Coupled Boundary Conditions Research Articles

Modelling of the transport phenomena for an atmospheric-pressure plasma jet in contact with liquid

The paper presents the results of a modelling study on the transport phenomena for a turbulent atmospheric-pressure plasma jet in contact with liquid. The focus is on the convective flow field in the gas and liquid phases and the transport of plasma generated long-lived hydrophilic species into the liquid. The flow field is studied by solving the Navier–Stokes equations using the finite-element method. The transport of species from the gas into the liquid phase is studied on the example of hydrogen peroxide by solving the convection-diffusion equation. Special attention is given to the implementation of the coupling boundary conditions at the gas–liquid interface. The computations are performed for the interaction of an argon jet with liquid under typical experimental conditions. The modelling results agree well with available experimental data. It is found that the three-dimensional nature of the flow in the liquid might be important in interpreting the experimental data. The model is shown to provide a reliable estimate of the hydrogen peroxide diffusion flux from the gas into the liquid phase.

DRBEM solution to MHD flow in ducts with thin slipping side walls and separated by conducting thick Hartmann walls

In this study, the dual reciprocity boundary element method (DRBEM) solution to magnetohydrodynamic (MHD) flow is given in a single and two ducts stacked in the direction of external magnetic field. The duct walls perpendicular to the applied magnetic field (Hartmann walls) are conducting, thick and no-slip whereas the horizontal walls (side walls) are insulated, thin and allow the velocity slip. The DRBEM transforms the convection diffusion type MHD equations in the duct and Laplace equation in the thick walls to boundary integral equations which are discretized by using constant elements. The resultant matrix–vector equations are solved as a whole with the coupled boundary conditions on the common boundaries between the fluid and the thick walls. The effects of the slip length, thickness of conducting walls and the applied magnetic field strength are shown inthe flow and the induced magnetic field. It is found that, in the absence of the slip, as Hartmann number (Ha) increases, the flow is concentrated in front of the side walls in terms of two side layers, and this separation is happened for much smaller value of Ha when the thickness of the conducting walls is increased. The continuation of induced magnetic fields to the thick walls is well observed in both co-flow and counter flow cases. When the side walls admit slip, opposite to the no-slip case, an increase in the conductivity of the fluid enlarges the core region where the fluid is stagnant. The proposed numerical scheme DRBEM is capable of capturing the well known MHD flow characteristics in ducts with thick walls as well as perturbations in the behaviors of the flow and the induced magnetic field due to the thin slip walls.

DIFFERENCE METHODS TO ONE AND MULTIDIMENSIONAL INTERDIFFUSION MODELS WITH VEGARD RULE

In this work we consider the one and multidimensional diffusional transport in an s-component solid solution. The new model is expressed by the nonlinear parabolic-elliptic system of strongly coupled differential equations with the initial and the nonlinear coupled boundary conditions. It is obtained from the local mass conservation law for fluxes which are a sum of the diffusional and Darken drift terms, together with the Vegard rule. The considered boundary conditions allow the physical system to be not only closed but also open. We construct the implicit finite difference methods (FDM) generated by some linearization idea, in the one and two-dimensional cases. The theorems on existence and uniqueness of solutions of the implicit difference schemes, and the theorems concerned convergence and stability are proved. We present the approximate concentrations, drift and its potential for a ternary mixture of nickel, copper and iron. Such difference methods can be also generalized on the three-dimensional case. The agreement between the theoretical results, numerical simulations and experimental data is shown.

Existence of positive solutions for a system of semipositone coupled discrete boundary value problems

ABSTRACTWe study the existence of positive solutions for a system of nonlinear second-order difference equations with parameters and sign-changing nonlinearities, subject to multi-point coupled boundary conditions. In the proof of our main theorems we use the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.

Experimental statics calibration of a multi-constraint parallel continuum robot

A multi-constraint parallel continuum robot (MPCR) is composed of parallel flexible legs under multiple constraints. Compared with a rigid parallel robot, the model of MPCR, which is formulated based on Cosserat rod equations and coupled boundary conditions, is a boundary value problem (BVP) with only numerical solutions instead of analytical solutions, and the Jacobian matrix in calibration is ill-conditioned due to the parallel structure. Therefore, traditional calibration techniques cannot be used directly on MPCR. In this paper, we present a framework to calibrate this model with tip position data, including identifiability analysis and an optimization method that combines Levenberg-Marquadt method and interior point method. Simulation results of the method show the numerical solvability of the error model and its performance under noise disturbance. The calibration method is then validated experimentally on a prototype. The results show that the model matches experimental tip positions with an average and maximum error of 0.8% and 1.8% respectively of nominal total length, which verifies the effectiveness of the proposed calibration method.

Positive solutions for Caputo fractional differential system with coupled boundary conditions

This paper focuses on the Caputo fractional differential system involving coupled integral boundary conditions and parameters. Using the properties of the Green function, the Leray–Schauder’s alternative and the Banach contraction principle, the existence and uniqueness results of the system are established. An example is then given to demonstrate the validity of the result.

The role of submerged berms on the momentary liquefaction around conventional rubble mound breakwaters

Berms deployed at the toe of conventional rubble mound breakwaters can be very effective in improving the stability of the armor layer. Indeed, their design is commonly tackled by paying attention to armor elements dimensioning. Past research studies showed how submerged berms can increase the stability of the armor layer if compared to straight sloped conventional breakwaters without a berm. To fill the gap of knowledge related to the interaction between breakwaters with submerged berm, waves and soil, this research aims to evaluate how submerged berms configuration influences the seabed soil response and momentary liquefaction occurrences around and beneath breakwaters foundation, under dynamic wave loading. The effects of submerged berms on the incident waves transformation have been evaluated by means of a phase resolving numerical model for simulating non-hydrostatic, free-surface, rotational flows. The soil response to wave-induced seabed pressures has been evaluated by using an ad-hoc anisotropic poro-elastic soil solver. Once the evaluation of the seabed consolidation state due to the presence of the breakwater has been performed, the dynamic interaction among water waves, soil and structure has been analyzed by using a one-way coupling boundary condition. A parametric study has been carried out by varying the berm configuration (i.e. its height and its length), keeping constant the offshore regular wave condition, the berm and armor layer porosity values, the water depth and the elastic properties of the soil. Results indicate that the presence of submerged berms tends to mitigate the liquefaction probability if compared to straight sloped conventional breakwater without a berm. In addition, it appears that the momentary liquefaction phenomena are more influenced by changing the berm length rather than the berm height.

Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain

In this paper, we derive existence and uniqueness results for a coupled system of nonlinear third order ordinary differential equations equipped with nonlocal multi-point anti-periodic type coupled boundary conditions. Leray-Schauder alternative and Banach contraction mapping principle are the main tools of our study. Examples are constructed for illustrating the obtained results. Under appropriate conditions, our results correspond to the ones for an ant-periodic boundary value problem of nonlinear third order ordinary differential equations.

Unsteady three-dimensional stagnation point magnetohydrodynamic flow of bionanofluid with variable properties

Unsteady three-dimensional laminar stagnation point forced convective boundary layer magnetohydrodynamic flow of a bionanofluid with variable transport properties is studied theoretically and numerically. Thermal convective and zero mass flux boundary conditions are incorporated in this study. The transport properties are assumed to be a function of nanoparticle volume fraction to get physically realistic results. The dimensional boundary layer equations along with the coupled boundary conditions are transformed via similarity transformations into a system of ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth-, fifth-order numerical method. The effect of selected governing parameters, namely, viscosity, thermal conductive, mass diffusivity, microorganism diffusivity, magnetic field and bioconvection Schmidt number, on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism, skin friction coefficient, heat transfer rate, mass transfer rate and microorganism transfer rate, is illustrated graphically and interpreted in detail. Comparisons with previous works are carried out for some limiting cases and found to be in good agreement.

MODELING AND SIMULATION OF THE NANOFLUID TRANSPORT VIA ELASTIC SHEETS

The field of nanofluidics research has spanned over the past decade with a variety of promising applications. We investigate the “laminar boundary layer flow” of a Newtonian nanofluid past a moving extendable/contractable horizontal plate with surface velocity and thermal slip effects. The passively controlled nanofluid model (PCM) is considered. Such models are physically more realistic as compared to the “actively controlled models” (ACM). Using Lie symmetry group method, the governing equations are reduced by a set of highly coupled nonlinear ODE’s with thermo-solutal coupled boundary conditions. The reduced equations are solved numerically by a generalized collocation method. The influences of the emerging parameters on the local skin friction factor and the local Nusselt number are depicted numerically. The skin friction is decreased as the thermophoresis and buoyancy ratio parameters are decreased. The heat transfer rates reduce with thermophoresis and buoyancy ratio parameters. Velocity slip also leads to a rise in wall temperature gradient. This study is relevant to near-wall flows in nanofluid fuel cells, nano-materials processing, etc.

Numerical Simulation of Nuclear Secondary Bellows Globe Valve under Transient Thermal Shock

Abstract: In order to study the effect of the transient thermal shock on the structural strength and fatigue life of the nuclear secondary bellows globe valve, the hot-fluid-solid coupling analysis of the nuclear secondary globe valve body was carried out by Fluent and ANSYS software, based on the theory of fluid-solid coupling and thermal boundary condition. The effects of the temperature field, thermal stress and fatigue life of the monitoring point at different time points and the effect of the thermal shock time on the fatigue life of the degree of sensitivity were studied. The results showed that the effects of the transient pressure on the temperature field, structural strength, fatigue life and sensitivity of the valve body was huge, and have to be eliminated to ensure the high safety of the nuclear secondary bellows globe valve.

The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions

We discuss the uniqueness of the solution to a class of differential systems with coupled integral boundary conditions under a Lipschitz condition. Our main method is the linear operator theory and the solvability for a system of inequalities. Finally, an example is given to demonstrate the validity of our main results.

Aero-thermo-elastic flutter analysis of coupled plate structures in supersonic flow with general boundary conditions

The coupled plates are commonly seen in flight vehicle structures, which are always subjected to a severe combination of thermal, aerodynamic and mechanical loads during the cruise. In this paper, a unified solution is derived for the aero-thermo-elastic flutter problems of the coupled plate structure with general boundary conditions, in which the classical and elastic boundary conditions can be dealt with. The Mindlin plate theory in conjunction with the supersonic piston theory to consider the supersonic flow effect is adopted to formulate the theoretical model of the heated coupled plate structure subjected to supersonic flow. Each displacement component of the coupled plate is constructed as a two-dimensional Fourier series supplemented with auxiliary functions in order to satisfy the possible boundary conditions. The flutter analysis of a single flat plate, to which great efforts have been devoted, can be considered as a special case in the proposed model by setting the coupling angle of the coupled plate equal to zero. A considerable number of numerical cases are presented to show the accuracy and efficiency of the proposed method. The effects of the aerodynamic pressure, boundary condition, coupling spring and temperature change on the flutter characteristics of the coupled plate are also discussed in detail. The present formulation permits to analyze the flutter problems of the coupled plate having arbitrary coupling angles and boundary conditions.

A hydrodynamic model of bridle towed system

To determine the parameters of bridle towed systems in preliminary design and describe the configuration and dynamic behavior of bridle cables during tow-ship changes its speed and course, a tug–cable–barge coupling motion model for bridle towed system is proposed. The governing equation of towing bridle was established based on finite difference method and the six-degrees-of-freedom equations of motion for tug and barge were adopted according to the MMG modeling theory. The dynamic coupling boundary conditions for bridle towed system are derived. The steady- state motion parameters of towing bridle were confirmed by double bisection method. The equations of towing bridle are solved by Newton iteration method. Tug and barge motion equations are solved by Runge–Kutta method. The computing results indicate that the model and algorithm in this paper can be used to predict the configuration and dynamic behavior, and determine the parameters in preliminary design of bridle towed systems.

Existence of Solutions for a System of Fractional Differential Equations with Coupled Nonlocal Boundary Conditions

AbstractWe study the existence of solutions for a system of nonlinear Caputo fractional differential equations with coupled boundary conditions involving Riemann-Liouville fractional integrals, by using the Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type. Two examples are given to support our main results.

On a Cahn–Hilliard system with convection and dynamic boundary conditions

This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn–Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the system, is also present in the equation. Either regular or singular potentials are admitted in the bulk and on the boundary. Both the viscous and pure Cahn–Hilliard cases are investigated, and a number of results are proven about existence of solutions, uniqueness, regularity, continuous dependence, uniform boundedness of solutions, strict separation property. A complete approximation of the problem, based on the regularization of maximal monotone graphs and the use of a Faedo–Galerkin scheme, is introduced and rigorously discussed.

Viscous Fluid–Thin Elastic Plate Interaction: Asymptotic Analysis with Respect to the Rigidity and Density of the Plate

A two-dimensional time dependent model of an interaction between a thin elastic plate and a Newtonian viscous fluid described by the non-steady Stokes equations is considered. It depends on a small parameter $$\varepsilon $$ that is the ratio of the thicknesses of the plate and the fluid layer. The Young’s modulus of the plate and its density may be great or small parameters equal to some powers (positive or negative) of $$\varepsilon $$ while the density and the viscosity of the fluid are supposed to be of order one. An asymptotic expansion is constructed and justified for various magnitudes of the rigidity and density of the plate. The limit problems are studied in all these cases. They are Stokes equations with some special coupled or uncoupled boundary conditions modeling the interaction with the plate. The estimates of the difference between the exact solution and a truncated asymptotic expansion are established. These estimates justify the asymptotic approximations.

某耦合边界条件下四阶常微分算子特征值的秩

某耦合边界条件下四阶常微分算子特征值的秩

The modified Parseval equality of Sturm-Liouville problems with coupled boundary condition

The modified Parseval equality of Sturm-Liouville problems with coupled boundary condition

Positive Solutions for a System of Fractional Differential Equations with Parameters and Coupled Multi-point Boundary Conditions

Positive Solutions for a System of Fractional Differential Equations with Parameters and Coupled Multi-point Boundary Conditions