Hamilton’s principle based on thermomass theory

Abstract

Based on thermomass theory, the Hamilton's principle as well as the Lagrangian equations governing the motion of thermomass were established by methods analogous to those of classical mechanics. With the kinetic energy of thermomass taken into consideration, the Hamiltons principle for thermomass is expected to be capable of dealing with non-Fourier phenomena. When the kinetic energy is small enough to be ignored, the principle gets back to Fourier transfer. The application of Lagrangian equations was illustrated by the approximate solution of a 1D transient heat conduction problem with heat source. The unification of thermal and mechanical theories was demonstrated from the perspective of analytical mechanics, the drawbacks of existing theory are discussed, a new way to the approximate solution of heat transfer problem was suggested, and in the meantime the concepts of thermomass and energy of thermomass were to some extent justified.