Hyperbolic heat equations in laser generated ultrasound models

Abstract

The generation of ultrasound by pulsed lasers is a thermoelastic process, and in the literature on general thermoelasticity there are presently three different forms of the heat equation in popular use, the classical, Lord-Schulman (LS), and Green-Lindsay (GL) heat equations. The question may thus arise as to which heat equation should be used to model laser generated ultrasound. The purpose of this work is to summarize the current rationale for using these different heat equations, in order to provide a basis for choosing one of the forms. A review of the classical, LS and GL theories is given, and the potential advantages of hyperbolic heat flow theories in laser ultrasonics are discussed. A numerical example is given that clearly shows the small time differences these theories predict, and also points out potential problems with using hyperbolic heat equations on small time scales.