Estimation of time-dependent wall heat flux from single thermocouple data

Surface mounted sensors disturb the phenomena they are expected to record and are prone to damage in harsh environments, leading to incorrect measurements. The present study examines a robust alternative via the inverse estimation of time-dependent wall heat flux using single thermocouple data, as against an array of embedded thermocouples. The Levenberg-Marquardt algorithm for parameter estimation is employed with an even extension of truncated Fourier series as the trial function for inversion. The inversion error decreases with the length of the signal, number of harmonics in the even extension of truncated Fourier series, and proximity of the thermocouple relative to the boundary of interest. The method is numerically validated as well as experimentally benchmarked, against constant, periodic, and transient wall heat flux data in one-dimensional heat conduction problems and is seen to match the exact solution quite well. The developed method is very well suited for sensor development, particularly for application involving high heat flux.