A Review of Multiscale Mathematical Models for Nanoscale Heat Transport Phenomena: Intelligent Modeling, Electronics Integration, and Real-World Applications

Abstract

Nanoscale heat transport has emerged as a critical domain in modern electronics, energy systems, and advanced materials, where classical Fourier-based models fail to capture non-equilibrium and quantum effects. This paper presents a comprehensive review of multiscale mathematical models for nanoscale heat transport, emphasizing intelligent modeling techniques, integration with electronic systems, and real-world applications. The study synthesizes recent advancements spanning deterministic, stochastic, and hybrid approaches, including Boltzmann transport equation (BTE)-based models, molecular dynamics (MD), lattice dynamics, and machine learning-assisted frameworks. Special attention is given to the role of intelligent systems in bridging scale gaps, improving prediction accuracy, and enabling adaptive thermal management in microelectronic devices. The review identifies key trends such as the convergence of physics-based and data-driven methods, the growing role of AI in parameter estimation and model reduction, and the integration of thermal models into semiconductor design workflows. Furthermore, the paper highlights challenges including computational complexity, model validation, and scalability. The contributions of this work lie in providing a unified perspective on multiscale modeling techniques, evaluating their strengths and limitations, and outlining future research directions for intelligent thermal modeling in next-generation electronic systems.