Effect Of Boundary Conditions Research Articles

Homogenization of enhancing thin layers

This paper derives an explicit formula for the effective diffusion tensor by using the solutions to some effective cell problems after homogenizing Road effective boundary conditions (EBCs). The concept of Road EBCs was proposed recently by H. Li and X. Wang, and in this paper, we extend the effective conditions on closed curves to those on patterns, especially on the included nodes. We also prove that homogenization process commutes with the derivation of Road EBCs. By analyzing the effective diffusion tensor, we obtain several rules for maximizing its trace with given Road-effective-diffusivity/scale and length/scale in each cell and define a notion of balanced patterns. Moreover, we give an estimate of the trace of the effective diffusion tensor of patterns satisfying some connectedness as Road-effective-diffusivity/scale goes to infinity.

Quasi-adiabatic approximation for thermoelastic surface waves in orthorhombic solids

An asymptotic model for time-harmonic motion in fully-coupled linear thermoelastic orthorhombic materials is presented. The asymptotic approach takes advantage of the observation that the parameter expressing departure from the purely adiabatic regime is extremely small in practice. Consequently, the leading order bulk response turns out to be non-dissipative, and is governed by the usual equations of elastodynamics with adiabatic material constants. In the case of isothermal stress-free boundary conditions, it is shown that thermoelastic interaction is dominated by a thermoelastic boundary layer. Hence, effective boundary conditions may be constructed, which duly account for the influence of this boundary layer and successfully describe dispersion and dissipation of surface waves to leading order. As an illustration, in the special case of an isotropic half-space with free isothermal boundary conditions, we recover the asymptotic results by Chadwick and Windle (1964). Numerical comparison of the dispersion curves for surface waves in an orthorhombic half-space shows excellent agreement between the exact fully-coupled thermoelastic problem and the corresponding quasi-adiabatic approximation, even for relatively large wavenumbers.

Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature

Abstract Generalized impedance boundary conditions are effective approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes materials with a thin coating (with the thickness of the coating as the small scale) and strongly absorbing materials. For the acoustic scattering from generalized impedance boundary conditions, the approach taken here first determines the Dirichlet and Neumann boundary data from a system of time-dependent boundary integral equations with the usual boundary integral operators, and then the scattered wave is obtained from the Kirchhoff representation. The system of time-dependent boundary integral equations is discretized by boundary elements in space and convolution quadrature in time. The well-posedness of the problem and the stability of the numerical discretization rely on the coercivity of the Calderón operator for the Helmholtz equation with frequencies in a complex half-plane. Convergence of optimal order in the natural norms is proved for the full discretization. Numerical experiments illustrate the behaviour of the proposed numerical method.

Scattering by thin shells in fluids: Fast solver and experimental validation.

A numerical model facilitating fast analysis of acoustic scattering by thin shells immersed in fluids is presented. The shell is simulated by an effective boundary condition, in which the inertial properties of the shell are taken into account while the elastic ones are neglected. The problem reduces to a hypersingular surface integral equation, which is solved using the boundary element method accelerated by the multilevel nonuniform grid approach. The validity of the numerical method and the adopted physical approximations were tested by comparison with a water tank experiment on acoustic scattering from cylindrical metallic shells filled with water.

Computational kinematic characterization of flow past a bluff body for type 304 stainless steel material using ANSYS workbench

Current computational Analysis deals with the velocity analysis of G/D 0.5 at different time frames. Type 304 stainless steel is used as it is an austenitic steel with excellent corrosion resistant properties. Finite size vortex has been made by translating circular cylinder that was permitted to move at a consistent speed over a zero pressure-gradient shear layer. The regulated vortex makes an extremely powerless stream astute pressure gradient that destabilized the level plate shear layer at subcritical Reynolds number. 2D fluid domain of 0.5 G/D is designed, modeled, meshed and the effective boundary conditions are applied. Different Models are highlighted in the current research such as Mass Conservation Equation, Momentum Conservation Equation, Energy equation, k –ω Model and Shear Stress Transport Turbulence Model. The governing equations are also elaborated. The Velocity Comparison at Point 1,2,3,4 for G/D 0.5 at different time steps is analysed. Also the Velocity Contour for different locations like front, left, right and mid view is computationally analysed. It is finally concluded that the disturbance in flow with lower G/D (less than 0.5) ratio in near wall zone is suppressed completely over the time and steady condition can be achieved after sufficient amount of time. The magnitude of the change in the kinematic properties are analysed and discussed. Specifically, the 304 stainless steel material is used in order to work on product development just after the positive results. The major significance of the current research is to provide all the governing equations, proper methodology, process and finally the trend at different locations based on computational techniques. Fluid flow is simulated in all the three cases with uniform velocity 1.76 m/s by using ANSYS Fluent Solver. The Future scope for the current computational Analysis is to change the G/D values and take different time step size for micro or even Nano kinematic analysis.

Enhanced saturation of liquid-saturated porous medium with atmosphere gases due to surface temperature oscillations

We study the non-isothermal diffusion transport of a poorly soluble substance in a porous liquid-saturated medium being in contact with the reservoir of this substance. The surface temperature of a half-space porous medium oscillates in time, which creates a decaying temperature wave propagating deep into sediments. Since the solubility exponentially strongly depends on temperature, a decaying running solubility wave forms in the porous medium. In such a system, the zones of saturated solution and non-dissolved phase coexist with the zones of undersaturated solution. The effect is considered for the case of annual oscillation of the surface temperature of water-saturated ground being in contact with atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation for one- and two-component solutes. In the case of a two-component solute, the solubility depends on the composition of the nondissolved phase, which necessitates the construction of a corresponding mathematical model of dissolution of multicomponent mixtures. We develop an analytical theory of the phenomenon of formation of the bubbly horizon. In both analytical theory and numerical simulations, the temperature dependence of the molecular diffusion coefficient is taken into account. In the presence of a propagating temperature wave, the nonlinear interaction between this dependence and the temperature dependence of the solubility creates an additional nonzero contribution to the mean-over-period mass flux. For multicomponent solutions, we report the formation of a diffusive boundary layer, which is not possible for single-component solutions. We construct an analytical theory for this boundary layer and derive effective boundary conditions for the problem of the diffusive transport beyond this layer. Theoretical results are in fair agreement with the results of numerical simulation.

Analysis of Boundary Layer Effects Due to Usual Boundary Conditions or Geometrical Defects in Elastic Plates Under Bending: An Improvement of the Love-Kirchhoff Model

We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two first terms of the outer expansion must satisfy. The new boundary value problems thus obtained are studied and compared with the classical Love-Kirchhoff plate model. Two examples of application illustrate the results.

Proposal of Effective Near-Field Wrap Boundary Condition under Coexistence of Radiation and Damping Components

We have developed an effective boundary condition that can naturally interconnect the discretized field at the boundary to the continuum field outside the analysis domain. The interconnection must ...

Effective Navier-slip in non-Newtonian fluid flows over corrugated surfaces

In this study, we show that complex local flow fields, particularly those near corrugated surfaces, can be accurately reproduced with effective Navier-slip boundary conditions over an imaginary smooth surface, in which the normalized slip length can be considered as a surface property even for non-Newtonian fluid flows. The expression for the normalized slip length was derived analytically using the effective viscosity and effective shear rate in a pressure-driven channel flow with a corrugated surface, based on the two-parameter model by separating geometrical and rheological factors with the effective viscosity concept. Our framework was established on the combination of the force balance approach for slip length characterization and the flow quantification method based on the energy dissipation rate. Effects of corrugated patterns with various aspect ratios were investigated. For verification, an example stick–slip–stick flow problem was tested and the results were compared with those of direct simulations. We report that the dimensionless normalized slip length appears to be almost constant and independent of the flow rate (or pressure drop). This implies that the normalized slip length is nearly independent of rheological properties. In addition, the dimensionless slip length of non-Newtonian fluids was found to be close to that of a Newtonian fluid, and it depends on the flow geometry itself.

Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition

<p style='text-indent:20px;'>This article is focused on the slip effect in the unsteady flow of MHD Oldroyd-B fluid over a moving vertical plate with velocity <inline-formula><tex-math id="M1">\begin{document}$ U_{o}f(t) $\end{document}</tex-math></inline-formula>. The Laplace transformation and inversion algorithm are used to evaluate the expression for fluid velocity and shear stress. Fractional time derivatives are used to analyze the impact of fractional parameters (memory effect) on the dynamics of the fluid. While making a comparison, it is observed that the fractional-order model is best to explain the memory effect as compared to the classical model. The behavior of slip condition as well as no-slip condition is discussed with all physical quantities. The influence of dimensionless physical parameters like magnetic force <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>, retardation time <inline-formula><tex-math id="M3">\begin{document}$ \lambda_{r} $\end{document}</tex-math></inline-formula>, fractional parameter <inline-formula><tex-math id="M4">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>, and relaxation time <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> on fluid velocity has been discussed through graphical illustration. Our results suggest that the velocity field decreases by increasing the value of the magnetic field. In the absence of a slip parameter, the strength of the magnetic field is maximum. Furthermore, it is noted that the Atangana-Baleanu derivative in Caputo sense (ABC) is the best to highlight the dynamics of the fluid.</p>

Hopf bifurcation in a reaction-diffusion-advection equation with nonlocal delay effect

This paper investigates the dynamics of a general reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition. The existence and stability of positive spatially nonhomogeneous steady state solution are shown. By analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized equation, the existence of Hopf bifurcation is proved. We introduce the weighted space to overcome the hurdle from advection term. We also show that the effect of adding a term advection along environmental gradients to Hopf bifurcation values for a Logistic equation with nonlocal delay.

Electronic States in a Doubly Eccentric Cylindrical Quantum Wire

Electronic states of a single electron in doubly eccentric cylindrical quantum wire are theoretically investigated in this paper. The motion of electron in quantum wire is free along axial direction in a cylindrical quantum wire and restricted in annular regions by three different parallel finite cylindrical barriers as soft wall confinement. The effective mass Schrödinger equation with effective mass boundary conditions is used to find energy eigenvalues and corresponding wavefunctions. Addition theorem for cylindrical Bessel functions is used to shift the origin for applying boundary conditions at different circular boundaries. Fourier expansion is applied after addition theorem to get wavefunctions in analytical form. A determinant equation is obtained as a result of applications of effective mass boundary conditions which roots gives energy of various electronic states. The lowest root gives ground state energy. The variation in ground state energy with eccentricity is obtained numerically and presented graphically. Electronic states in massive wall confinement and hard wall confinement is further obtained as limiting behavior of the states obtained in soft wall confinement. The knowledge of electronic states in such cylindrical hetrostructures semiconductor material can lead to improve the efficiency of many quantum devices.

General criteria for the estimation of effective slip length over corrugated surfaces

In this work, we aim to develop an effective hydrodynamic boundary condition over patterned surfaces for the application to microfluidics. Four different criteria to estimate the effective Navier-slip length and their performance are investigated for flows over corrugated surfaces, such as patterned surfaces or porous interfaces, which can be applied for efficient flow simulations. Four distinctive methods were discussed in the estimation of slip length, namely: mass conservation, balance of energy dissipation rate, force balance, and interfacial slip velocity averaging. Expressions of slip length were derived analytically for each criterion in a pressure-driven flat channel flow and the slip length was determined using a combination of analytic and numerical methods. We report that (i) the slip length from force balance appears to be the most accurate and exactly the same as that from interfacial slip velocity averaging, (ii) the slip length from mass conservation deviates from that of force balance, though minor, particularly for a small relative channel height to the length scale of patterns or pores, and (iii) the energy balance yields significantly different slip lengths. The slip length reduces to a single value for a sufficiently large relative channel height, which indicates that it can be considered as a surface property in general, when the pattern dimension is much smaller than the length scale of flow.

A Correlation for Nusselt Number of Slip Gas Flow in Confined Porous Media

Abstract A clear understanding of flow and heat transfer at pore-scale level in microporous media is a topic of concern in microcooling/heating systems. In this work, a multiple-relaxation-time lattice Boltzmann method (LBM) is employed to study flow and heat transfer of gas in microporous media. Curved boundaries are treated using an effective boundary condition, which is formed by combining nonequilibrium extrapolation with counterextrapolation methods. The method also incorporates velocity slip and temperature jump on gas–solid interface. A two-dimensional (2D) porous domain composed of microcylinders, is considered from a representative element volume (REV) for the simulation. Porosity of the domain is variated by altering diameter of microcylinders. Nusselt number is calculated by varying Knudsen number (0.0–0.1), Reynolds number (5–50) and porosity (0.4–0.8). Based on the obtained numerical predictions, a new Nusselt number correlation is proposed for the first time in this work which can accurately predict the heat transfer for slip gas flow in confined porous media.

Effective boundary conditions at a rough wall: a high-order homogenization approach

Effective boundary conditions, correct to third order in a small parameter epsilon, are derived by homogenization theory for the motion of an incompressible fluid over a rough wall with periodic micro-indentations. The length scale of the indentations is l, and epsilon = l/L ll 1, with L a characteristic length of the macroscopic problem. A multiple scale expansion of the variables allows to recover, at leading order, the usual Navier slip condition. At next order the slip velocity includes a term arising from the streamwise pressure gradient; furthermore, a transpiration velocity {mathcal {O}}(epsilon ^{2}) appears at the fictitious wall where the effective boundary conditions are enforced. Additional terms appear at third order in both wall-tangent and wall-normal components of the velocity. The application of the effective conditions to a macroscopic problem is carried out for the Hiemenz stagnation point flow over a rough wall, highlighting the differences among the exact results and those obtained using conditions of different asymptotic orders.

Hopf Bifurcation for Semilinear FDEs in General Banach Spaces

In this paper, we extend the equivariant Hopf bifurcation theory for semilinear functional differential equations in general Banach spaces and then apply it to reaction–diffusion models with delay effect and homogeneous Dirichlet boundary condition on a general open domain with a smooth boundary. In the process we derive the criteria for the existence and directions of branches of bifurcating periodic solutions, avoiding the process of center manifold reduction.

Numerical Study on Gas Transport in Shale Kerogen with Adsorption Effect Using LBM

Gas transport and storage mechanism in gas reservoirs with complex pore size distribution play a key role in gas production. In the nano-scale, during the process of density disturbance caused by depressurization development, notable output gas collides with the wall as they convey along the channel. The continuum assumption of fluid flow is therefore invalid, and taking the influence of particles to collide with solid walls into account is necessary. The effective viscosity and slip boundary conditions were introduced in the simulation. Meanwhile, because of the adsorption effect is one of the most important intrinsic properties of shale, the impact of surface adsorption on the solid wall by using Langmuir adsorption kinetics was also involved in our investigation. In this work, a unified LB model was developed for gas multiple transports and surface adsorption in nanopores. In the model, the double distribution function was employed for a coupled bulk flow and gas diffusion model. The model is valid within the range of the continuum regime to the transition regime and has been verified by the analytical solution and the results of some previously published works. The results show that (1) the driven force of the fluid, the combination coefficient of slippage and the Knudsen number of the flow have an impact on the adsorption rate, (2) adsorption effect only directly influence the local small region of the solid surface, and the induced concentration gradient makes the global concentration variation, (3) once acting the surface adsorption on the boundary, the flux falls more significant as Knudsen number increases.

B EFFECT OF BOUNDARY CONDITIONS ON BUCKLING LOAD FOR LAMINATED COMPOSITE DECKS PLATES

Finite element (FE) method is presented for the analysis of thin rectangular laminatedcomposite decks plates under the biaxial action of in – plane compressive loading. Theanalysis uses the classical laminated plate theory (CLPT) which does not account for sheardeformations. In this theory it is assumed that the laminate is in a state of plane stress, theindividual lamina is linearly elastic, and there is perfect bonding between layers. The classicallaminated plate theory (CLPT), which is an extension of the classical plate theory (CPT)assumes that normal to the mid – surface before deformation remains straight and normal tothe mid – surface after deformation. Therefore, this theory is only adequate for bucklinganalysis of thin laminates. A Fortran program has been developed. New numerical results aregenerated for in – plane compressive biaxial buckling which serve to quantify the effect ofboundary conditions on buckling loading. It is observed that, for all cases the buckling loadincreases with the mode number but at different rates depending on whether the plate is simplysupported, clamped or clamped – simply supported. The buckling load is a minimum whenthe plate is simply supported and a maximum when the plate is clamped. Because of therigidity of clamped boundary condition, the buckling load is higher than in simply supportedboundary condition. It is also observed that as the mode number increases, the plate needsadditional supp

Self-similar grooving solutions to the Mullins’ equation

In 1957, Mullins proposed surface diffusion motion as a model for thermal grooving. By adopting a small slope approximation, he reduced the model to the Mullins’ linear surface diffusion equation, ( M E ) y t + B y x x x x = 0 , \begin{equation} \nonumber ({\mathrm {ME}})\quad \quad y_t + B y_{xxxx}=0, \end{equation} known also more simply as the Mullins’ equation. Mullins sought self-similar solutions to (ME) for planar initial conditions, prescribing boundary conditions at the thermal groove, as well as far field decay. He found explicit series solutions which are routinely used in analyzing thermal grooving to this day. While (ME) and the small slope approximation are physically reasonable, Mullins’ choice of boundary conditions is not always appropriate. Here we present an in depth study of self-similar solutions to the Mullins’ equation for general self-similar boundary conditions, explicitly identifying four linearly independent solutions defined on R ∖ { 0 } \mathbb {R}\setminus \{0\} ; among these four solutions, two exhibit unbounded growth and two exhibit asymptotic decay, far from the origin. We indicate how the full set of solutions can be used in analyzing the effective boundary conditions from experimental profiles and in evaluating the governing physical parameters.

Effective Boundary Conditions for the Heat Equation with Interior Inclusion

Effective Boundary Conditions for the Heat Equation with Interior Inclusion