Thermal effects in materials with continuously varying optical and thermal properties in one dimension

Abstract

The complex heat-flow pattern in a heterogeneous sample makes the thermal analysis of these materials difficult. In this paper, we consider heterogeneous materials with continuously varying parameters in one dimension. Although this analysis is directed toward photothermal applications, specifically those using broad-beam illumination, it has many features in common with general harmonic heat flow.The analysis shows that harmonic heat flow is interrupted by spatial variations in the sample's thermal and optical properties via two different types of heat barriers, one depending exclusively on thermal properties (thermal barriers) and the other depending upon both optical and thermal properties (optical–thermal barriers). Thermal barriers are created by spatial variations in thermal effusivity whereas the optical-thermal barriers are created by spatial variations in the ratio of the thermal-diffusion length to the optical-absorption length. The character of the optical–thermal barriers is affected by optical saturation in the sample.The temperature distribution in a heterogeneous sample is interpreted in terms of thermal waves providing an intuitive guide for analyzing heat flow in heterogeneous materials.The surface temperature is also obtained in a general form suitable for both heterogeneous and homogeneous calculations.