Quantitative thermal-wave depth profiles of solids with spatially variant cooling coefficients imaged using lock-in thermography

Abstract

A generalized treatment of the thermal-wave boundary-value problem in a solid slab strip with large sidewalls exposed to the ambient and third-kind boundary conditions over the extended sidewall surfaces was presented. Unlike conventional heat conduction theoretical practice, it was found that the cooling coefficient h is not constant and depends on the thermal gradient variation with depth/length. The exponential damping of the TW amplitude with depth presented an ideal condition to reveal the depth dependence of h which under normal steady heat transfer conditions might appear approximately constant in a non-steeply changing thermal field. The observed depth dependence of the heat loss coefficient can be used to establish the physically expected constancy of thermal diffusivity at different modulation frequencies in juxtaposition to some published reports. It is expected that this work can be used to optimize other thermophysical parameters for materials subject to periodic heating.