Heating of inhomogeneous electron flow in the hydrodynamic regime

We study the electron temperature profiles for an inhomogeneous flow in hydrodynamic regime. assume that inhomogeneity is due to a weakly nonuniform distribution of momentum relaxation time within spherically constricted area. show profile dramatically depends on drive strength and viscosity liquid. In absence viscosity, Landauer-dipole-like distribution, asymmetrically deformed along current by inelastic electron-phonon scattering, emerges around inhomogeneity. find both Landauer-dipole its asymmetry direction driving electric field exist all dimensionalities are, therefore, universal features flow. further demonstrate suppresses thermal Landauer dipole leads appearance ``hot spot'' exactly at center constriction. also calculate phonon which can be directly measured experiments nanoimaging.