Oscillation Flow of Viscous Electron Fluids in Conductors of Rectangular Cross-Section

The article presents results of an analytical and numerical modeling of electron fluid motion and heat generation in a rectangular conductor at an alternating electric potential. The analytical solution is based on the series expansion solution (Fourier method) and double series solution (method of eigenfunction decomposition). The numerical solution is based on the lattice Boltzmann method (LBM). An analytical solution for the electric current was obtained. This enables estimating the heat generation in the conductor and determining the influence of the parameters characterizing the conductor dimensions, the parameter M (phenomenological transport time describing momentum-nonconserving collisions), the Knudsen number (mean free path for momentum-nonconserving) and the Sh number (frequency) on the heat generation rate as an electron flow passes through a conductor.