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The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

The selection of sensitive temperature measurement points is the premise of thermal error modeling and compensation. However, most of the sensitive temperature measurement point selection methods do not consider the influence of the variability of thermal sensitive points on thermal error modeling and compensation. This paper considers the variability of thermal sensitive points, and aims to propose a sensitive temperature measurement point selection method and thermal error modeling method that can reduce the influence of thermal sensitive point variability.

Taking the truss robot as the experimental object, the finite element method is used to construct the simulation model of the truss robot, and the temperature measurement point layout scheme is designed based on the simulation model to collect the temperature and thermal error data. After the clustering of the temperature measurement point data is completed, the improved attention mechanism is used to extract the temperature data of the key time steps of the temperature measurement points in each category for thermal error modeling.

By comparing with the thermal error modeling method of the conventional fixed sensitive temperature measurement points, it is proved that the method proposed in this paper is more flexible in the processing of sensitive temperature measurement points and more stable in prediction accuracy.

The Grey Attention-Long Short Term Memory (GA-LSTM) thermal error prediction model proposed in this paper can reduce the influence of the variability of thermal sensitive points on the accuracy of thermal error modeling in long-term processing, and improve the accuracy of thermal error prediction model, which has certain application value. It has guiding significance for thermal error compensation prediction.

Information technology (IT) systems are already ubiquitous, and their future growth is expected to drive the global economy for the next several decades. However, energy consumption by these systems is growing rapidly, and their sustained growth requires curbing the energy consumption, and the associated heat removal requirements. Currently, 20-50 percent of the incoming electrical power is used to meet the cooling demands of IT facilities. Careful co-optimization of electrical power and thermal management is essential for reducing energy consumption requirements of IT equipment. Such modeling based co-optimization is complicated by the presence of several decades of spatial and temporal scales. The purpose of this paper is to review recent approaches for handling these challenges.

In this paper, the authors illustrate the challenges and possible modeling approaches by considering three examples. The multi-scale modeling of chip level transient heating using a combination of Progressive Zoom-in, and proper orthogonal decomposition (POD) is an effective approach for chip level electrical/thermal co-design for mitigation of reliability concerns, such as Joule heating driven electromigration. In the second example, the authors will illustrate the optimal microfluidic thermal management of hot spots, and large background heat fluxes associated with future high-performance microprocessors. In the third example, data center facility level energy usage reduction through a transient measurements based POD modeling framework will be illustrated.

Through modeling based electrical/thermal co-design, dramatic savings in energy usage for cooling are possible.

The multi-scale nature of the thermal modeling of IT systems is an important challenge. This paper reviews some of the approaches employed to meet this challenge.

The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process.

In this study, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples.

The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error.

This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermal camera data from large parts.

The DED process is particularly valuable for near-net shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation.

This paper presents a new mesh-free computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.

Reinforced concrete structural frames with masonry infills (infill-frames) are commonly used for construction worldwide. While the behavior of such frames has been studied extensively in the context of earthquake loading, studies related to their fire performance are limited. Therefore, this study aims to characterize the behavior of infill-frames under fire exposure by presenting a state-of-the-art literature review of the same.

Both experimental and computational studies have been included with a special emphasis on numerical modeling (simplified as well as advanced). The cold behavior of the infill-frame and its design requirements in case of fire exposure are first reviewed to set the context. Subsequently, the applicability of numerical modeling strategies developed for modeling cold infill-frames to simulate their behavior under fire is critically examined.

The major hurdles in developing generic numerical models for analyzing thermo-mechanical behavior of infill-frames are identified as: lack of temperature-dependent material properties, scarcity of experimental studies for validation and idealizations in coupling between thermal and structural analysis.

This study presents one of the most popular research problems connected with practical and reliable utilization of numerical models, as a good alternative to expensive traditional furnace testing, in assessing fire resistance of infill-frames. It highlights major challenges in thermo-mechanical modeling of infill-frames and critically reviews the available approaches for modeling infill-frames subjected to fire.

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

The functionality of personal mobile electronics continues to increase, in turn driving the demand for higher logic-to-memory bandwidth. However, the number of inputs/outputs supported by the current packaging technology is limited by the smallest achievable electrical line spacing, and the associated noise performance. Also, a growing trend in mobile systems is for the memory chips to be stacked to address the growing demand for memory bandwidth, which in turn gives rise to heat removal challenges. The glass interposer substrate is a promising packaging technology to address these emerging demands, because of its many advantages over the traditional organic substrate technology. However, glass has a fundamental limitation, namely low thermal conductivity (∼1 W/m K). The purpose of this paper is to quantify the thermal performance of glass interposer-based electronic packages by solving a multi-scale heat transfer problem for an interposer structure. Also, this paper studies the possible improvement in thermal performance by integrating a fluidic heat spreader or vapor chamber within the interposer.

This paper illustrates the multi-scale modeling approach applied for different components of the interposer, including Through Package Vias (TPVs) and copper traces. For geometrically intricate and repeating structures, such as interconnects and TPVs, the unit cell effective thermal conductivity approach was used. For non-repeating patterns, such as copper traces in redistribution layer, CAD drawing-based thermal resistance network analysis was used. At the end, the thermal performance of vapor chamber integrated within a glass interposer was estimated by using an enhanced effective thermal conductivity, calculated from the published thermal resistance data, in conjunction with the analytical expression for thermal resistance for a given geometry of the vapor chamber.

The limitations arising from the low thermal conductivity of glass can be addressed by using copper structures and vapor chamber technology.

A few reports can be found on thermal performance of glass interposers. However thermal characteristics of glass interposer with advanced cooling technology have not been reported.

Latest Computational Fluid Dynamics (CFDs) tools allow modeling more finely the conjugate thermo-fluidic behavior of a single electronic component mounted on a Printed Wiring Board (PWB). A realistic three-dimensional representation of a large set of electric copper traces of its composite structure is henceforth achievable. The purpose of this study is to confront the predictions of the fully detailed numerical model of an electronic board to a set of experiment results to assess their relevance.

The present study focuses on the case of a Ball Grid Array (BGA) package of 208 solder balls that connect the component electronic chip to the Printed Wiring Board. Its complete geometrical definition has to be coupled with a realistic board layers layout and a fine description of their numerous copper traces to appropriately predict the way the heat is spread throughout that multi-layer composite structure. The numerical model computations were conducted on four CFD software then compare to experiment results. The component thermal metrics for single-chip packages are based on the standard promoted by the Joint Electron Device Engineering Council (JEDEC), named JESD-51. The agreement of the numerical predictions and measurements has been done for free and forced convection.

The present work shows that the numerical model error is lower than 2 per cent for various convective boundary conditions. Moreover, the establishment of realistic numerical models of electronic components permits to properly apprehend multi-physics design issues, such as joule heating effect in copper traces. Moreover, the practical modeling assumptions, such as effective thermal conductivity calculation, used since decades, for characterizing the thermal performances of an electronic component were tested and appeared to be tricky. A new approach based on an effective thermal conductivity matrix is investigated to reduce computation time. The obtained numerical results highlight a good agreement with experimental data.

The study highlights that the board three-dimensional modeling is mandatory to properly match the set of experiment results. The conventional approach based on a single homogenous layer using effective thermal conductivity calculation has to be banned.

The thermal design of complex electronic components is henceforth under increasing control. For instance, the impact of gold wire-bonds can now be investigated. The three-dimensional geometry of sophisticated packages, such as in BGA family, can be imported with all its internal details as well as those of its associated test board to build a realistic numerical model. The establishment of behavioral models such as DELPHI Compact Thermal Models can be performed on a consistent three-dimensional representation with the aim to minimize computation time.

The study highlights that multi-layer copper trace plane discretization could be used to strongly reduce computation time while conserving a high accuracy level.

Additive manufacturing (AM) is revolutionizing the manufacturing industry due to several advantages and capabilities, including use of rapid prototyping, fabrication of complex geometries, reduction of product development cycles and minimization of material waste. As metal AM becomes increasingly popular for aerospace and defense original equipment manufacturers (OEMs), a major barrier that remains is rapid qualification of components. Several potential defects (such as porosity, residual stress and microstructural inhomogeneity) occur during layer-by-layer processing. Current methods to qualify AM parts heavily rely on experimental testing, which is economically inefficient and technically insufficient to comprehensively evaluate components. Approaches for high fidelity qualification of AM parts are necessary.

This review summarizes the existing powder-based fusion computational models and their feasibility in AM processes through discrete aspects, including process and microstructure modeling.

Current progresses and challenges in high fidelity modeling of AM processes are presented.

Potential opportunities are discussed toward high-level assurance of AM component quality through a comprehensive computational tool.

An experimental and numerical study of thermal profiles of 316 L stainless steel during selective laser melting (SLM) was developed. This study aims to present a novel approach to determine the significance and contribution of thermal numerical modeling enhancement factors of SLM.

Surface and volumetric heat models were proposed to compare the laser interaction with the powder bed and substrate, considering the powder size, absorptance and propagation of the laser energy through the effective depth of the metal layer. The approach consists in evaluating the contribution of the thermal conductivity anisotropic enhancement factors to establish the factors that minimized the error of the predicted results vs the experimental data.

The level of confidence of the carried-out analysis is of 97.8% for the width of the melt pool and of 99.8% for the depth of the melt pool. The enhancement factors of the y and z spatial coordinates influence the most in the predicted melt pool geometry.

Nevertheless, the methodology presented in this study is not limited to 316 L stainless steel and can be applied to any metallic material used for SLM processes.

This study is focused on 316 L stainless steel, which is commonly used in SLM and is considered a durable material for high-temperature, high-corrosion and high-stress situations.

The additive manufacturing (AM) technology is a relatively new technology becoming global. The AM technology may have health benefits when compared to the conventional industrial processes, as the workers avoid extended periods of exposure present in conventional manufacturing.

This study presents a novel approach to determine the significance and contribution of thermal numerical modeling enhancement factors of SLM. It was found that the volumetric heat model and anisotropic enhancement thermal approaches used in the present research, had a good agreement with experimental results.