Thermal Waves for Material Inspection

Abstract

A thermal wave is the description of how a temperature modulation propagates as a function of time and coordinate. Compared to light (or generally electromagnetic) waves and even to sound waves, thermal waves are very slow. They are also strongly damped. Within one wavelength their amplitude is reduced to 0. 2 %. The final reason for both the low velocity and the attenuation is the diffusion process that describes heat propagation. The parabolic differential equation for this process has only one parameter, which is thermal diffusivity λ, If a sinusoidal temperature modulation is generated at a frequency ω, then one finds1 that group velocity vg of the thermal wave produced this way is $${\text{v}}_{\text{g}} = \sqrt {2\,\lambda \,\omega \,{\text{.}}} $$ (1)