Abstract
Abstract: A transformative calibration methodology is presented for predicting transient
surface temperatures in a thermally conducting medium from in-depth, time-varying temperature
measurements. The surface temperature is resolved using two experimental runs
and a newly devised first-kind Volterra integral equation. The first experimental run involves
calibration with known surface temperature while the second run involves resolving the surface
temperature of interest through the ill-posed integral equation. This paper presents the
concept genesis and numerically demonstrates the concept for feasibility, robustness, stability
and accuracy. From this demonstration, we propose to implement surface placed thermographic
phosphors in the calibration stage of the inverse method for estimating the required
surface temperature. As a preliminary study, we consider transient, constant property, onedimensional
heat conduction in a semi-infinite medium. It is mathematically demonstrated
that a Volterra integral equation of the first kind is developed for estimating the surface
temperature using a calibrated system (host material and sensor). Sensor characterization,
explicit sensor positioning and thermophysical properties are implicitly contained in the new
calibration integral equation. The calibration integral equation displays only four terms;
namely, the measured front surface temperature and corresponding measured in-depth temperature
response associated with the calibration run; and, the unknown surface temperature
and its measured in-depth temperature response associated with the second run. Preliminary
numerical results indicate the merit of the concept. This paper suggests using thermographic
phosphors for estimating the surface temperature in the calibration portion of the process
owing to their rapid thermal response, good surface thermal contact characteristics and lack
of capacitance for assuring minimal delay. Though the present paper describes the theoretical
basis for resolving such problems, it is intended for near-term application using the
UTK’s high-heat flux laser facility which is presently under development