Search results for: boundary value problem

Authors: K. Manmi, Q. X. Wang

Abstract:

This paper investigates microbubble dynamics subject to ultrasound in a weakly viscous fluid near a rigid boundary. The phenomenon is simulated using a boundary integral method. The weak viscous effects are incorporated into the model through the normal stress balance across the bubble surface. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble for several cycles. The effects of the fluid viscosity in the bubble dynamics are analyzed, including jet development, centroid movement and bubble volume.

Keywords: microbubble dynamics, bubble jetting, viscous effect, boundary integral method

Procedia PDF Downloads 444

Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

Abstract:

Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control

Procedia PDF Downloads 328

Authors: Shamsul Chowdhury

Abstract:

The objective of this paper is to present the detailed analysis of the turbulent wave boundary layer produced by progressive finite-amplitude waves theory. Most of the works have done for the mass transport in the turbulent boundary layer assuming the eddy viscosity is not time varying, where the sediment movement is induced by the mean velocity. Near the ocean bottom, the waves produce a thin turbulent boundary layer, where the flow is highly rotational, and shear stress associated with the fluid motion cannot be neglected. The magnitude and the predominant direction of the sediment transport near the bottom are known to be closely related to the flow in the wave induced boundary layer. The magnitude of water particle velocity at the Crest phase differs from the one of the Trough phases due to the non-linearity of the waves, which plays an important role to determine the sediment movement. The non-linearity of the waves become predominant in the surf zone area, where the sediment movement occurs vigorously. Therefore, in order to describe the flow near the bottom and relationship between the flow and the movement of the sediment, the analysis was done using the non-linear boundary layer equation and the finite amplitude wave theory was applied to represent the velocity fields in the turbulent wave boundary layer. At first, the calculation was done for turbulent wave boundary layer by two-dimensional model where throughout the calculation is non-linear. But Stokes second order wave profile is adopted at the upper boundary. The calculated profile was compared with the experimental data. Finally, the calculation is done based on various modes of the velocity and turbulent energy. The mean velocity is found to differ from condition of the relative depth and the roughness. It is also found that due to non-linearity, the absolute value for velocity and turbulent energy as well as Reynolds stress are asymmetric. The mean velocity of the laminar boundary layer is always positive but in the turbulent boundary layer plays a very complicated role.

Keywords: wave boundary, mass transport, mean velocity, shear stress

Procedia PDF Downloads 231

Authors: Xuan Zhou, Litian Zhang, Shuixiang Li

Abstract:

Mesh deformation using radial basis function interpolation method has been demonstrated to produce quality meshes with relatively little computational cost using a concise algorithm. However, it still suffers from the limited deformation ability, especially in large deformation. In this paper, a pre-displacement improvement is proposed to improve the problem that illegal meshes always appear near the moving inner boundaries owing to the large relative displacement of the nodes near inner boundaries. In this improvement, nodes near the inner boundaries are first associated to the near boundary nodes, and a pre-displacement based on the displacements of associated boundary nodes is added to the nodes near boundaries in order to make the displacement closer to the boundary deformation and improve the deformation capability. Several 2D and 3D numerical simulation cases have shown that the pre-displacement improvement for radial basis function (RBF) method significantly improves the mesh quality near inner boundaries and deformation capability, with little computational burden increasement.

Keywords: mesh deformation, mesh quality, background mesh, radial basis function

Procedia PDF Downloads 331

Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

Abstract:

The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

Procedia PDF Downloads 325

Authors: Anna Bykalyuk, Frédéric Kuznik, Kévyn Johannes

Abstract:

In this paper, the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).

Keywords: CFD modeling, natural convection, thermal conductive plate, time-depending boundary conditions

Procedia PDF Downloads 244

Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

Abstract:

In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

Procedia PDF Downloads 403

Authors: Yuan Yan Tang, Lina Yang, Hong Li

Abstract:

Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

Procedia PDF Downloads 518

Authors: Abdon Choque-Rivero

Abstract:

The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

Procedia PDF Downloads 111

Authors: Dhahri Maher, Aouinet Hana

Abstract:

The presence of bubbles in the boundary layer introduces corrections into the log law, which must be taken into account. In this work, a logarithmic wall law was presented for bubbly two phase flows. The wall law presented in this work was based on the postulation of additional turbulent viscosity associated with bubble wakes in the boundary layer. The presented wall law contained empirical constant accounting both for shear induced turbulence interaction and for non-linearity of bubble. This constant was deduced from experimental data. The wall friction prediction achieved with the wall law was compared to the experimental data, in the case of a turbulent boundary layer developing on a vertical flat plate in the presence of millimetric bubbles. A very good agreement between experimental and numerical wall friction prediction was verified. The agreement was especially noticeable for the low void fraction when bubble induced turbulence plays a significant role.

Keywords: bubbly flows, log law, boundary layer, CFD

Procedia PDF Downloads 243

Authors: Md. Fazlul Karim, Ahmad Izani Md. Ismail, Mohammed Ashaque Meah

Abstract:

This paper focuses on the development of a 2-D Boundary Fitted and Nested Grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia. In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers. This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: boundary fitted nested model, tsunami, Penang Island, 2004 Indonesian Tsunami

Procedia PDF Downloads 288

Authors: Abhilash Sahu, Amit Priyadarshi

Abstract:

In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

Procedia PDF Downloads 206

Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied. The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length. To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed. Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition. The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work. The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: buckling, finite strip, different sides support, plates on foundation

Procedia PDF Downloads 211

Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

Procedia PDF Downloads 346

Authors: Alsaidi M. Altaher, Mohd Tahir Ismail

Abstract:

Wavelet thresholding has been a power tool in curve estimation and data analysis. In the presence of outliers this non parametric estimator can not suppress the outliers involved. This study proposes a new two-stage combined method based on the use of the median filter as primary step before applying wavelet thresholding. After suppressing the outliers in a signal through the median filter, the classical wavelet thresholding is then applied for removing the remaining noise. We use automatic boundary corrections; using a low order polynomial model or local polynomial model as a more realistic rule to correct the bias at the boundary region; instead of using the classical assumptions such periodic or symmetric. A simulation experiment has been conducted to evaluate the numerical performance of the proposed method. Results show strong evidences that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating outlier’s sensitivity.

Keywords: boundary correction, median filter, simulation, wavelet thresholding

Procedia PDF Downloads 391

Authors: Végh Ádám, Mekler Csaba, Dezső András, Szabó Dávid, Stomp Dávid, Kaptay György

Abstract:

Grain boundary segregation transition (GBST) has been calculated by a thermodynamic model in binary alloys. The method is used on cementite (Fe3C) segregation in base-centered cubic (ferrite) iron (Fe) in the Fe-C binary system. The GBST line is shown in the Fe3C lacking part of the phase diagram with high solvent (Fe) concentration. At a lower solute content (C) or at higher temperature the grain boundary is composed mostly of the solvent atoms (Fe). On higher concentration compared to the GBST line or at lower temperature a phase transformation occurs at the grain boundary, the latter mostly composed of the associates (Fe3C). These low-segregation and high-segregation states are first order interfacial phase transitions of the grain boundary and can be transformed into each other reversibly. These occur when the GBST line is crossed by changing the bulk composition or temperature.

Keywords: GBST, cementite, segregation, Fe-C alloy

Procedia PDF Downloads 549

Authors: Saghar Heidari

Abstract:

In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

Procedia PDF Downloads 103

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

Procedia PDF Downloads 126

Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

Abstract:

In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

Procedia PDF Downloads 241

Authors: Bakur Gulua

Abstract:

In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

Procedia PDF Downloads 92

Authors: Chinsuk Hong

Abstract:

This paper investigates the characteristics of wall pressure fluctuations in naturally developing boundary layer flows on axisymmetric bodies experimentally. The axisymmetric body has a modified ellipsoidal blunt nose. Flush-mounted microphones are used to measure the wall pressure fluctuations in the boundary layer flow over the body. The measurements are performed in a low noise wind tunnel. It is found that the correlation between the flow regime and the characteristics of the pressure fluctuations is distinct. The process from small fluctuation in laminar flow to large fluctuation in turbulent flow is investigated. Tollmien-Schlichting wave (T-S wave) is found to generate and develop in transition. Because of the T-S wave, the wall pressure fluctuations in the transition region are higher than those in the turbulent boundary layer.

Keywords: wall pressure fluctuation, boundary layer flow, transition, turbulent flow, axisymmetric body, flow noise

Procedia PDF Downloads 315

Authors: Lawrence A. Farinola

Abstract:

Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

Procedia PDF Downloads 97

Authors: Abdallah Benaissa

Abstract:

In this paper, we consider the problem of asymptotics of double oscillatory integrals in the case of critical points of the second kind, the order of contact between the boundary and a level curve of the phase being even, the situation when the order of contact is odd will be studied in other occasions. Complete asymptotic expansions will be derived and the coefficient of the leading term will be computed in terms of the original data of the problem. A multitude of people have studied this problem using a variety of methods, but only in a special case when the order of contact is minimal: the more cited papers are a paper of Jones and Kline and an other one of Chako. These integrals are encountered in many areas of science, especially in problems of diffraction of optics.

Keywords: asymptotic expansion, double oscillatory integral, critical point of the second kind, optics diffraction

Procedia PDF Downloads 315

Authors: Po-Chun Wang, Yan-Ru Lai, Sophia I. C. Lin, Alvin W. Y. Su

Abstract:

The Generative Theory of Tonal Music (GTTM) provides systematic approaches to recognizing local boundaries of music. The rules have been implemented in some automated melody segmentation algorithms. Besides, there are also deep learning methods with GTTM features applied to boundary detection tasks. However, these studies might face constraints such as a lack of or inconsistent label data. The GTTM database is currently the most widely used GTTM database, which includes manually labeled GTTM rules and local boundaries. Even so, we found some problems with these labels. They are sometimes discrepancies with GTTM rules. In addition, since it is labeled at different times by multiple musicians, they are not within the same scope in some cases. Therefore, in this paper, we examine this database with musicians from the aspect of classical music and relabel the scores. The relabeled database - GTTM Database v2.0 - will be released for academic research usage. Despite the experimental and statistical results showing that the relabeled database is more consistent, the improvement in boundary detection is not substantial. It seems that we need more clues than GTTM rules for boundary detection in the future.

Keywords: dataset, GTTM, local boundary, neural network

Procedia PDF Downloads 99

Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

Procedia PDF Downloads 126

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

Abstract:

In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

Procedia PDF Downloads 504

Authors: Rehan Ali Shah, A. M. Siddiqui, T. Haroon

Abstract:

Slip boundary value problem in wire coating analysis with heat transfer is examined. The fluid is assumed to be viscoelastic PTT (Phan-Thien and Tanner). The rheological constitutive equation of PTT fluid model simulates various polymer melts. Therefore, the current consequences are valuable in a number of realistic situations. Effects of slip parameter γ as well as εDec^2 (viscoelastic index) on the axial velocity, shear stress, normal stress, average velocity, volume flux, thickness of coated wire, shear stress, force on the total wire and temperature distribution profiles have been investigated. A new direction is explored to analyze the flow with the slip parameter. The slippage at the boundaries plays an important role in thickness of coated wire. It is noted that as the slip parameter increases the flow rate and thickness of coated wire increases while, temperature distribution decreases. The results reduce to no slip when the slip parameter is vanished. Furthermore, we can obtain the results for Maxwell and viscous model by setting ε and λ equal to zero respectively.

Keywords: wire coating, straight annular die, PTT fluid, heat transfer, slip boundary conditions

Procedia PDF Downloads 328

Authors: Manana Chumburidze, David Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

Procedia PDF Downloads 473

Authors: Spandan Sahu, Amiya Kumar Pati, Kishanjit Kumar Khatua

Abstract:

River is our main source of water which is a form of open channel flow and the flow in open channel provides with many complex phenomenon of sciences that needs to be tackled such as the critical flow conditions, boundary shear stress and depth averaged velocity. During floods, part of a river is carried by the simple main channel and rest is carried by flood plains. For such compound asymmetric channels, the flow structure becomes complicated due to momentum exchange between main channel and adjoining flood plains. Distribution of boundary shear in subsections provides us with the concept of momentum transfer between the interface of main channel and the flood plains. Experimentally, to get better data with accurate results are very complex because of the complexity of the problem. Hence, CES software has been used to tackle the complex processes to determine the shear stresses at different sections of an open channel having asymmetric flood plains on both sides of the main channel and the results is compared with the symmetric flood plains for various geometrical shapes and flow conditions. Error analysis is also performed to know the degree of accuracy of the model implemented.

Keywords: depth average velocity, non prismatic compound channel, relative flow depth, velocity distribution

Procedia PDF Downloads 118

Authors: Arcady Ponosov

Abstract:

Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

Procedia PDF Downloads 209