Thermal wave propagation in thin films on substrate: the time‐harmonic thermal transfer function

Abstract

We present an analytical description of thermal wave propagation for cylindrical symmetry based on a transfer function concept which is analogous to optics. This concept leads to a general criterion for the spatial resolution and to computational benefits. It is applied to a medium consisting of a thermally thin layer of highly heat conductive material on a finite substrate. The result is then specialized to the two cases of highly heat conductive layer on quasi-infinite substrate and finite substrate with no additional layer. This completes the theory of heat propagation between the thermally thick and thermally thin cases. We encounter the mathematical necessity to revise the definition of the latter terms, taking into account the lateral modulation of the thermal signal. The derived expressions are verified experimentally using infrared lock-in thermography.