Modeling the Impact of Lattice Vibrations on Thermal Transport Energy Generation and Diffusivity Modulation Approaches

الملخص

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