Modeling the Impact of Lattice Vibrations on Thermal Transport: Energy Generation and Diffusivity Modulation Approaches
DOI:
https://doi.org/10.36602/jsba.2025.20.74الكلمات المفتاحية:
Heat conduction، phonon dynamics، thermal transport modeling، diffusivity modulationالملخص
Two supplementary modeling methods are introduced in this study to examine the impact of lattice vibrations (phonons) on one-dimensional heat transmission in solids. The initial approach in Program 1 uses a velocity-squared source term added to the traditional heat equation to depict the direct heat produced by atomic motion and incorporate a dynamic phonon-heat interaction. The second technique in Program 2 indirectly captures the impact of phonons by enabling the thermal diffusivity coefficient to change as a function of lattice displacement, both temporally and spatially. Both models were applied to two representative materials, silicon (a high-conductivity semiconductor) and alumina (a low-conductivity ceramic), using finite-difference simulation in MATLAB program. The results show that there are material-specific thresholds for phonon-induced instability. In the case of Program 1, thermal breakdown occurs at βcritical=10-8 K.s/m2 for silicon and βcritical=10-11 K·s/m2 for alumina. The highest possible stable values of the coupling parameter C (in m/s) in Program 2 are 2.23 for time-dependent diffusivity and 1.27 for space-dependent diffusivity across both materials. According to the findings, a thorough description of thermal transport in thermally sensitive or micro-structured materials requires consideration of both phonon-induced energy generation and phonon-modulated diffusivity.
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