Multiscale mathematical models for nanoscale heat transport phenomena

Multiscale mathematical models offer a mathematically sound basis to study heat transport phenomena in the nanoscale range for which classical continuum-based models are not applicable.In this study, a full mathematical formulation is introduced that combines Fourier heat conduction, Boltzmann Transport Equation, dual-phase-lag and hyperbolic heat conduction, as well as molecular dynamics approaches to account for the thermal behavior at various spatial and temporal scales.The numerical solution algorithms are used to investigate heat propagation, temperature evolution and phonon transport phenomena at the nanoscale.The proposed framework enhances the ability to predict the heat transfer, which is represented by both ballistic and diffusive heat transfer, while retaining the computational efficiency.The convergence is shown to be better compared to the conventional single-scale approach, while the stability is improved and the thermal prediction error is smaller than those of existing methods, through a comparative numerical evaluation.