Calibration errors induced by substrate thermal conduction in high-temperature thin-film sensors: A theoretical study

High-temperature thin-film thermocouples represent a promising non-intrusive measurement technique for turbine blade surface temperature monitoring. However, the application of conventional calibration methodologies, originally developed for standard armored thermocouples, to thin-film sensors introduces significant systematic errors attributable to substrate conduction effects. Unlike conventional thermocouples, thin-film sensors must be calibrated in conjunction with their substrate, and conductive heat transfer through the substrate establishes a temperature gradient between the sensor surface and the furnace air where the reference thermocouple is normally positioned. This study presents a theoretical heat transfer analysis of the calibration system to quantify the calibration errors induced by substrate conduction. The temperature distribution within the substrate was analytically determined, revealing substantial discrepancies between the thin-film hot-junction temperature and the furnace air temperature. Parametric investigations were conducted to elucidate the influence of substrate geometry and thermal properties on the temperature difference. Based on these findings, optimization strategies for the calibration system were proposed, encompassing substrate geometry selection and positioning within the calibration furnace. The results demonstrate that the systematic error attributable to substrate conduction can be suppressed below 1% when the governing dimensionless parameter α exceeds 5.