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

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.