Influence of specularity factor on heat transport in nanoribbons of different sizes

In this paper, the phonon heat transfer in two-dimensional conductors with different types of phonon reflection from the boundaries is examined. Heat conductors with arbitrary ratios of width W to length L are studied assuming that the mean free path between phonon-phonon collisions is infinite. The integral equations for the angular distribution functions of the incident and reflected phonons at a specific point on the conductor boundary were proposed. To solve these integral equations a new iterative method is proposed. The proposed iterative approach formally corresponds to taking into account subsequent collisions of phonons with the edges of the conductor. It ensures the convergence of the desired solution for any W/L ratio and for any value of the specularity coefficient p. Interpolation formulae are found to describe with sufficient accuracy the solution of the system of integral equations in the entire region of the specularity coefficient p from 0 to 1, and the W/L ratios ranging from 10 to 0.01. These formulae allow the construction of the isolines of the thermal conductance coefficient values, from which it is possible to determine the necessary values of W/L and parameter p to get the desired value of the thermal conductance.