A numerical correlation development study for the determination of Nusselt numbers during boiling and condensation of R134a inside smooth and corrugated tubes

Abstract

In this study, the closed form of artificial neural network method is used to have a reliable empirical correlation to estimate the measured Nusselt numbers of R134a flowing downward and horizontally inside smooth and corrugated copper tubes by means of some dimensionless numbers. R134a and water are used as working fluids flowing in the tube side and annular side of a double tube heat exchanger, respectively. The training sets have the experimental data of in-tube condensation and in-tube boiling tests including various mass fluxed and saturation temperatures of R134a. Inputs of the formula are the dimensionless numbers obtained from measured values of test section such as Froude number, Weber number, Bond number, Lockhart and Martinelli number, void fraction, the ratio of density to dynamic viscosity, liquid, vapor and equivalent Reynolds numbers, surface tension parameter and liquid Prandtl number, while the output of the formula is the experimental Nusselt numbers in the analysis. Nusselt numbers of R134a are modeled using closed form of multi-layer perceptron (MLP) method of artificial neural network (ANN). Analyses of the ANN method are accomplished by means of 1177 data points. The performance of the closed form of multi-layer perceptron (MLP) with three inputs and one hidden neuron architecture was found to be in good agreement, predicting the experimental Nusselt numbers with their deviations being within the range of 30% for all tested conditions. Empirical correlations are proposed for both condensation and boiling flows separately. A single empirical correlation is found to be capable of predicting the experimental Nusselt numbers of both condensation and boiling flows together. Dependency of output of the ANNs from input values is also investigated in the paper. Vapor Reynolds number, equivalent Reynolds number, Weber number and Froude number are found to be the most affective parameters as a result of the dependency analyses. (C) 2013 Elsevier Ltd. All rights reserved.