface integrals arising in boundary integrals equations of a potential theory is obtained for arbitrary coplanar polygonal surfaces. The solution method is based on the construction of exact differential forms followed by the application of Stokes' theorem for each surface integral. As a result, the 4-D double surface integral is reduced to a 2-D double line integral. By an appropriate change of variables, the integrand is transformed into a separable function of integration variables. The closed-form solutions to the corresponding 1-D integrals are readily available in the integration tables. Previously closed-form solutions were known only for the case of coincident triangle surfaces and coplanar rectangles. Solutions for these cases were obtained by surface-specific ad-hoc methods, while the present method is general. The method also works for non-polygonal surfaces. As an example, we compute in closed form the 4-D integral for the case of coincident surfaces in the shape of a circular disk. For an arbitrarily shaped surface, the proposed method provides an efficient quadrature rule. Extensions of the method for non-coplanar surfaces and other than 1/R integral kernels are also discussed.

Keywords: boundary integral equations, differential forms, integration, stokes' theorem

Procedia PDF Downloads 302

Authors: A. Abdikian

Abstract:

Using the linearized quantum hydrodynamic model (QHD) and by considering the role of quantum parameter (Bohm’s potential) and electron exchange-correlation potential in conjunction with Maxwell’s equations, electromagnetic wave propagation in a single-walled carbon nanotubes was studied. The electronic excitations are described. By solving the mentioned equations with appropriate boundary conditions and by assuming the low-frequency electromagnetic waves, two general expressions of dispersion relations are derived for the transverse magnetic (TM) and transverse electric (TE) modes, respectively. The dispersion relations are analyzed numerically and it was found that the dependency of dispersion curves with the exchange-correlation effects (which have been ignored in previous works) in the low frequency would be limited. Moreover, it has been realized that asymptotic behaviors of the TE and TM modes are similar in single wall carbon nanotubes (SWCNTs). The results show that by adding the function of electron exchange-correlation potential lead to the phenomena and make to extend the validity range of QHD model. The results can be important in the study of collective phenomena in nanostructures.

Keywords: transverse magnetic, transverse electric, quantum hydrodynamic model, electron exchange-correlation potential, single-wall carbon nanotubes

Procedia PDF Downloads 442

Authors: Pranjal Srivastava, Piyali Sengupta

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The performance of marine drilling risers is crucial in the offshore oil and gas industry to ensure safe drilling operation with minimum downtime. Experimental investigations on marine drilling risers are limited in the literature owing to the expensive and exhaustive test setup required to replicate the realistic riser model and ocean environment in the laboratory. Therefore, this study presents an analytical model of marine drilling riser for determining its fragility under ocean environmental loading. In this study, the marine drilling riser is idealized as a continuous beam having a concentric circular cross-section. Hydrodynamic loading acting on the marine drilling riser is determined by Morison’s equations. By considering the equilibrium of forces on the marine drilling riser for the connected and normal drilling conditions, the governing partial differential equations in terms of independent variables z (depth) and t (time) are derived. Subsequently, the Runge Kutta method and Finite Difference Method are employed for solving the partial differential equations arising from the analytical model. The proposed analytical approach is successfully validated with respect to the experimental results from the literature. From the dynamic analysis results of the proposed analytical approach, the critical design parameters peak displacements, upper and lower flex joint rotations and von Mises stresses of marine drilling risers are determined. An extensive parametric study is conducted to explore the effects of top tension, drilling depth, ocean current speed and platform drift on the critical design parameters of the marine drilling riser. Thereafter, incremental dynamic analysis is performed to derive the fragility functions of shallow water and deep-water marine drilling risers under ocean environmental loading. The proposed methodology can also be adopted for downtime estimation of marine drilling risers incorporating the ranges of uncertainties associated with the ocean environment, especially at deep and ultra-deepwater.

Keywords: drilling riser, marine, analytical model, fragility

Procedia PDF Downloads 135

Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

Procedia PDF Downloads 84

Authors: Sugeng Rianto, P.W. Arinto Yudi, Soemarno Muhammad Nurhuda

Abstract:

A computation of a 3D compressible fluid flow for virtual environment with haptic interaction can be a non-trivial issue. This is especially how to reach good performances and balancing between visualization, tactile feedback interaction, and computations. In this paper, we describe our approach of computation methods based on parallel programming on a GPU. The 3D fluid flow solvers have been developed for smoke dispersion simulation by using combinations of the cubic interpolated propagation (CIP) based fluid flow solvers and the advantages of the parallelism and programmability of the GPU. The fluid flow solver is generated in the GPU-CPU message passing scheme to get rapid development of haptic feedback modes for fluid dynamic data. A rapid solution in fluid flow solvers is developed by applying cubic interpolated propagation (CIP) fluid flow solvers. From this scheme, multiphase fluid flow equations can be solved simultaneously. To get more acceleration in the computation, the Navier-Stoke Equations (NSEs) is packed into channels of texel, where computation models are performed on pixels that can be considered to be a grid of cells. Therefore, despite of the complexity of the obstacle geometry, processing on multiple vertices and pixels can be done simultaneously in parallel. The data are also shared in global memory for CPU to control the haptic in providing kinaesthetic interaction and felling. The results show that GPU based parallel computation approaches provide effective simulation of compressible fluid flow model for real-time interaction in 3D computer graphic for PC platform. This report has shown the feasibility of a new approach of solving the compressible fluid flow equations on the GPU. The experimental tests proved that the compressible fluid flowing on various obstacles with haptic interactions on the few model obstacles can be effectively and efficiently simulated on the reasonable frame rate with a realistic visualization. These results confirm that good performances and balancing between visualization, tactile feedback interaction, and computations can be applied successfully.

Keywords: CIP, compressible fluid, GPU programming, parallel computation, real-time visualisation

Procedia PDF Downloads 427

Authors: Min-Kook Park, Deuck Hang Lee, Hyun Mo Yang, Jae Hyun Kim, Kang Su Kim

Abstract:

Prestressed hollow-core slabs (HCS) are structurally optimized precast units with light-weight hollowed-sections and very economical due to the mass production by a unique production method. They have been thus widely used in the precast concrete constructions in many countries all around the world. It is, however, difficult to provide shear reinforcement in HCS units produced by the extrusion method, and thus all the shear forces should be resisted solely by concrete webs in the HCS units. This means that, for the HCS units, it is very important to estimate the contribution of web concrete to the shear resistance accurately. In design codes, however, the shear strengths for HCS units are estimated by the same equations that are used for typical prestressed concrete members, which were determined from the calibrations to experimental results of conventional prestressed concrete members other than HCS units. In this study, therefore, shear test results of HCS members with a wide range of influential variables were collected, and the shear strength equations in design codes were thoroughly examined by comparing to the experimental results in the shear database of HCS members. Acknowledgement: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning(NRF-2016R1A2B2010277).

Keywords: hollow-core, web-shear, precast concrete, prestress, capacity

Procedia PDF Downloads 500

Authors: Nur Sarma, Paul M. Tuohy, Siniša Djurović

Abstract:

This paper presents an in-depth investigation of the effects of several grid supply harmonic voltages on the stator currents of an example wound rotor induction machine. The observed effects of higher order grid supply harmonics are identified using a finite element time stepping transient model, as well as a time-stepping electromagnetic model. In addition, a number of analytical equations to calculate the spectral content of the stator currents are presented in the paper. The presented equations are validated through comparison with the obtained spectra predicted using the finite element and electromagnetic models. The presented study provides a better understanding of the origin of supply harmonic effects identified in the stator currents of the example wound rotor induction machine. Furthermore, the study helps to understand the effects of higher order supply harmonics on the harmonic emissions of the wound rotor induction machine.  

Keywords: wound rotor induction machine, supply harmonics, current spectrum, power spectrum, power quality, harmonic emmisions, finite element analysis

Procedia PDF Downloads 171

Authors: Ali Reza Tahavvor‚ Saeed Hosseini, Behnam Amiri

Abstract:

Concentric and eccentric annulus is used frequently in technical and industrial applications such as nuclear reactors, thermal storage system and etc. In this paper, computational fluid dynamics (CFD) is used to investigate two dimensional free convection of laminar flow in annulus with isotherm cylinders surface and cooler inner surface. Problem studied in thirty different cases. Due to natural convection continuity and momentum equations are coupled and must be solved simultaneously. Finite volume method is used for solving governing equations. The purpose was to obtain the eccentricity effect on Nusselt number in different Rayleight numbers, so streamlines and temperature fields must be determined. Results shown that the highest Nusselt number values occurs in degree of eccentricity equal to 0.5 upward for inner cylinder and degree of eccentricity equal to 0.3 upward for outer cylinder. Side eccentricity reduces the outer cylinder Nusselt number but increases inner cylinder Nusselt number. The trend in variation of Nusselt number with respect to eccentricity remain similar in different Rayleight numbers. Correlations are included to calculate the Nusselt number of the cylinders.

Keywords: natural convection, concentric, eccentric, Nusselt number, annulus

Procedia PDF Downloads 356

Authors: Mostafa Zandi, Ramin Mansouri

Abstract:

Spillways are one of the most important hydraulic structures of dams that provide the stability of the dam and downstream areas at the time of flood. Morning-Glory spillway is one of the common spillways for discharging the overflow water behind dams, these kinds of spillways are constructed in dams with small reservoirs. In this research, the hydraulic flow characteristics of a morning-glory spillways are investigated with CFD model. Two dimensional unsteady RANS equations were solved numerically using Finite Volume Method. The PISO scheme was applied for the velocity-pressure coupling. The mostly used two-equation turbulence models, k- and k-, were chosen to model Reynolds shear stress term. The power law scheme was used for discretization of momentum, k , and  equations. The VOF method (geometrically reconstruction algorithm) was adopted for interface simulation. The results show that the fine computational grid, the input speed condition for the flow input boundary, and the output pressure for the boundaries that are in contact with the air provide the best possible results. Also, the standard wall function is chosen for the effect of the wall function, and the turbulent model k -ε (Standard) has the most consistent results with experimental results. When the jet is getting closer to end of basin, the computational results increase with the numerical results of their differences. The lower profile of the water jet has less sensitivity to the hydraulic jet profile than the hydraulic jet profile. In the pressure test, it was also found that the results show that the numerical values of the pressure in the lower landing number differ greatly in experimental results. The characteristics of the complex flows over a Morning-Glory spillway were studied numerically using a RANS solver. Grid study showed that numerical results of a 57512-node grid had the best agreement with the experimental values. The desired downstream channel length was preferred to be 1.5 meter, and the standard k-ε turbulence model produced the best results in Morning-Glory spillway. The numerical free-surface profiles followed the theoretical equations very well.

Keywords: morning-glory spillway, CFD model, hydraulic characteristics, wall function

Procedia PDF Downloads 66

Authors: Sadia Siddiqa, Z. Khan, M. A. Hossain

Abstract:

In this article, the effect of thermal radiation on mixed convection boundary layer flow of a viscous fluid along a highly heated vertical flat plate is considered with varying density and volumetric expansion coefficient. The density of the fluid is assumed to vary exponentially with temperature, however; volumetric expansion coefficient depends linearly on temperature. Boundary layer equations are transformed into convenient form by introducing primitive variable formulations. Solutions of transformed system of equations are obtained numerically through implicit finite difference method along with Gaussian elimination technique. Results are discussed in view of various parameters, like thermal radiation parameter, volumetric expansion parameter and density variation parameter on the wall shear stress and heat transfer rate. It is concluded from the present investigation that increase in volumetric expansion parameter decreases wall shear stress and enhances heat transfer rate.

Keywords: thermal radiation, mixed convection, variable density, variable volumetric expansion coefficient

Procedia PDF Downloads 359

Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

Procedia PDF Downloads 69

Authors: Muhammad Umar Kiani, Muhammad Shahbaz, Hassan Akbar

Abstract:

Simulation of a high speed inviscid steady ideal air flow around a 2D/axial-symmetry body was carried out by the use of mb_cns code. mb_cns is a program for the time-integration of the Navier-Stokes equations for two-dimensional compressible flows on a multiple-block structured mesh. The flow geometry may be either planar or axisymmetric and multiply-connected domains can be modeled by patching together several blocks. The main simulation code is accompanied by a set of pre and post-processing programs. The pre-processing programs scriptit and mb_prep start with a short script describing the geometry, initial flow state and boundary conditions and produce a discretized version of the initial flow state. The main flow simulation program (or solver as it is sometimes called) is mb_cns. It takes the files prepared by scriptit and mb_prep, integrates the discrete form of the gas flow equations in time and writes the evolved flow data to a set of output files. This output data may consist of the flow state (over the whole domain) at a number of instants in time. After integration in time, the post-processing programs mb_post and mb_cont can be used to reformat the flow state data and produce GIF or postscript plots of flow quantities such as pressure, temperature and Mach number. The current problem is an example of supersonic inviscid flow. The flow domain for the current problem (strake configuration wing) is discretized by a structured grid and a finite-volume approach is used to discretize the conservation equations. The flow field is recorded as cell-average values at cell centers and explicit time stepping is used to update conserved quantities. MUSCL-type interpolation and one of three flux calculation methods (Riemann solver, AUSMDV flux splitting and the Equilibrium Flux Method, EFM) are used to calculate inviscid fluxes across cell faces.

Keywords: steady flow simulation, processing programs, simulation code, inviscid flux

Procedia PDF Downloads 423

Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

Abstract:

The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

Procedia PDF Downloads 122

Authors: Utkarsh Tripathi, Bikalp C. Mandal, Ravi Kumar Umrao, Sirsha Das, M. K. Bhowmic, Joyesh Bagchi, Hemant Kumar

Abstract:

The Central India Diamond Province (CIDP) is known for the occurrences of primary and secondary sources for diamonds from the Vindhyan platformal sediments, which host several kimberlites, with one operating mine. The known kimberlites are Neo-Proterozoic in age and intrude into the Kaimur Group of rocks. Based on the interpretation of areo-geomagnetic data, three potential zones were demarcated in parts of Chitrakoot and Banda districts, Uttar Pradesh, and Satna district, Madhya Pradesh, India. To validate the aero-geomagnetic interpretation, ground magnetic coupled with a gravity survey was conducted to validate the anomaly and explore the possibility of some pipes concealed beneath the Vindhyan sedimentary cover. Geologically the area exposes the milky white to buff-colored arkosic and arenitic sandstone belonging to the Dhandraul Formation of the Kaimur Group, which are undeformed and unmetamorphosed providing almost transparent media for geophysical exploration. There is neither surface nor any geophysical indication of intersections of linear structures, but the joint patterns depict three principal joints along NNE-SSW, ENE-WSW, and NW-SE directions with vertical to sub-vertical dips. Aeromagnetic data interpretation brings out three promising zones with the bi-polar magnetic anomaly (69-602nT) that represent potential kimberlite intrusive concealed below at an approximate depth of 150-170m. The ground magnetic survey has brought out the above-mentioned anomalies in zone-I, which is congruent with the available aero-geophysical data. The magnetic anomaly map shows a total variation of 741 nT over the area. Two very high magnetic zones (H1 and H2) have been observed with around 500 nT and 400 nT magnitudes, respectively. Anomaly zone H1 is located in the west-central part of the area, south of Madulihai village, while anomaly zone H2 is located 2km apart in the north-eastern direction. The Euler 3D solution map indicates the possible existence of the ultramafic body in both the magnetic highs (H1 and H2). The H2 high shows the shallow depth, and H1 shows a deeper depth solution. In the reduced-to-pole (RTP) method, the bipolar anomaly disappears and indicates the existence of one causative source for both anomalies, which is, in all probabilities, an ultramafic suite of rock. The H1 magnetic high represents the main body, which persists up to depths of ~500m, as depicted through the upward continuation derivative map. Radially Averaged Power Spectrum (RAPS) shows the thickness of loose sediments up to 25m with a cumulative depth of 154m for sandstone overlying the ultramafic body. The average depth range of the shallower body (H2) is 60.5-86 meters, as estimated through the Peters half slope method. Magnetic (TF) anomaly with BA contour also shows high BA value around the high zones of magnetic anomaly (H1 and H2), which suggests that the causative body is with higher density and susceptibility for the surrounding host rock. The ground magnetic survey coupled with the gravity confirms a potential target for further exploration as the findings are co-relatable with the presence of the known diamondiferous kimberlites in this region, which post-date the rocks of the Kaimur Group.

Keywords: Kaimur, kimberlite, Euler 3D solution, magnetic

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Authors: Mahyar Maali, Merve Sagiroglu, Mahmut Kilic, Abdulkadir Cuneyt Aydin

Abstract:

In order to evaluate the residual strength of S235 (St37) steel structures after the fire, an experimental program was undertaken to investigate the post-fire mechanical properties. Tensile coupons taken from S235 sheets were exposed to varying temperatures as 200°C, 400°C, 600°C, and 800 °C. The samples were then allowed to cool down to ambient temperature before they were tested to failure. To obtain the mechanical properties of steels; tensile tests are performed, and the post-fire stress-strain curves are evaluated. The microstructures of the heat-treated specimens were examined by Scanning Electron Microscope (SEM). It is seen that morphology and size of the precipitates in the specimens change, as the heat increases. The modulus of elasticity decreases, and deformation increases with temperature. Energy dissipation decreases due to lower stress according to the stress-strain curves of the specimens. Especially, the mechanical properties were decreased compared with the pre-fire ones. As a result of the post-fire and pre-fire behavior of S235, a set of equations is evaluated to predict the mechanical properties after the fire. These types of equations may allow the structural and/or fire engineers to predict accurately the post-fire behavior of the buildings constructed with S235 type steel.

Keywords: post-fire behavior, stress-strain curves, experimental study, S235 steel

Procedia PDF Downloads 336

Authors: M. A. Talha, M. Osman Gani, M. Ferdows

Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: convection flow, similarity, numerical analysis, spectral method, Williamson nanofluid, internal heat generation

Procedia PDF Downloads 170

Authors: Xu Rumin, Chen Jianyi, Yue Ti, Wang Yaan

Abstract:

With the rapid development of subsea oil and gas exploitation, the demand for the related underwater process equipment is increasing fast. In order to reduce the energy consuming, people tend to separate the gas and oil phase directly on the seabed. Accordingly, an advanced separator is needed. In this paper, the pressure drop of a new type of separator named Gas Liquid Cylindrical Cyclone (GLCC) which is used in the subsea system is investigated by both experiments and numerical simulation. In the experiments, the single phase flow and gas-liquid two phase flow in GLCC were tested. For the simulation, the performance of GLCC under both laboratory and industrial conditions was calculated. The Eulerian model was implemented to describe the mixture flow field in the GLCC under experimental conditions and industrial oil-natural gas conditions. Furthermore, a relationship among Euler number (Eu), Reynolds number (Re), and Froude number (Fr) is generated according to similarity analysis and simulation data, which can present the GLCC separation performance of pressure drop. These results can give reference to the design and application of GLCC in deep sea.

Keywords: dimensionless analysis, gas-liquid cylindrical cyclone, numerical simulation, pressure drop

Procedia PDF Downloads 162

Authors: Darius Diogo Barreto, Ajeet Kumar, Sushma Santapuri

Abstract:

We present an axisymmetric variational formulation for coupled extension-torsion-inflation deformation in magnetoelastomeric thin tubes when both azimuthal and axial magnetic fields are applied. The tube's material is assumed to have a preferred magnetization direction which imparts helical magnetic anisotropy to the tube. We have also derived the expressions of the first derivative of free energy per unit tube's undeformed length with respect to various imposed strain parameters. On applying the thin tube limit, the two nonlinear ordinary differential equations to obtain the in-plane radial displacement and radial component of the Lagrangian magnetic field get converted into a set of three simple algebraic equations. This allows us to obtain simple analytical expressions in terms of the applied magnetic field, magnetization direction, and magnetoelastic constants, which tell us how these parameters can be tuned to generate positive/negative Poisson's effect in such tubes. We consider both torsionally constrained and torsionally relaxed stretching of the tube. The study can be useful in designing magnetoelastic tubular actuators.

Keywords: nonlinear magnetoelasticity, extension-torsion coupling, negative Poisson's effect, helical anisotropy, thin tube

Procedia PDF Downloads 111

Authors: Wu Di, Yeo Khoon Seng, Lim Tee Tai

Abstract:

The typical insects employ a flapping-wing mode of flight. The numerical simulations on free flight of a model fruit fly (Re=143) including hovering and are presented in this paper. Unsteady aerodynamics around a flapping insect is studied by solving the three-dimensional Newtonian dynamics of the flyer coupled with Navier-Stokes equations. A hybrid-grid scheme (Generalized Finite Difference Method) that combines great geometry flexibility and accuracy of moving boundary definition is employed for obtaining flow dynamics. The results show good points of agreement and consistency with the outcomes and analyses of other researchers, which validate the computational model and demonstrate the feasibility of this computational approach on analyzing fluid phenomena in insect flight. The present modeling approach also offers a promising route of investigation that could complement as well as overcome some of the limitations of physical experiments in the study of free flight aerodynamics of insects. The results are potentially useful for the design of biomimetic flapping-wing flyers.

Keywords: free hovering flight, flapping wings, fruit fly, insect aerodynamics, leading edge vortex (LEV), computational fluid dynamics (CFD), Navier-Stokes equations (N-S), fluid structure interaction (FSI), generalized finite-difference method (GFD)

Procedia PDF Downloads 400

Authors: M. Karthigayan, M. Rizon, Sazali Yaacob, R. Nagarajan, M. Muthukumaran, Thinaharan Ramachandran, Sargunam Thirugnanam

Abstract:

In this paper, using a set of irregular and regular ellipse fitting equations using Genetic algorithm (GA) are applied to the lip and eye features to classify the human emotions. Two South East Asian (SEA) faces are considered in this work for the emotion classification. There are six emotions and one neutral are considered as the output. Each subject shows unique characteristic of the lip and eye features for various emotions. GA is adopted to optimize irregular ellipse characteristics of the lip and eye features in each emotion. That is, the top portion of lip configuration is a part of one ellipse and the bottom of different ellipse. Two ellipse based fitness equations are proposed for the lip configuration and relevant parameters that define the emotions are listed. The GA method has achieved reasonably successful classification of emotion. In some emotions classification, optimized data values of one emotion are messed or overlapped to other emotion ranges. In order to overcome the overlapping problem between the emotion optimized values and at the same time to improve the classification, a fuzzy clustering method (FCM) of approach has been implemented to offer better classification. The GA-FCM approach offers a reasonably good classification within the ranges of clusters and it had been proven by applying to two SEA subjects and have improved the classification rate.

Keywords: ellipse fitness function, genetic algorithm, emotion recognition, fuzzy clustering

Procedia PDF Downloads 539