Numerical investigation of heat transfer in a helically coiled tube using copper/water nano-fluid under constant heat flux and prediction of the results using perceptron and radial basis function networks

Abstract

This study investigated the numerical analysis of Nusselt number and entropy generation of copper/water nano-fluid under turbulent flow conditions at volume fraction ranges of 1–5% within a helical coil under constant heat flux. The nano-fluid behavior was modeled through a single-phase model. Flow and heat transfer governing equations were discretized using finite volume method, and the SIMPLE algorithm was used to solve pressure-velocity coupling equations. The turbulence modelling was done by k-e turbulence model in ANSYS FLUENT 15. Then, the examination and prediction of the resulted data were carried out using perceptron and radial basis function networks. The innovation of the present study was the application of an unsupervised method (namely, SOM) to specify the winner neuron. Input data of the artificial network included Reynolds number, input temperature, constant heat flux, nano-fluid thermal conductivity coefficient and nano-fluid volume fraction, while output parameters included Nusselt number and total entropy generation. The results showed that Nusselt number, entropy generation yielded from heat transfer, and friction increased as the Reynolds number increased. With an increase in the volume fraction, entropy generation yielded from heat transfer and friction decreased and increased, respectively. The results of artificial networks revealed that self-organizing map (SOM) model had 25 neurons, possessing the highest amount of data. Moreover, Mean Squared Error (MSE), correlation coefficient, and maximum error, Nusselt number and total entropy generation for perceptron neural network were 5.0103,0.996,9.1865, 4.389 × 10−5, and 0.998,0.0259, respectively, confirming a successful prediction. In addition to radial basis function networks, the values of Mean Squared Error (MSE), Root Mean Squared Error (RMSE), standard deviation(σ) and a kind of Error(μ) for Nusselt number and entropy generation total were 8.2255 × 10−8,0.0002868,0.00028718,4.741 × 10−6 and 6.0157 × 10−8,0.00024527,0.00024549,7.9006 × 10−6, respectively.