HYPERBOLIC HEAT-EQUATIONS IN LASER-GENERATED ULTRASOUND MODELS

The generation of ultrasound by pulsed lasers is a thermoelastic proce ss, and in the literature on general thermoelasticity there are presen tly three different forms of the heat equation in popular use, the cla ssical, Lord-Schulman (LS), and Green-Lindsay (GL) heat equations. The question may thus arise as to which heat equation should be used to m odel laser generated ultrasound. The purpose of this work is to summar ize the current rationale for using these different heat equations, in order to provide a basis for choosing one of the forms. A review of t he classical, LS and GL theories is given, and the potential advantage s of hyperbolic heat flow theories in laser ultrasonics are discussed. A numerical example is given that clearly shows the small time differ ences these theories predict, and also points out potential problems w ith using hyperbolic heat equations on small time scales.