Heat transport considerations in the mathematical analysis of the photoacoustic and photothermal effects

Abstract

In this work, we solve the problem of modeling the generation of an acoustic pulse produced by the incidence of a pulsed laser light upon an elastic material. Our concern is about the heat transport during the absorption of electromagnetic radiation. We assume that the pulse duration is of the order of nanoseconds, and asses if under these conditions the contribution of the heat transport in the sample is an essential consideration in the description of the phenomena or if we can ignore it in the model. We begin with the energy balance analysis over the initial interaction of radiation with matter in the context of the formulation Meixner-Prigonine which is called the linear irreversible thermodynamics to describe the induced temperature field. Then we carry a momentum balance which yields the macroscopic elasticity equations with a heat source for the induced pressure field. Once established the equations for temperature and displacement fields, we solve them for the one-dimensional case, showing that the induced pressure has two components, one fast component and one slow component which is due to heat transport in the sample, which is one of the main contributions of the paper.