Nonlinear Thermal Waves: Part II - Analytical Solutions for Pulses

Abstract

The weak shock theory developed by Cramer (1994) is used to derive explicit solutions for the evolution of one-dimensional weakly, nonlinear, weakly relaxing heat pulses in rigid conductors. Formulas and differential equations governing the evolution of general heat inputs are derived and applied to the special cases of a square-wave heat input and a finite width sine-wave heat input. Numerical solutions to the exact Maxwell-Cattaneo theory are also presented and show excellent agreement with these analytical solutions.