Heat flux determination from measured heating rates using thermographic phosphors

Abstract

A new method for measuring the heating rate (defined as the time rate of change of temperature) and estimating heat flux from the heating rate is proposed. The example problem involves analytic heat conduction in a one-dimensional slab, where the measurement location of temperature or heating rate coincides with the location of the estimated heat flux. The new method involves the solution to a Volterra equation of the second kind, which is inherently more stable than Volterra equations of the first kind. The solution for heat flux from a measured temperature is generally a first kind Volterra equation. Estimates from the new approach are compared to estimates from measured temperatures. The heating rate measurements are accomplished by leveraging the temperature dependent decay rate of thermographic phosphors (TGP). Results indicate that the new data-reduction method is far more stable than the usual minimization of temperature residuals, which results in errors that are 1.5–12 times larger than those of the new approach. Furthermore, noise in TGP measurements was found to give an uncertainty of 4% in the heating rate measurement, which is comparable to the noise introduced in the test case data. Results of the simulations and the level of noise in TGP measurements suggest that this novel approach to heat flux determination is viable.