Determination of surface heat flux and temperature using in-depth temperature data - Experimental verification

- The modified calibration integral equation method is experimentally investigated.
- The modifications account for the effects of temperature dependent properties.
- Forty-two cases of high-temperature experimental data are examined.
- Proof of concept for high-temperature and heat flux calibrated gauge is presented.
- The calibrated plug-type sensor can be used in high-temperature applications.

This paper presents an experimental investigation of the accuracy of two previously reported formulations of the modified one-probe calibration integral equation method (CIEM) using high temperature (to 837 °C) and heat flux (to 83.1 W/cm2) experimental data. The data was collected from an AISI type 304 stainless steel plug-type test sample heated with a laser power source. The one-probe CIEM requires the knowledge of the surface thermal boundary condition of a calibration test along with temperature data from one in-depth probe in order to predict the surface thermal boundary condition of an unknown (reconstruction) heating process given the temperature data from the same probe. Two modified versions of the CIEM that account for temperature dependent properties are investigated. The first modified version utilizes rescaling the time domain to account for temperature dependent thermal diffusivity and rescaling the heat flux to account for temperature dependent thermal conductivity. The Kirchhoff transformation is used in the second version to account for temperature dependent thermal conductivity while employing the same time domain rescaling approach. Seven calibration tests and six reconstruction tests were conducted which allows forty-two test cases consisting of pairs of calibration test data and reconstruction test data to be investigated. The average value of the standard deviations of the 42 net surface heat flux prediction errors obtained from the rescaling model was 0.82 W/cm2. The average value of the standard deviations of the 42 surface temperature prediction errors obtained from the Kirchhoff transformation model was 1.03 °C. This study demonstrates that a calibrated plug-type sensor can be used in high temperature applications to accurately reconstruct the surface heat flux and temperature of an unknown surface heating process. The stainless steel test sample is a proof of concept for a future prototype of this kind of calibrated dual measurement gauge.