Neural net-based surrogate square pin fin correlations for thermal-fluid design optimization under developing flow conditions

Heat exchangers and cold plates are widely used for thermal management of electronic devices and in energy storage applications. Accurate prediction of the thermal-fluid transport performance of heat transfer surfaces is crucial for design optimization of these thermal management components. Microscale pin fin structures are commonly employed for enhancement of convection heat transfer. Previous studies have focused on fully developed flow through circular and square pin fins in staggered arrangements, leaving a gap in predictive correlations available for in-line arrangements of square pin fins with consideration of hydrodynamic and thermal developing effects. This study aims to investigate and develop robust friction factor (<i>f</i>) and Nusselt number (<i>Nu</i>) correlations for developing flow through in-line square microscale pin fin structures. Traditional empirical correlations are highly geometry dependent and assume functional forms that could introduce inaccuracies. On the other hand, accurate data may be available at specific points, but continuous evaluation of the function value and derivatives as needed for design optimization processes is difficult. To overcome these limitations, artificial neural network (ANN)-based surrogate models are developed to provide accurate and continuous-valued correlations. The proposed models, trained on numerically simulated data using water as the working fluid, provide accurate predictions of <i>f</i> and <i>Nu</i>, with a near exact match to the training data as well as on unseen testing data. Furthermore, the outputs of the ANNs are inspected to propose new analytical correlations to estimate the hydrodynamic and thermal entrance lengths for flow through square pin fin arrays. The ML models are also shown to be useable for fluids other than water, employing physics-based, Prandtl-number-dependent scaling relations. These generalized ML models have promise to significantly reduce computation cost in the design optimization of thermal management components having pin fin structures for enhanced convection, but without loss in prediction accuracy associated with alternative reduced-order correlations.