On the wave treatment of the conduction of heat in photothermal experiments with solids

Abstract

In this paper we discuss the conduction of heat in solids excited by a periodically time-dependent source, commonly encountered in photothermal experiments. In the analysis, we take into account the relaxation time necessary for the onset of the heat flux which leads to a second time derivative in the heat diffusion equation. It is shown that there exists a critical modulation frequency at which the heat flux changes its diffusive character to a wave propagation process with the velocity of sound. Evidence is provided for the possibility of detecting second sound in solids by means of a photothermal experiment.

Time Varying Heat Conduction in Solids

“…Note that the thermal wave behaviour depends on the values of both, thermal effusivity, with determines the wave amplitude at x=0, and the thermal diffusivity, from which the attenuation and wave velocity depend. Among other characteristics [Marín et al, 2002] a thermal wave described by Eq. (24) has a phase velocity, v f ==(2) 1/2 .…”

Characterization of Clay Ceramics Based on the Recycling of Industrial Residues – On the Use of Photothermal Techniques to Determine Ceramic Thermal Properties and Gas Emissions during the Clay Firing Process

“…The thermal conductivity (κ) is associated with thermal conduction, which is the phenomenon where the heat is carried from regions of high temperature to regions of low temperature in a material. The thermal effusivity (ε) denotes the material thermal impedance and is a measurement of the heat energy stored in a solid per degree of temperature rise from the start of a surface heating process (Marín et al, 2002). Here, thermal conductivity and thermal effusivity are reached applying the following expressions:…”

“…In the early eighties, a new physical device to generate and detect thermal waves was proposed (Vargas and Miranda, 1988). It has been widely used in last few years as a tool to measure the thermal properties of a large range of materials (Marín et al, 2002;Faria et al, 2005). The photoacoustic (PA) technique via OPC (an open photoacoustic cell) is used to evaluate the thermal diffusivity, an important parameter that determines the light-to-heat conversion efficiency, and furthermore, it allows us to study how heat diffuses through the sample (Perondi and Miranda, 1987).…”

On oscillating flows in randomly heterogeneous porous media

“…The dissipating wave equation is widely used to describe finite correlation-time phenomena in diverse areas of physics, including granular system stress dynamics , the so-called second sound of thermo-acoustics (Chester 1963), heat conduction and thermo-elasticity (Marín et al 2002;Khisaeva & Ostoja-Starzewski 2006) and in chemical reaction-diffusion (Manne et al 2000).…”