Conducting Boundary Conditions Research Articles

The John Mitchell Lecture 2022: thinking conceptually about groundwater problems

Many excavations and tunnels experience problems and instability caused by uncontrolled groundwater inflows or groundwater pressures that influence stability and soil behaviour. A range of groundwater control measures can be used to overcome these problems and create stable and workably dry conditions below groundwater level. A key challenge for designers is that the performance of the various different techniques is strongly influenced by the hydrogeological conditions at a site. Furthermore, the available ground investigation data may have data gaps or considerable uncertainty regarding key parameters such as hydraulic conductivity or hydraulic boundary conditions. This means that, when working with real-world data sets, there are some groundwater problems where analysis involves so many assumptions and uncertainties that the design outcomes are of little practical value. This paper will discuss how thinking conceptually about groundwater problems can be of great benefit when developing of groundwater control schemes, and that a robust conceptual model helps reduce the risk of designs being developed using inappropriate techniques. Historic examples from the 19 th Century and early 20 th century (before sophisticated methods of groundwater analysis were available) are described, where developing a conceptual understanding of groundwater conditions was vital in developing practical engineering solutions.

A contour integral-based method for nonlinear eigenvalue problems for semi-infinite photonic crystals

In this study, we introduce an efficient method for determining isolated singular points of two-dimensional semi-infinite and bi-infinite photonic crystals, equipped with perfect electric conductor and quasi-periodic mixed boundary conditions. This specific problem can be modeled by a Helmholtz equation and is recast as a generalized eigenvalue problem involving an infinite-dimensional block quasi-Toeplitz matrix. Through an intelligent implementation of cyclic structure-preserving matrix transformations, the contour integral method is elegantly employed to calculate the isolated eigenvalue and to extract a component of the associated eigenvector. Moreover, a propagation formula for electromagnetic fields is derived. This formulation enables rapid computation of field distributions across the expansive semi-infinite and bi-infinite domains, thus highlighting the attributes of edge states. The preliminary MATLAB implementation is available at https://github.com/FAME-GPU/2D_Semi-infinite_PhC.

Local geometric properties of conductive transmission eigenfunctions and applications

Abstract The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$ , $n=2,3$ . Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [26] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [26] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [26] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.

Uniform regularity and vanishing dissipation limit for the 3D magnetic Bénard equations in half space

In this paper, we are concerned with the uniform regularity and zero dissipation limit of solutions to the initial boundary value problem of 3D incompressible magnetic Bénard equations in the half space, where the velocity field satisfies the no-slip boundary conditions, the magnetic field satisfies the perfect conducting boundary conditions, and the temperature satisfies either the zero Neumann or zero Dirichlet boundary condition. With the assumption that the magnetic field is transverse to the boundary, we establish the uniform regularity energy estimates of solutions as both viscosity and magnetic diffusion coefficients go to zero, which means there is no strong boundary layer under the no-slip boundary condition even the energy equation is included. Then the zero dissipation limit of solutions for this problem can be regarded as a direct consequence of these uniform regularity estimates by some compactness arguments.

Investigation of The Effect of Geometrical Parameters And Fluid Properties of Heat Sinks on Cooling By RSM Method

This study investigated the effect of the response surface method (RSM) on heat sinks designed in block types and using various fluids. The RSM method was applied to the data obtained from heat sinks designed in block type placed in both vertical and horizontal directions using water, mono, nanofluids, and hybrid nanofluids. The data were collected under five different pressure boundary conditions and applied to 144 data sets. The Box-Behnken method was used to analyze the design parameters and derive equations for seven different parameters: density, viscosity, specific heat, thermal conductivity, block thickness, block distances, and inlet pressure boundary conditions. The equations were used to determine the average CPU temperature, thermal resistance, and Performance Evaluation Criteria (PEC). The findings show that the R2 values for thermal resistance (Rth), average CPU temperature (Tm), and performance evaluation criteria (PEC) for flat arrangements are 99.21%, 99.21%, and 99.37%, respectively. The R2 values for the vertically designed geometries are 97.66%, 97.66%, and 98.45%, indicating a strong correlation between the results obtained from FLUENT and the ANOVA statistical results. The linear, square, and cubic effects of each variable had a significant impact on each solution. The study concluded that the RSM method has a significant effect on heat sinks with higher R2 values in horizontal arrangements and a higher distance between blocks. Another important result showed that increasing the block thickness also has a significant effect on Rth and Tm, homogenizing the temperature distribution while increasing the cooling capacity.

A new transformerless buck‐boost converter with improved voltage gain and continuous input current

AbstractThis paper proposes a new transformerless buck‐boost converter with an extended voltage conversion ratio. This converter has semi‐quadratic voltage gain, which provides more gain with lower duty cycles. This converter has a simple structure and easy implementation, which reduces the cost and increases efficiency. The proposed converter operates in continuous conduction mode and provides two operation modes by turning on and off the switches. The suggested converter has continuous input current and low input current ripple, which is important when utilizing renewable energy sources. The calculation of the proposed converter includes ideal and practical voltage gain, current calculations, voltage stresses of the switches and diodes, current stress of the switches, parameter design, efficiency, and a brief analysis of discontinuous conduction mode and boundary conditions. The proposed converter provides efficiency of about 93.1% in boost mode and 92.14% in buck mode at 50 W output power. The suggested converter varies the input voltage from 20 to 48 V in boost mode and changes the input voltage from 20 to 10.4 V in buck mode. Finally, a laboratory prototype has been built to prove and evaluate the simulation results and theoretical analysis of the proposed converter.

An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole

The application of analytical methods to solve the problem of an anisotropic semi-infinite plane with a hole has not been observed thus far. This paper presents an analytical solution for an orthotropic semi-infinite plane with an arbitrary-shaped hole, considering the condition of a uniform stress applied at the hole boundary. First, the shapes of holes on the z 1 - and z 2 -planes are determined based on the shape of the hole on the z-plane. Next, the regions outside the holes on these physical planes are mapped to the rings on the ζ 1 - and ζ 2 -planes, respectively. Therefore, the boundary conditions with ζ 1 and ζ 2 as independent variables are established. Then, the boundary collocation method is used to solve the stress boundary conditions along the upper boundary and the hole boundary, thereby obtaining two analytical functions for calculating the stress and displacement of the structure. Finally, the correctness of the proposed method is verified by conducting boundary condition checks and comparing the stress and displacement results obtained by the proposed method with those obtained from ANSYS, and further investigates the influence of anisotropic parameters on normal stress and displacement.

Linear modeling analysis of the heat balance of the transmission line in high frequency critical ice melting state

Abstract The icing of transmission lines can cause many problems such as increased line load, unbalanced tension, and galloping, posing a serious threat to the reliable operation of the power system. Therefore, linear modeling analysis of the heat balance under a high-frequency critical ice melting state of transmission lines is studied. The thermal conduction states of melting, heating, twisting, rotating melting, and ice layer detachment of ice melting conductors are analyzed. Based on the heat conduction process of thermal melting of ice on transmission lines, a simplified calculation formula for thermal melting ice time is derived to calculate times for heating, ice layer torsion, and air gap increase. At the same time, based on the law of conservation of energy, thermodynamic boundary conditions for iced conductors were established and corresponding physical models were constructed. Based on this model, we conduct a linear modeling of the heat balance in the melting state in order to provide a more accurate prediction of temperature distribution. The experimental results show that there is a negative correlation between environmental temperature and critical melting current, and the melting time decreases with the increase of environmental temperature.

Bioconvective flow of Maxwell nanoparticles with variable thermal conductivity and convective boundary conditions

Owing to recent development in the thermal sciences, scientists are focusing towards the wide applications of nanofluids in industrial systems, engineering processes, medical sciences, enhancing the transport sources, energy production etc. In various available studies on nanomaterials, the thermal significance of nanoparticles has been presented in view of constant thermal conductivity and fluid viscosity. However, exponents verify that in many industrial and engineering process, the fluid viscosity and thermal conductivity cannot be treated as a constant. The motivation of current research is to investigates the improved thermal aspects of magnetized Maxwell nanofluid attaining the variable viscosity and thermal conductivity. The nanofluid referred to the suspension of microorganisms to ensure the stability. The insight of heat transfer is predicted under the assumptions of radiated phenomenon. Additionally, the variable thermal conductivity assumptions are encountered to examine the transport phenomenon. Whole investigation is supported with key contribution of convective-Nield boundary conditions. In order to evaluating the numerical computations of problem, a famous shooting technique is utilized. After ensuring the validity of solution, physical assessment of problem is focused. It is claimed that velocity profile boosted due to variable viscosity parameter. A reduction in temperature profile is noted due to thermal relaxation constant.

Regularized factorization method for a perturbed positive compact operator applied to inverse scattering

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are advantageous to use due to the fact that they are computationally simple and require little a priori knowledge of the object one wishes to reconstruct. The main focus of this paper is to prove that the regularization strategy presented here produces stable reconstructions. We will show this is the case analytically and numerically for the inverse shape problem of recovering an isotropic scatterer with a conductive boundary condition. We also provide a strategy for picking the regularization parameter with respect to the noise level. Numerical examples are given for a scatterer in two dimensions.

Effect of Robin boundary conditions on the onset of convective torsional flows in rotating fluid spheres

Torsional flows are preferred at the onset of thermal convection in fluid spheres with stress-free and perfectly conducting boundary conditions, in a narrow region of the parameter space for Prandtl numbers Pr≲0.9 and ratios Pr/Ek=O(10), with Ek being the Ekman number. In this case, the transport of heat to the exterior is supposed instantaneous. When the thermal conductivity of the internal fluid is large, and the external convective heat transfer or radiative emissivity is low, the heat transmission is less efficient, and the thermal energy retained in the interior increases, enhancing the onset of convection. This study is devoted to analyzing the combined influence of the thermal conductivity and external conditions (temperature and resistance to heat transport) on the onset of the torsional convection by taking a Robin boundary condition for the temperature at the surface of the sphere. It is shown, by means of the numerical computation of the curves of simultaneous transitions to torsional flows and Rossby waves, that when the heat flux through the boundary decreases, the region where the axisymmetric flows are preferred shrinks, but it never strangles to an empty set. It has been found that with adequate scalings the curves delimiting the transition to torsional flows, and those of the critical Rayleigh number, Rac, and the frequencies of the modes vs Ek become almost independent of the parameter of the Robin boundary condition.

Lipschitz Continuous Solutions of the Vlasov–Maxwell Systems with a Conductor Boundary Condition

Lipschitz Continuous Solutions of the Vlasov–Maxwell Systems with a Conductor Boundary Condition

The Maxwell system in nonhomogeneous anisotropic waveguides with slowly stabilizing characteristics of the filling medium

In a domain having several cylindrical outlets to infinity, the stationary Maxwell system with perfectly conductive boundary conditions is studied. The dielectric permittivity and magnetic permeability are assumed to be arbitrary positive definite matrix-valued functions that slowly stabilize at infinity. The authors introduce the scattering matrix, establish the unique solvability of the problem with radiation conditions at infinity, and describe the asymptotics of solutions.

Experimental Evaluation of Thermoelectric Generator Performance under Different Heat Conduction Boundary Conditions

Heat conduction boundary conditions play a crucial role in the performance of thermoelectric generators (TEG). The TEG output voltage and power were measured under constant temperature boundary and heat flux conditions to evaluate the TEG performance under different heat conduction boundary conditions. External loading pressure and thermal interface material (TIM) were applied to reduce the interfacial thermal contact resistance. In our measurement setup, a fast-response electronic load was used for the rapid current-voltage scan, which can eliminate the thermal drift caused by the Peltier effect. A guard heater arrangement is used to minimize heat loss. In constant temperature boundary conditions, reducing the thermal contact resistance can increase the effective temperature drop across the TEG module and significantly improve the output voltage and power. But in the constant heat flux conditions, since the heat flux flow through the TEG is unchanged, the temperature drop across the TEG was unaffected by the thermal contact resistance. As a result, the TEG performance was lightly influenced by the thermal contact resistance.

Switchable edge-line coupler based on parity time-reversal duality symmetry

A compact broadband Edge-Line Coupler (ELC) based on Parity Time-reversal Duality (PTD) symmetry has been conceived, designed, constructed and measured. The coupler connects four PTD bifilar edge lines (BELs), recently introduced by the authors. The PTD-BELs are constituted by a parallel plate waveguide whose walls are formed by a junction between Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions. Reversing the axis orthogonal to the plates interchanges the position of PEC and PMC. Such a waveguide supports unimodal transverse electromagnetic (TEM) propagation, extremely confined along the top and bottom junction edges; its propagation is protected against backscattering from any discontinuity that preserves the PTD symmetry. The ELC presented here is constituted by a 4-port junction in which each port is intrinsically matched due to the PTD symmetry, strongly coupled with a second port, strongly decoupled with a third port, and weakly coupled with a fourth port. The ELC is designed by using a mushroom metasurface for the PMC portion of the device; the connection is based on a switch circuit which imposes open and short conditions on the two opposite sides of the structure. Switching simultaneously the open and short circuits reroutes the signal in a different port, while maintaining the same level of coupling with the other ports. A static prototype has been built and its measurements have confirmed the matching performance and the good directionality of the coupler in a broadband frequency range between 24 and 30 GHz.

Angular-spatial upwind element differential method for radiative heat transfer in a concentric spherical participating medium

Radiative intensity with high directional and spatial resolutions can provide abundant useful information for combustion diagnosis systems based on radiative images. In this paper, an angular-spatial upwind element differential method (ASUEDM) is developed to discretize angular direction and spatial domain of radiative transfer equation (RTE) in a spherically participating medium. Because of the strong convection characteristic of radiative transfer equation, an upwind scheme is adopted to suppress the numerical oscillation. Meanwhile, Chebyshev-Gauss-Lobatto nodes are used to minimize the effect of the Runge phenomenon. Unlike conductive or convective boundary conditions, radiative boundary condition is unidirectional boundary condition, and a singularity node exists at the boundary. To deal with this singularity, we propose a discontinuous strategy. Three examples of radiative heat transfer in concentric spheres are chosen to test the capability of ASUEDM. Compared with benchmark solutions, ASUEDM can provide higher accuracy than discrete ordinates method or finite volume method. Besides, ASUEDM can flexibly provide hp convergence rate and achieve high-resolution characterization in angular direction and spatial domain.

Global solutions to an initial boundary problem for the compressible 3D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains

An initial boundary value problem for compressible magnetohydrodynamics (MHD) is considered on an exterior domain (with the vanishing first Betti number) in in this paper. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established. Moreover the explicit decay rate is given. In particular, the results obtained in this paper also imply the global existence of classical solutions for the full compressible Navier–Stokes equations with Navier-slip boundary conditions on exterior domains in three dimensions, which was not available in literature prior to the work in this paper, to the best of knowledge of the authors’.

A novel hybrid method based cubic B-spline for one-dimensional Stefan problem with moving PCM, size-dependent thermal conductivity and periodic boundary condition

A novel hybrid method based cubic B-spline for one-dimensional Stefan problem with moving PCM, size-dependent thermal conductivity and periodic boundary condition

Uniqueness of Inverse Transmission Scattering with a Conductive Boundary Condition by Phaseless Far Field Pattern

Uniqueness of Inverse Transmission Scattering with a Conductive Boundary Condition by Phaseless Far Field Pattern

{mathcal{H}}-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations

The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of {mathcal{H}}-matrices. Under a technical assumption on the mesh, we prove that root exponential convergence in the block rank can be achieved, if the block structure conforms to a standard admissibility criterion.