Abstract
The Linear relativistic energy-momentum relation together with Schrodinger's wave function for frictional mediums are used to derive quantum heat flow equation. This equation is reduced to the Hai-Bing –Zeng classical relation for steady heat flow rates. The Quantum Thin Films Electronic coefficient is nonsingular, where one assumes the phonon kinetic energy to generate matter thermal energy, thus this expression agrees with observations which say that thermal conductivity is always finite. The relation between thermal conductivity resembles the empirical observations for carbon nano tubes.