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Thermal solidification processes are an important concern in today’s manufacturing technology. Because of the complex geometric nature of real‐world problems, analytical techniques with closed‐form solutions are scarce and/or not feasible. As a consequence, various numerical techniques have been employed for the numerical simulations. Of interest in the present paper are thermal solidification problems involving single or multiple arbitary phases. In order to effectively handle such problems, the finite element method is employed in conjunction with adaptive time stepping approaches to accurately and effectively track the various phase fronts and describe the physics of phase front interactions and thermal behaviour. In conjunction with the enthalpy method which is employed to handle the latent heat release, a fixed‐grid finite element technique and an automatic time stepping approach which uses the norm of the temperature distribution differences between adjacent time step levels to control the error are employed with the scale of the norm being automatically selected. Several numerical examples, including single and multiple phase change problems, are described.

The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.

The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which ensures an oscillation‐free solution.

The proposed “diffusion‐split” method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well as an industrial application, for which a well‐behaved numerical solution is available.

The proposed method should be helpful for computational engineers and software developers in the field of heat transfer analysis. It can be implemented in most existing finite element codes with minimal effort.

Although most physical problems in fluid mechanics and heat transfer are governed by nonlinear differential equations, it is less common to be confronted with a “so – called” implicit differential equation, i.e. a differential equation where the highest order derivative cannot be isolated. The purpose of this paper is to derive and analyze an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach.

Here we discuss an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach. Due to the implicit nature of this problem, standard integration schemes, e.g. Runge‐Kutta, are not conveniently applied to this problem. Moreover, numerical solutions do not provide the insight afforded by an analytical solution.

A predictor predictor‐corrector scheme with secant iteration is presented which readily integrates differential equations where the derivative cannot be explicitly obtained. These solutions are compared to numerical integration of the equations and show good agreement.

The paper emphasizes that although large‐scale, multi‐dimensional time‐dependent heat transfer simulation tools are routinely available, there are instances where unsteady, engineering models such as the one discussed here are both adequate and appropriate.

This paper numerically investigates the effect of cavity radiation on the thermal response of hollow aluminium tubes and facade systems subjected to fire.

Finite element simulations were performed using ABAQUS 6.14. The accuracy of the numerical model was established through experimental and numerical results available in the literature. The proposed numerical model was utilised to study the effect of cavity radiation on the thermal response of aluminium hollow tubes and facade system. Different scenarios were considered to assess the applicability of the commonly used lumped capacitance heat transfer model.

The effects of cavity radiation were found to be significant for non-uniform fire exposure conditions. The maximum temperature of a hollow aluminium tube with 1-sided fire exposure was found to be 86% greater when cavity radiation was considered. Further, the time to attain critical temperature under non-uniform fire exposure, as calculated from the conventional lumped heat capacity heat transfer model, was non-conservative when compared to that predicted by the proposed simulation approach considering cavity radiation. A metal temperature of 550 °C was attained about 18 min earlier than what was calculated by the lumped heat capacitance model.

The present study will serve as a basis for the study of the effects of cavity radiation on the thermo-mechanical response of aluminium hollow tubes and facade systems. Such thermo-mechanical analyses will enable the study of the effects of cavity radiation on the failure mechanisms of facade systems.

Cavity radiation was found to significantly affect the thermal response of hollow aluminium tubes and façade systems. In design processes, it is essential to consider the potential consequences of non-uniform heating situations, as they can have a significant impact on the temperature of structures. It was also shown that the use of lumped heat capacity heat transfer model in cases of non-uniform fire exposure is unsuitable for the thermal analysis of such systems.

This is the first detailed investigation of the effects of cavity radiation on the thermal response of aluminium tubes and façade systems for different fire exposure conditions.

The homographic approximation, in which the Heaviside step function is replaced by a continuous smooth curve, is applied to the enthalpy method for heat transfer problems with isothermal phase change. Both the finite difference and finite element implementations, based on the basic enthalpy, the apparent heat capacity and the source term formulations, are considered. A 1‐D Stefan problem of melting a solid is used as a test problem. The accuracy of the numerical solutions is measured globally using L2 error norms and comparison is made between the solutions using homographic approximation and those using linear approximation. The advantages of using homographic approximation are examined.

The purpose of this paper is to explore the functioning of very‐large‐scale integration (VLSI) interconnects and modeling of interconnects and evaluate different approaches of testing interconnects.

In the past, on‐chip interconnect wires were not considered in circuit analysis except in high precision analysis. Wiring‐up of on‐chip devices takes place through various conductors produced during fabrication process. The shrinking size of metal‐oxide semiconductor field effect transistor devices is largely responsible for growth of VLSI circuits. With deep sub‐micron (DSM) technology, the interconnect geometry is scaled down for high wiring density. The complex geometry of interconnects and high operational frequency introduce wire parasitics and inter‐wire parasitics. These parasitics causes delay, power dissipation, and crosstalk that may affect the signal integrity in VLSI system. Accurate analysis, sophisticated design, and effective test methods are the requirement to ensure the proper functionality and reliability of VLSI circuits. The testing of interconnect is becoming important and a challenge in the current technology.

The effects of interconnect on signal integrity, power dissipation, and delay emerges significantly in DSM technology. For proper performance of the circuit, testing of interconnect is important and emerging challenge in the nanotechnology era. Although some work has been done for testing of interconnect, however, it is still an open area to test the parasitics effects of VLSI/ultra‐large‐scale integration interconnects. Efforts are required to analyze and to develop test methods for crosstalk, delay and power dissipation in current technology with solutions to minimize this effect.

This paper reviews the functioning of VLSI interconnects from micrometer to nanometer technology. The development of various interconnect models from simple short circuit to latest resistance inductance capacitance transmission line model are discussed. Furthermore, various methodologies such as built‐in self test and other techniques for testing interconnect for crosstalk and delay are discussed.

This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique.

The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable.

The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena.

Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

The purpose of this paper is to gain a better understanding on how metasurfaces behave, in terms of currents in each unit cell. A better knowledge of their behavior could lead to an ad-hoc design for specific applications.

The methodology used is both theoretical and numerical; it is based on circuit theory and on an optimization procedure.

The results show that when the knowledge of the current in each unit cell of a metasurface is needed, the most common approximations currently used are often not accurate. Furthermore, a procedure for the termination of a metasurface, with application-driven goals, is given.

This paper investigates the distribution of the currents in a 2D metamaterial realized with magnetically coupled resonant coils. Different models for the analysis of these structures are illustrated, and the effects of the approximations they introduce on the current values are shown and discussed. Furthermore, proper terminations of the resonators on the boundaries have been investigated by implementing a numerical optimization procedure with the purpose of achieving a uniform distribution of the resonator currents. The results show that the behavior of a metasurface (in terms of currents in each single resonator) depends on different properties; as a consequence, their design is not a trivial task and is dependent on the specific applications they are designed for. A design strategy, with lumped impedance termination, is here proposed.

The purpose of this paper is to develop a modeling method for the analysis of low-frequency metamaterials (MTMs) and their near-field applications.

The Euler–Lagrange method is introduced. An MTM is modeled as a multi-degree-of-freedom system without homogenization. The properties and the responses of the MTM in a near-field device are readily and rigorously studied through the motion equation derived from the Lagrange equations. The resonance frequencies and the corresponding resonance modes are solved from the characteristic equation.

The numerical results of the proposed method show good agreement with the experimental ones. A measurement of MTM-core coil resistance and inductance shows high accuracy of the proposed method.

The proposed Euler–Lagrange method provides a new study perspective and enables more flexible, rigorous and straightforward analysis of low-frequency MTMs in near-field applications. Consequently, the presented work greatly facilitates further explorations and studies on various novel MTM-based low-frequency near-field devices and systems.

Intumescent coatings are nowadays a dominant passive system used to protect structural materials in case of fire. Due to their reactive swelling behaviour, intumescent coatings are particularly complex materials to be modelled and predicted, which can be extremely useful especially for performance-based fire safety designs. In addition, many parameters influence their performance, and this challenges the definition and quantification of their material properties. Several approaches and models of various complexities are proposed in the literature, and they are reviewed and analysed in a critical literature review.

Analytical, finite-difference and finite-element methods for modelling intumescent coatings are compared, followed by the definition and quantification of the main physical, thermal, and optical properties of intumescent coatings: swelled thickness, thermal conductivity and resistance, density, specific heat capacity, and emissivity/absorptivity.

The study highlights the scarce consideration of key influencing factors on the material properties, and the tendency to simplify the problem into effective thermo-physical properties, such as effective thermal conductivity. As a conclusion, the literature review underlines the lack of homogenisation of modelling approaches and material properties, as well as the need for a universal modelling method that can generally simulate the performance of intumescent coatings, combine the large amount of published experimental data, and reliably produce fire-safe performance-based designs.

Due to their limited applicability, high complexity and little comparability, the presented literature review does not focus on analysing and comparing different multi-component models, constituted of many model-specific input parameters. On the contrary, the presented literature review compares various approaches, models and thermo-physical properties which primarily focusses on solving the heat transfer problem through swelling intumescent systems.

The presented literature review analyses and discusses the various modelling approaches to describe and predict the behaviour of swelling intumescent coatings as fire protection for structural materials. Due to the vast variety of available commercial products and potential testing conditions, these data are rarely compared and combined to achieve an overall understanding on the response of intumescent coatings as fire protection measure. The study highlights the lack of information and homogenisation of various modelling approaches, and it underlines the research needs about several aspects related to the intumescent coating behaviour modelling, also providing some useful suggestions for future studies.