Analytical approaches to describe phonon heat transfer in two-dimensional nanoconductors

The analytical description of heat flow in nanoribbons with diffuse reflection of phonons from the boundary has been worked out. To describe the length dependence of the nanoribbon thermal conductivity coefficient, we propose and implement methods for obtaining explicit analytical expressions for the thermal conductance of nanoribbons of various lengths. In particular, three independent methods are proposed: an iterative analytical technique, a method of cubic addition to a linear dependence, and a fitting-coefficient method for improving a simple linear dependence. Consequently, explicit analytical formulas are obtained for the thermal conductivity coefficient for nanoribbons, which cover a wide range of width-to-length ratios ranging from 0.01 to 10.