A Review of Multiscale mathematical models for nanoscale heat transport phenomena: Intelligent Modeling, Electronics Integration, and Real-World Applications

Abstract

The rapid advancement of nanoscale devices and miniaturized electronic systems has intensified the need for accurate and efficient modeling of heat transport phenomena beyond classical regimes. At nanoscales, traditional Fourier-based heat conduction models fail to capture non-equilibrium effects, ballistic transport, and phonon scattering mechanisms. This paper presents a comprehensive review of multiscale mathematical models for nanoscale heat transport, integrating perspectives from intelligent modeling, electronics integration, and real-world applications. The study examines deterministic, stochastic, and hybrid frameworks including the Boltzmann Transport Equation, molecular dynamics, lattice dynamics, and machine learning-assisted approaches. Key findings highlight the growing importance of hybrid multiscale frameworks that bridge atomistic and continuum regimes while incorporating data-driven intelligence for enhanced predictive capability. The paper contributes by synthesizing recent developments from 2018 to 2025, identifying research gaps in model scalability, computational efficiency, and integration with modern software engineering pipelines, and proposing future directions emphasizing AI-assisted modeling and real-time thermal management systems.