Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain

Abstract

We deal with unsteady ballistic heat transport in a semi-infinite Hooke chain with free end caused by instantaneous heat pulse. An analytical description of the evolution of the kinetic temperature is proposed in both discrete and continuum formulations in the frameworks of the lattice dynamics approach. We show analytically a property of thermal wave to reflect from the free end. Continuum description of the transient processes, caused by this reflection, has restrictions. In particular, the kinetic temperature field near the boundary and also evolution of the kinetic temperature at the boundary are inadequately described via the continuum model. Based on the comparison of descriptions of heat propagation in the semi-infinite and infinite Hooke chains, we formulate the principles of symmetry of the discrete and continuum solutions.