Multi-scale Thermal Modeling Research Articles

Graph neural network-based multiscale thermal modeling for heterogeneous materials with complex structures

This study presents a novel GNN-based model for multiscale thermal characterization of heterogeneous materials with complex microstructures. It incorporates relationships between composition, structure, and thermal transport across multiple scales, leveraging the structure of GNNs. Results demonstrate enhanced performance of the GNN-based model compared with existing methods. Specifically, the GNN model improved thermal conductivity prediction with a mean absolute error of 0.18 W/mK (15 % improvement over the Bayesian neural network-based model) and provided a 30x speedup in computation time. The model successfully connected atomic-scale interactions to macroscale properties, achieving less than 5 % error in predicting effective thermal conductivity from one scale to another. Furthermore, it demonstrated the ability to capture nonlinear thermal transport phenomena with 92 % accuracy. The model also improved the prediction of the transient thermal responses by 20 %, accurately capturing the time-varying behaviour of materials. This work also proved the model’s ability to handle new material systems with transfer learning, achieving 88 % accuracy. Finally, Bayesian neural networks integrated into the model provided uncertainty quantification, with 95 % of experimental measurements falling within the predicted bounds. This work demonstrated the ability of the framework to handle complex microstructures, nonlinear phenomena, and transient responses while maintaining a computationally efficient model that can enable real-time applications in design and optimization needed in modern materials innovation. It represents a powerful tool for data-driven multiscale mechanics that could accelerate materials research and development for the aerospace, electronics cooling, and additive manufacturing industries.

Multi-scale thermal modeling, experimental validation, and thermal characterization of a high-power lithium-ion cell for automobile application

Detailed thermal analysis of individual cell types used to power electric propulsion systems is rarely performed. Nano structured lithium-iron-phosphate or LFP cathodes show great promise in automobile application due to stable discharge profile and excellent safety features. This study is aimed at thermal characterization of a commercially favored lithium-ion cell under variable loads and operating conditions. An innovative reduced order electrochemical-thermal coupled model is developed using multi-scale multi-domain (MSMD) approach. A pseudo 2D (1D + 1D) electrochemical heat generation model is dynamically coupled to a 3D heat transport model. 3D cell domain is discretized using finite element (FE) mesh. Six representative discretization elements are selected for coupling. Electrochemical model is solved using a C-based code for each of the six elements. Model is validated using experimentally measured data and found to be in good agreement. Reduced order coupled model adequately captures temporal as well as spatial variations in cell temperature with sufficiently moderate computational expense. Simulation results show that lower operating temperatures and higher applied currents erode cell capacity. Optimum operating temperature window for the selected cell is found between 10 °C and 50 °C.

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

Multi-scale thermal modeling of glass interposer for mobile electronics application

Purpose – 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. Design/methodology/approach – 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. Findings – The limitations arising from the low thermal conductivity of glass can be addressed by using copper structures and vapor chamber technology. Originality/value – 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.

Numerical Study on Some Improvements in the Passive Cooling System of a Radio Base Station Base on Multiscale Thermal Modeling Methodology–Part I: Confirmation of Simplified Models

Passive cooling schemes, such as natural convection, are the most reliable heat dissipation apprpaches for electronic equipment. Some times, the highest temperature of the printed circuit board (PCB), rather than the highest of chips, is very much concern because of some technological reasons. In order to reduce the maximum PCB temperature, this article analyze the PCB temperature distribution by multiscale simulation. A top-to-down approach is adopted in order to reveal the details of temperature distribution of some interested local position. In the top-to-down approach, the system level simulation by a not-too-fine grid system is the key to obtain a reliable solution. In order to reach such a goal each component of the PCB should be reasonably simplified. The thermal analysis method is proposed to simplify the components, and the implementation details are provided for three types of components. In the companion article, the settlement of boundary conditions from the data of system level simulation and several improvements in heat transfer by numerical simulation will be presented.

Numerical Study on Some Improvements in the Passive Cooling System of a Radio Base Station Base on Multiscale Thermal Modeling Methodology—Part II—Results of Multiscale Numerical Simulation and Subsequent Improvements of Cooling Techniques

In the companion article (Part I), simplified compact model of components in a system level model was established based on heat transfer path and thermal resistance network analysis. In this article, component level simulation and lead level simulation was conducted by assiging the boundary conditions from the data of the higher level simulation, and effects of different boundary conditions on numerical accuracy and stability are studied. Comparison shows that multiscale thermal modeling methodology can save 87% of the total computation time compared with full simulation with a fine grid system, and can greatly improve the resolution of the calculation result. Mainly based on the multiscale simulation five improvements for the reduction of the maximum PCB temperature are proposed. This article also provides an example that by a careful numerical thermal design, a passive cooling mode can sometimes meet the cooling requirement of a PCB with high power input in some extent.

A multiscale thermal modeling approach for ballistic and diffusive heat transport in two dimensional domains

The modeling of heat transport for small length scales requires accounting for the physics of heat carrier transport such as the propagation, scattering, and relaxation of phonons. However, the models used to describe such phenomena are often too computationally expensive to model large domains where relevant system boundaries are far removed from the region where ballistic-diffusive phonon transport is dominant. To address the response of such systems to its far field thermal boundary conditions, a multiscale thermal model is needed to efficiently account for transport phenomena in each domain. In this work, a multiscale thermal modeling approach is presented where the transport of phonons is treated with a Finite Volume Discrete Ordinates Model (FVDOM) solution to the phonon Boltzmann Transport Equation (BTE) which is embedded in a region treated by diffusive thermal transport. The approach shows that it is possible to create a coupled multiscale model where the boundary conditions of the FVDOM model are derived from the diffusive transport model. The limitations of the method and the key parameters for accurate modeling are investigated and discussed. The final model is used to explore the impact of the size of heat generation regions with respect to the overall domain size on the peak temperature. The results show that by using such a model it is possible to capture the ballistic-diffusive transport in pertinent areas of a domain that is mostly dominated by diffusive transport.

Multiscale thermal device modeling using diffusion in the Boltzmann Transport Equation

Thermal modeling of some nano-scale devices requires attention to multiple length scales and physical phenomena, ranging from continuum level heat diffusion to atomic-scale interactions and phonon confinement. At the nanometer-scale, thermal phenomena such as ballistic phonon transport may be important. The present paper uses a multiscale thermal modeling approach including diffusion in the Boltzmann Transport Equation (BTE) to study heat transport in several applications like Silicon on Insulator transistors, Si thin films with heat pulse, a Si thin film sandwiched between two bulk layers of Silicon dioxide as in solar cells. Analytical solutions of both a multilayered Fourier model and a simple gray BTE with and without a diffusion term in the steady state are computed. Thermal modeling and analysis of some of these applications is performed using the COMSOL Multiphysics finite element software package. The BTE model with and without diffusion for multilayers is discussed for interface conditions involving reflectance and transmittance of phonons. The results obtained from the models are compared to existing published results for Si/Si, Si/Diamond layers and are found to be in good agreement.

Multiscale Thermal Modeling Methodology for Thermoelectrically Cooled Electronic Cabinets

A multiscale thermal modeling methodology is reported for multienclosure electronic cabinets incorporating thermoelectric cooling. A multilayer compact model for a thermoelectric module is used in combination with a reduced-order fluid flow model for a single enclosure, constructed using proper orthogonal decomposition with a flux-matching technique. A reduction by an order of magnitude of 105 in the degrees of freedom of the system, with an accuracy better than 92%, is achieved. An entire cabinet consisting of multiple enclosures is modeled by combining the compact subsystem models, with an estimation error of less than 10%.