Different Kinds Of Boundary Conditions Research Articles

Thermal Circuit Models of Microstrip Lines Based on Precise Heat Spreading Angles and Convection Boundary Conditions

In this paper, the equivalent thermal circuits of microstrip lines are proposed based on the equivalent heat spreading angle (ESA) model and convection boundary conditions. Unlike the conventional constant-angle assumption, the ESAs corresponding to the situations of conductor and dielectric losses of microstrip lines are determined precisely by means of the modified parallel-plate model, which are associated with the geometry and material of the microstrip lines. Further, different kinds of boundary conditions are considered in the thermal circuit models, especially the impact of heat convection condition which matters in realistic situations. In addition, the thermal circuit models are extended to the case of coupled microstrip lines. The calculated results of the proposed model agree well with those simulated by the multiphysics solver.

Nonlinear Thermal Analysis of AlGaN/GaN HEMTs With Temperature-Dependent Parameters

In this article, an efficient numerical algorithm is proposed to capture the thermal profile of AlGaN/GaN high electron mobility transistors (HEMTs) with nonlinear electrothermal coupling effects. The finite element method is employed to solve the steady heat conduction equation with different kinds of boundary conditions. To accurately evaluate the temperature distribution of AlGaN/GaN HEMTs, the temperature-dependent properties of both thermal conductivity and heat source are taken into consideration. In order to accelerate the convergence in simulation, the Anderson acceleration (AA) scheme is utilized to solve the nonlinear coupling problems. Numerical examples demonstrate the high accuracy and excellent convergence of the proposed method for nonlinear thermal analysis of AlGaN/GaN HEMTs.

A detailed study of mode II test specimen with elastic or plastic crack tips by using boundary element method

In linear elastic fracture mechanics the stress and strain magnification at the crack tip is characterized by stress intensity factors which have been obtained for a large variety of loading and specimen geometries and of course mode II test specimen included. In this paper not only different kinds of boundary conditions of the contact surfaces of the elastic crack tip will be discussed but the plastic one. The rotation of the center line of the specimen will also be discussed. The results show the powerful application of the BEM model in the specimen.

Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

In this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian Δ(Δu(k-1)p-2Δu(k-1))+a(k)u(k)p-2u(k)=0\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\Delta (\\left| \\Delta u(k-1)\\right| ^{p-2}\\Delta u(k-1))+a(k)\\left| u(k)\\right| ^{p-2}u(k)=0 \\end{aligned}$$\\end{document}with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

Thermal Elastic–Plastic Analysis of Three-Dimensional Structures Using Face-Based Smoothed Point Interpolation Method

In this work, a face-based smoothed point interpolation method (FS-PIM) is formulated for three-dimensional (3D) thermal elastic-plastic analysis of structures. For this method, field functions are approximated using second order PIM shape functions and the face-based smoothing domains are used to perform the numerical integration. The material properties are considered to be temperature-dependent and the plastic behavior is studied through the Von Mises yield function. Numerical examples with different kinds of boundary conditions are investigated to verify the validity of the present method. The obtained results indicate that FS-PIM is an effective technique for the thermal elastic-plastic analysis of structures.

Numerical solution of DPL heat transfer model in multi-layer biological skin tissue of the living body during hyperthermia treatment

The procedure in which a spatial heat source is subjected to tumor position to destroy the tumor cells without affecting the neighboring healthy tissues is known as hyperthermia treatment. During this process, accurate prediction and control of temperature is very important for the successful hyperthermia treatment. In this paper, we considered a mathematical heat transfer model in multi-layer skin tissue in the bounded domain in order to predict the temperature profile at the tumor position during the treatment. A multi-layer skin tissue consisting of three different layers known as epidermis, dermis, subcutaneous layer is presented in the following study. The Dual-phase-lag model of bio-heat transfer in multi-layer skin tissue is combined with Gaussian (Normal) distribution heat source term during the hyperthermia treatment under the general boundary conditions. The finite element scheme of Runge-Kutta (4, 5) has been used to solve the DPL (dual-phase-lag) heat transfer model. Effect of different parameters like water diffusion, water vaporization, blood perfusion, heat source due to metabolism, external heat source term, time lag due to heat flux, time lag due to temperature gradient, and different kind of boundary conditions in multi-layer skin tissue during hyperthermia treatment are discussed in detail and the results are presented graphically. The study concludes with the discussion of a better approach to treat the tumor cells during the hyperthermia treatment in such a way that no harm caused to the neighboring healthy tissues making this study significant for future clinical applications.

An inverse Lax-Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary

In this paper, we reconsider the inverse Lax-Wendroff (ILW) procedure, which is a numerical boundary treatment for solving hyperbolic conservation laws, and propose a new approach to evaluate the values on the ghost points. The ILW procedure was firstly proposed to deal with the “cut cell” problems, when the physical boundary intersects with the Cartesian mesh in an arbitrary fashion. The key idea of the ILW procedure is repeatedly utilizing the partial differential equations (PDEs) and inflow boundary conditions to obtain the normal derivatives of each order on the boundary. A simplified ILW procedure was proposed in [28] and used the ILW procedure for the evaluation of the first order normal derivatives only. The main difference between the simplified ILW procedure and the proposed ILW procedure here is that we define the unknown u and the flux f(u) on the ghost points separately. One advantage of this treatment is that it allows the eigenvalues of the Jacobian f′(u) to be close to zero on the boundary, which may appear in many physical problems. We also propose a new weighted essentially non-oscillatory (WENO) type extrapolation at the outflow boundaries, whose idea comes from the multi-resolution WENO schemes in [32]. The WENO type extrapolation maintains high order accuracy if the solution is smooth near the boundary and it becomes a low order extrapolation automatically if a shock is close to the boundary. This WENO type extrapolation preserves the property of self-similarity, thus it is more preferable in computing the hyperbolic conservation laws. We provide extensive numerical examples to demonstrate that our method is stable, high order accurate and has good performance for various problems with different kinds of boundary conditions including the solid wall boundary condition, when the physical boundary is not aligned with the grids.

Simulation of Wastewater Discharge in a Coastal Plain River Network Considering Different Boundary Conditions

Fu, L.; Wang, J.M., and Peng, Z.H., 2020. Simulation of wastewater discharge in a coastal plain river network considering different boundary conditions. In: Guido Aldana, P.A. and Kantamaneni, K. (eds.), Advances in Water Resources, Coastal Management, and Marine Science Technology. Journal of Coastal Research, Special Issue No. 104, pp. 529–534. Coconut Creek (Florida), ISSN 0749-0208.Owing to a rapidly developing economy and society, coastal cities along the East China Sea face serious water pollution problems. A number of sewer plants were recently constructed to improve the water quality in the region. This study investigated the environmental effects of wastewater discharge from a newly constructed sewer plant as the wastewater passes through a typical coastal plain river network. Ammonia nitrogen (NH3-N) was selected as the typical pollutant, which was monitored and simulated using a two-dimensional model to demonstrate the effects of wastewater discharge. Different kinds of boundary conditions and the effects of tidal bores were represented in the simulation, and the risk of wastewater discharge in the coastal plain river network was also analyzed. An emergency plan is recommended to minimize the risk of wastewater discharge and prevent potential damage to the regional river network environment.

Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method.

In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial basis function network method. Previously, we obtained single-step spinning solutions of the equation using the Galerkin method. First, we verify the numerical solver through an exact solution of a forced version of the equation. Doing so, we compare the numerical results obtained for different space and time steps with the exact solution. Then, we apply the method to solve the NEP equation and reproduce the previously obtained spinning regimes. In the new series of numerical experiments, we find regimes in the form of spinning trains of steps/kinks comprising one, two, or three kinks. The evolution of the distance between the kinks is analyzed. Two different kinds of boundary conditions are considered: homogeneous and periodic. The dependence of the dynamics on the size of the domain is explored showing how larger domains accommodate multiple spinning fronts. We determine the critical domain size (bifurcation size) above which non-trivial settled regimes become possible. The initial condition determines the direction of motion of the kinks but not their sizes and velocities.

Black hole entropy and boundary conditions

It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models.

Efficient Transient Thermal Simulation of ICs and Packages With Laguerre-Based Finite-Element Method

In this article, an efficient approach based on Laguerre-based finite-element method (LBFEM) is proposed for transient thermal simulation of integrated circuits (ICs) and packages. The unconditionally stable marching-on-in-order scheme is developed by the weighted Laguerre polynomials and Galerkin testing procedure. In order to handle complicated ICs and packages, the finite-element method (FEM) is employed for spatial discretization and to obtain the Laguerre coefficients. The treatment of different kinds of boundary conditions is also discussed in detail. The accuracy and efficiency of the proposed method are demonstrated by numerical examples.

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

Abstract The one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

Finite Volume Monte Carlo (FVMC) method for the analysis of conduction heat transfer

The numerical solution of the heat equation is a particularly challenging subject in complex, practical applications such as functionally graded materials for which analytical solution is not available or hardly attainable. The Monte Carlo method is a powerful technique with some advantages compared to the conventional methods and is often used when all else fail. In this paper, we introduce the Finite Volume Monte Carlo (FVMC) method for solving 3D steady-state heat equation where, instead of using the usual finite difference scheme for discretization of the heat equation, the finite volume scheme is used. The FVMC method is tested for three problems to assess the robustness of the method, first one in a simple geometry for validation and evaluation of the predictive performance, the second one in a complex geometry with unstructured mesh and the last one in a problem with a variable heat source and different kinds of boundary conditions. Comparisons were made to the analytical solution in the first test case, whereas for the remaining test cases, the CFD methods were utilized in the absence of the analytical solutions. It was observed that the FVMC temperature distribution agrees perfectly with analytical and CFD solutions in all problems. Despite expecting computational accuracy to improve by increasing total number of particles in the FVMC method, a very good accuracy was obtained for all considered problems after a small number of walks, and the calculated relative root-mean-square errors were below 1%.

A Modified Fourier–Ritz Formulation for Vibration Analysis of Arbitrarily Restrained Rectangular Plate with Cutouts

A modified Fourier–Ritz method is developed for the flexural and in-plane vibration analysis of plates with two rectangular cutouts with arbitrary boundary conditions, aiming to provide a unified solving process for cases that the plate has various locations or sizes of cutout, and different kinds of boundary conditions. Under the current framework, modifying the position of the cutout or the boundary conditions of the plate is just as changing the geometric parameters of the plate, and there is no need to change the solution procedures. The arbitrary boundary conditions can be obtained by setting the stiffness constant of the boundary springs which are fixed uniformly along the edges of the plate at proper values. The strain and kinetic energy functions of a plate with rectangular cutout are derived in detail. The convergence and accuracy of the present method are demonstrated by comparing the present results with those obtained from the FEM software. In this paper, free in-plane and flexural vibration characteristics of the plate with rectangular cutout under general boundary conditions are studied. From the results, it can be found that the geometric parameters and positions of the cutout and the boundary conditions of the plate will obviously influence the natural vibration characteristics of the structures.

Analytical Solutions of a Conduction Problem with Two Different Kinds of Boundary Conditions

Analytical Solutions of a Conduction Problem with Two Different Kinds of Boundary Conditions

Vibration analysis of a complex fluid-conveying piping system with general boundary conditions using the receptance method

In this paper, a new set of six-variable linear partial differential equations of motion of fluid-conveying pipes with general boundary conditions are derived using the Hamilton principle and these equations are solved by the receptance method. The frequencies of the straight pipes conveying fluid with or without elastic supports are determined and the results are compared with experimental ones. Then a fluid-conveying, semi-circular pipe and complex piping system with different kinds of boundary conditions are studied. These pipes are divided into some straight pipe units and are assembled using the receptance method. The numerical results show that the receptance method is efficient for pipes with arbitrary geometrical layouts and support types, and once the dynamic receptance of the elastic support of a piping system is obtained via experiment, its dynamic stability at different fluid velocities can be analysed by the receptance method.

A Type of Brézis–Oswald Problem to the $${\Phi}$$ Φ - Laplacian Operator with Very Singular Term

In this work we consider existence and uniqueness of solutions for a quasilinear elliptic problem, which may be singular at the origin. Furthermore, we consider a comparison principle for subsolutions and supersolutions just in $${W^{1, \Phi}_{loc} (\Omega)}$$ to the problem $$\left\{\begin{array}{ll}-\Delta_{\Phi}u=f(x,u)\, {\rm in}\, \Omega,\\u > 0\, {\rm in} \, \Omega, u = 0 \,{\rm on}\, \partial\Omega,\end{array}\right.$$ where f has $${\Phi}$$ -sublinear growth. In our main results the function f(x, u) may be singular at u = 0 and the nonlinear term $${f(x, t)/t^{\ell-1}, t > 0}$$ is strictly decreasing for a suitable $${\ell > 1}$$ . Under different kind of boundary conditions we prove an improvement for the classical Brezis-Oswald and Diaz-Saa’s results in Orlicz- Sobolev framework for singular nonlinearities as well. Some results discussed here are news even for Laplacian or p-Laplacian operators.

Transient thermal radiation heat transfer in a reinforced plastic coating with anisotropic optical properties

Advanced fiber reinforced plastics, such as carbon fiber reinforced polymers (FRP), offer many advantages over more traditional materials such as metals. Their characteristics make them ideal for use in many sensitive applications. To maximize the use of these materials, there is a need to gain a better understanding of heat and temperature distribution in these materials under different boundary conditions. In this study transient radiative and conductive heat transfer in a FRP medium with anisotropic optical properties is investigated. The solution includes the radiative transfer equation (RTE) within the material coupled to a transient energy equation that contains both radiative and conductive terms. Two different kinds of boundary conditions are treated: when the temperatures imposed on the boundaries vary with time and when the medium is subject to a radiation source which varies with time. It is shown that radiative heat transfer has significant effect on heat transfer and temperature distribution within the layer.

Finite element analysis of vibrating micro-beams and -plates using a three-dimensional micropolar element

The micropolar theory (MPT), through taking the rotational degrees of freedom of material particles into account, is a suitable elasticity theory for the mechanical analysis of microstructures. In this article, the vibration behavior of microscale beams and plates is studied based on MPT. To this end, first, a three-dimensional (3D) formulation is developed for the micropolar continua which can be readily used in the finite element analyses. Then, a non-classical 3D element is introduced to investigate the free vibration characteristics of micropolar beams and plates. The microstructure effect on the frequencies of microbeams and microplates under different kinds of boundary conditions is illustrated. Also, the results of MPT are compared with those of classical theory and it is indicated that there is a considerable difference between their predictions at small scales.

Semi-analytical mechanical and thermal buckling analyses of 2D-FGM circular plates based on the FSDT

ABSTRACTIn the present paper, mechanical and thermal buckling analyses of two-directional functionally graded material (2D-FGM) circular plate are investigated. The motion equations have been derived based on the first-order shear deformation theory (FSDT) and power series method has been employed to solve the motion equations. Two different kinds of boundary condition including simply supported and fixed are considered. The material properties are assumed to vary in both transverse and radial directions according to power and exponential laws, respectively. Comparisons with available studies in the literature confirm the high accuracy of the current approach. The effects of geometrical parameters and 2D-FG power indices on the critical buckling load have been studied. It is shown that increase of modulus of elasticity of outer layers of plate due to higher presence of hard phase of FGM, in radius and thickness directions of the plate makes it possible to attain a more solid structure against mechanical buckling loads, while increase of coefficient of thermal expansion and coefficient of thermal conduction of outer layers of plate results in less stability against thermal buckling loads.