Investigation of heat generation and flow of viscous electron fluid in rectangular conductors

The study presents, for the first time, results on the flow of viscous electron liquids in conductors with a rectangular cross-section. Analytical results for the current carrier velocity were obtained using a Series solution (Fourier method). The problem was also solved numerically using the Lattice Boltzmann Method (LBM). Comparison of velocity profiles showed good agreement. A dimensionless criterion for the realization of ballistic and hydrodynamic regimes was obtained. An evaluation of heat release was provided as a function of a dimensionless parameter characterizing the conductor's size, as well as the time and mean free path length. It was shown that in the hydrodynamic regime, a reduction in the number of collisions leads to a decrease in heat release intensity.