Application of an improved parameter estimation approach to characterize enhanced heat exchangers

The main goals of this paper are twofold: to provide an improved parameter estimation procedure that enables the accurate evaluation of heat transfer correlations for the Nusselt number and to present a new procedure for identifying the presence of transition in the flow regime. In the first goal, it needs to be pointed out that although this kind of approach is based on temperature measurements, in the literature, the classical parameter estimation approach uses the overall heat transfer coefficient. To reduce uncertainty in the evaluation of internal and external heat transfer coefficients, in the improved procedure, the measured temperature data were directly used without any intermediate elaboration. The validation of the new procedure, carried out by means of synthetic data, highlighted that both the relative error on each estimated parameter and the amplitude of the confidence intervals were reduced by minimizing the objective function expressed in terms of outlet temperature of the tube side of the heat exchanger. With regard to the transition regime, the numerical outcomes revealed that both in the laminar and turbulent regimes, the amplitude of the confidence intervals of the estimated parameters was very small; in the transition regime, the amplitude became wide. Therefore, this parameter served as a useful indicator to identify the presence of transition in the flow regime. This finding enabled a new indirect methodology, called the transition alert procedure, to be developed for identifying the Reynolds number value at which transition of the flow regime occurred. This method is an iterative subsampling of the dataset based on the observation of the amplitude of the confidence intervals. To assess the robustness of the methodologies proposed here, the improved parameter estimation procedure and the transition alert procedure were applied to the obtained experimental data by analyzing a counter-flow heat exchanger with double corrugated tubes. In this kind of tube, the condition when the transition from the laminar to the turbulent flow regime occurs is not known a priori.