CAREER: Precise Mathematical Modeling and Experimental Validation of Radiation Heat Transfer in Complex Porous Media Using Analytical Renewal Theory Abstraction-Regressions

复杂介质中的辐射传热建模提出了一个重大而繁重的挑战，特别是当现有的计算解决方案没有充分发展到与现实世界应用的日益增长、多样性和复杂性相匹配时。在对热过程的精确控制和理解至关重要的领域，如先进材料工程、节能建筑设计和高性能计算系统，这一挑战尤为明显。通过开发先进的数学和计算模型，该项目旨在显著提高辐射传热估算的准确性、速度和适用性，超越现有方法的能力。这些模型的核心是在多孔介质辐射传输的数学推导中使用更新、破坏和剩余风险理论的新方法。这一努力的广泛影响延伸到它在革命性的多尺度能量传输量化和管理方面的潜力，影响从可再生能源到生物医学工程和气候学的各种应用。该项目的社会贡献不仅仅是推进科学知识，还包括开发更高效和可持续的能源技术。该项目的教育目标包括培养K-12学生的科学技术工程和数学参与，与总体研究目标无缝整合。本CAREER项目的技术目标是建立一种新的分析双抽象回归框架，用于表征和求解异质介质中的宏观辐射量。该方法将具有点向辐射特征张量的宏观配置抽象模型与基于更新/破产理论和Powers-Gerber-Shiu风险剩余理论的解析回归模型相结合。这些模型旨在精确地估计均匀微张量的辐射宏观性质，填补了该领域的关键知识空白。该项目包括三个主要研究目标：(i)理解风险剩余理论与辐射传热特性之间的联系；（ii）为精确的辐射估计开发双重抽象回归模型；（iii）通过实验验证评估框架的有效性。这个项目的知识意义在于它有可能改变辐射传热在复杂介质中的建模方式，特别是在目前方法不足的多孔结构中。更广泛的影响是深远的，包括增强太阳能系统，改善电子设备的热管理，并有助于开发具有优化热性能的新材料。这项研究有望在辐射传热的基础认识方面取得重大进展，推动辐射科学理论和应用方面的创新。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modeling radiation heat transfer in complex media presents a significant and burdensome challenge, particularly as the existing computational solutions have not adequately evolved to match the increasing growth, diversity, and complexity of real-world applications. This challenge is especially pronounced in fields where precise control and understanding of thermal processes are pivotal, such as in advanced materials engineering, energy-efficient building design, and high-performance computing systems. By developing advanced mathematical and computational models, this project aims to significantly improve the accuracy, speed, and applicability of radiation heat transfer estimations beyond the capabilities of existing methods. At the heart of these models is the novel use of Renewal, Ruin, and surplus risk theory in the mathematical derivations of radiative transfer in porous media. The broader impact of this endeavor extends to its potential in revolutionizing multi-scale energy transport quantification and management, influencing various applications from renewable energy to biomedical engineering and climatology. The societal contributions of the project extend beyond advancing scientific knowledge, encompassing the development of more efficient and sustainable energy technologies. The educational objectives of the project include fostering Science Technology Engineering and Mathematics engagement among K-12 students, seamlessly integrating with the overarching research goals.The technical objective of this CAREER project is to establish a novel analytical dual abstraction-regression framework for characterizing and solving macro radiative quantities in heterogeneous media. This approach combines abstraction models representing macro-configurations with point-wise radiative feature tensors with analytical regression models based on Renewal/Ruin and Powers-Gerber-Shiu risk surplus theories. These models are designed to precisely estimate radiative macro properties from homogenized micro tensors, filling a critical knowledge gap in the field. The project encompasses three main research objectives: (i) understanding the connections between risk surplus theory and radiation heat transfer characterization, (ii) developing dual abstraction-regression models for precise radiative estimations, and (iii) evaluating the framework's effectiveness through experimental validation. The intellectual significance of this project is rooted in its potential to transform the way radiation heat transfer is modeled in complex media, especially in porous structures where current methodologies fall short. The broader impact is far-reaching, with implications for enhancing solar energy systems, improving thermal management in electronic devices, and contributing to the development of new materials with optimized thermal properties. This research is expected to yield significant advancements in the fundamental understanding of radiation heat transfer, driving innovation in both theoretical and applied aspects of the science of radiation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.