Young Researchers Workshop: Kinetic theory with applications in physical sciences

Advances in thermal phonon transport modeling based on the multidimensional frequency-dependent Boltzmann equation

Chengyun Hua

California Institute of Technology

Thermal phonon transport at length scales comparable to mean free paths is governed by the Boltzmann transport equation (BTE), which is challenging to solve due to its high dimensionality. Here, we present two methods to efficiently solve the frequency-dependent, multidimensional Boltzmann equation under the relaxation time approximation. In the first method, we demonstrate that exact analytical solutions for the BTE for arbitrary heat inputs can be obtained using Fourier transforms in infinite or semi-infinite domains. The second method presents a semi-analytical series expansion solution of the BTE in a finite domain. Both methods enable simple closed-form solutions for a number of multidimensional problems for which the only prior solution methods have been computationally expensive numerical simulations. We then implement these two advances in modeling phonon transport to develop a general route to study microscopic processes governing interfacial heat conduction, which is essential for applications such as waste heat recovery using efficient thermoelectrics and thermal management problems in high power electronics.