Optimizing heat transfer in turbulent impinging jets array: A computational fluid dynamics investigation and machine learning approach for predicting the average Nusselt number

In this study, a computational fluid dynamics analysis is performed to explore how the number of nozzles (N) and the impingement height (H) influence heat transfer (HT) within an impinging jets array (IJA). To simulate the dynamic flow and the HT characteristics, the two-equation k–ω turbulence model was used. The results show that as the number of nozzles increases and impingement height decreases, local and mean Nusselt numbers increase. The greatest enhancement in the average Nusselt number (Nuavg) when reducing the impact height from H = 8 to 2 (57.4%) is noted for a maximum number of nozzles (N = 9). On the other hand, choosing a minimum impact height (H = 2) ensures a maximum improvement in (Nuavg) by 127% following the variation in the number of nozzles from 1 to 9. The streamlines contours of the turbulent flow indicate the presence of two types of vortices, simple vortices and counter-rotating vortices of different dimensions depending on (N) and (H) values. Non-dimensional velocity and static pressure contours highlight the complex interactions between the impingement plate and the flow, and the considerable effects of the number of nozzles and impingement height on the HT and turbulence levels. The linear regression method is adopted to estimate the average Nusselt number along the plate, and correlation given by this method shows moderate agreement with the numerical results. To improve the accuracy of the estimated values, artificial intelligence techniques are applied to find an optimal machine learning model for predicting the average Nusselt number based on a set of input features, including (N) and engineered polynomial transformations of (H). Modeling was accomplished using deep learning through a multi-layer neural network to capture complex relationships. The Adam optimizer and the mean squared error loss function were used to train the model, comparing predictions with actual simulation results. This research offers important insights into the design and optimization of the IJA for cooling applications.