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

模拟复杂介质中的辐射换热是一项重大而繁重的挑战，特别是在现有的计算解决方案尚未充分发展以适应现实世界应用的日益增长、多样性和复杂性的情况下。这一挑战在对热过程的精确控制和了解至关重要的领域尤其明显，例如在先进材料工程、节能建筑设计和高性能计算系统中。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热传递估计的准确性、速度和适用性，超出现有方法的能力。这些模型的核心是更新、破产和盈余风险理论在多孔介质中辐射传递的数学推导中的新应用。这一努力的更广泛影响延伸到其在变革多尺度能源运输量化和管理方面的潜力，影响到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促进科学知识的发展，还包括开发更高效和可持续的能源技术。该项目的教育目标是培养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结合。该职业项目的技术目标是建立一个新的解析双重抽象-回归框架，用于表征和求解非均匀介质中的宏观辐射量。该方法结合了代表宏观结构的抽象模型和逐点辐射特征张量，以及基于更新/破产和Power-Gerber-Shiu风险盈余理论的分析回归模型。这些模型旨在从均匀的微观张量中精确地估计辐射宏观性质，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)了解风险盈余理论和辐射换热特性之间的联系，(Ii)开发用于精确辐射估计的双重抽象-回归模型，以及(Iii)通过实验验证来评估框架的有效性。这个项目的学术意义在于它有潜力改变在复杂介质中模拟辐射热传递的方式，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，对增强太阳能系统、改善电子设备的热管理以及促进具有优化热性能的新材料的开发具有影响。这项研究预计将在辐射热传递的基本理解方面取得重大进展，推动辐射科学的理论和应用方面的创新。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.