Uncertainty analysis for the experimental estimation of heat transfer correlations combining the Wilson plot method and the Monte Carlo technique

Abstract

The present paper addresses several procedures for determining convective heat transfer coefficients based on the original Wilson plot method and its modified variants. Different thermal relationships based on thermal resistance and temperature differences are obtained from slight different applications of the Wilson plot method. Results from simple linear regression models extensively used in the archival literature are analyzed and compared with those obtained from weighted and unweighted nonlinear regression models, as well as with the results provided by Monte Carlo simulations.The analysis is focused on a specific problem where the heat transfer correlation to be obtained has three unknowns; however, the analysis is quite general and could be extended to more complex problems. Results show that weighted nonlinear regression models give more consistent results that unweighted methods; whereas unweighted simple linear regression analyses are not recommended. Finally, the suitability of implementing a Monte Carlo simulation is shown in terms of properly propagating the measured data uncertainty distribution through the heat transfer model.