1D analytic and numerical analysis of the depth response filter and semi-infinite limit of thin film heat transfer gauges

The impulse response method is widely used for heat transfer analysis in turbomachinery applications. Traditionally, the 1D method assumes linear time invariant, isotropic, semi-infinite material, which constrains the analysis to short duration tests. Known as the semi-infinite limit, this constraint is arbitrarily approximated by the simple unit step solution, misrepresenting the actual duration over which the analysis is considered reliable. This paper evaluates the true limit and demonstrates the error associated with unit step approximation. A novel impulse response depth filter is defined, enabling robust definition of the permitted test duration via direct simulation of the subsurface heat flux. Additionally, an inverse depth filter is presented for impulse response post-processing of embedded thermal measurements, inferring the exposed surface heat flux from a subsurface reference. This new technique extends the capability of thin film gauges for heat flux measurements in abrasive flow, utilising coverlay materials to protect the sensing element. The new depth response solutions are then combined with a Keras optimisation algorithm to solve unsteady surface heat flux. This paper defines the allowable limit for thin film gauge test duration and, together with the preceding publications, provides the necessary methodology to handle the complex case of embedded heat transfer measurements.