Flow boiling heat transfer coefficient in enhanced tubes: benchmark correlations and ANN comparison

Nowadays, refrigeration and air-conditioning industries are involved in a huge increase of demand, thus the heat transfer enhancement of heat exchangers is crucial to reduce both systems environmental impact and total costs. Fin and tube or shell and tube heat exchangers are widely employed in these sectors and since several enhancement have been reached for the one phase flow heat transfer (related mostly to air or water), having an approach between the internal and external heat transfer resistances, the two-phase heat transfer enhancement then has become a topic of interest. In particular, internal micro-fin tubes are commonly employed because of their enhancement effects such as promoting flow turbulence, delaying dry-out occurrence, mitigating boiling suppression due to forced convection and enlarging heat transfer surface. During the last 30 years, several experimental studies have been conducted to investigate the effect of different micro-fin geometries on flow boiling physics with the development of some predictive methods for heat transfer coefficient prediction. These methods have often been developed using small datasets in terms of operative conditions and fluids using frequently only one type of micro-fin geometry. Therefore, general accuracy is still an open question that drives the research towards the development of new predictive methods. Despite reduced parameters physical modelling has been for years the only way for predictive methods development, recently machine learning techniques have started to be accounted as a new predictive method. Among them, artificial neural networks seem to show a good potential due to their ability to create links between inputs and outputs replicating the non-linear relationships between variables involved in the physical phenomena. However, dataset needed to develop accurate and general neural networks should be large and accurate because this tool can be unreliable beyond development training ranges. For this reason, recent studies have started to analyse how to join machine learning techniques with physical knowledge, having the development of physics informed neural networks based on transfer learning techniques. According to the actual state of the art about predictive methods, a general assessment and comparison between reduced parameters physical modelling and artificial neural networks is something not very present in literature. In this regard, starting from a large experimental database collected from literature, the aim of the work is to present a comparison between benchmark flow boiling correlations and artificial neural networks, evaluating also correlations results as a parameter on which to build the network. The database has been collected from about 30 papers, with a total of 3179 points. It includes mass flow rates from 50 to 1000 kgm-2 s, vapour qualities from the onset of boiling to the dry-out occurrence and beyond, reduced pressure from 0.05 to 0.80 and fin tip diameters from 0.7 to 11.9 mm. Regarding micro-fin geometries, most studies focused on helical configuration, with trapezoidal micro-fin shape, having about 70% of the database with these features. Afterwards a literature review, six quoted correlations have been chosen for this work. In particular, starting from two of the first correlations for micro-fin tubes such as Thome et al. and Cavallini et al. ones, using the Chen assumption as a starting point of correlation development, more recent ones can be considered as evolution of the previous two such as Wu et al., Diani et al. and Tang and Li methods. Instead, considering also correlations developed using only regression analysis, the one by Rollman and Spindler is often cited. On the other hand, several artificial neural networks have been trained varying their structures in terms of layers number (1 to 4), neurons per layer (10 to 80) with uniform and not uniform distributions on neurons among layers. Input sets have been defined selecting the most influencing variables for output prediction, having dimensional, non-dimensional and mixed sets. According to the main idea of the transfer learning, also correlation results have been considered as possible inputs. Training processes based on backpropagation algorithm involving 70% of the database, while the remaining 30% was used for validation and test phases. Table 1 show the statistical comparison in terms of mean absolute percentage error (MAPE) and number of points within ±30% error band (𝛿±30%). Despite almost all correlation show an intermediate accuracy with the one by Wu at el. showing a 𝛿±30% of 57%, some common outliers can affect significantly their performance as shown in brackets. Also, Rollman and Spindler one is not usable on the whole dataset. Instead, artificial neural networks present a very good accuracy, outperforming correlations for both the one with mixed input and the one using Cavallini correlation as input However, in the local analysis shown in figure 1 it is clear that correlated informed neural network results in a more reliable predictive approach instead of standard artificial neural network that can bring to some unacceptable results. Therefore, artificial neural networks can be a useful tool in particular when predictions needed do not fall beyond training ranges, but using a physical approach could be a promising path to extend their reliability, resulting in a trade-off between correlations and pure machine learning.