The extraction of the temperature gradient from measured temperature profiles with uncertainty propagation, as applied to the high temperature test unit

Abstract

This paper highlights the usefulness of applying analytical methods for uncertainty analysis to a least-squares polynomial fit. It also presents an equation to calculate the confidence interval in the slope of a regression polynomial. The specific area of application is the determination of the temperature gradient as a function of position from a set of temperature measurements on a packed bed of spheres. Using the derivative of the regression polynomial was found to be the most accurate way to calculate the temperature gradient. An uncertainty analysis was used to relate the uncertainty in the predicted value to the regression errors and to the experimental uncertainty