We report the application of machine learning methods for predicting the effective diffusivity (D_e) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28–0.98), and effective diffusivity spanning more than one order of magnitude (0.1 ≲ D_e < 1), e.g., >95% of predicted D_e have truncated relative error of <10% when the true D_e is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with D_e < 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true D_e < 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.

An efficient segregated solution procedure for incompressible fluid flow and heat transfer problems is proposed. The new algorithm is called IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations). In the new algorithm there exist inner doubly iterative processes for the pressure equation, which almost completely overcome two approximations in the SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of the iteration process. The mathematical formulation and solution procedure of the IDEAL algorithm are described in this article. In Part II, application examples are provided to show the features and feasibility of the new algorithm.

With the rapid development of the Information Technology (IT) industry, the heat flux in integrated circuit (IC) chips cooled by air has almost reached its limit at about $100W∕cm2$. Some applications in high technology industries require heat fluxes well beyond such a limitation. Therefore, the search for a more efficient cooling technology becomes one of the bottleneck problems of the further development of the IT industry. The microchannel flow geometry offers a large surface area of heat transfer and a high convective heat transfer coefficient. However, it has been hard to implement because of its very high pressure head required to pump the coolant fluid through the channels. A normal channel size could not give high heat flux, although the pressure drop is very small. A minichannel can be used in a heat sink with quite a high heat flux and a mild pressure loss. A minichannel heat sink with bottom size of $20mm×20mm$ is analyzed numerically for the single-phase turbulent flow of water as a coolant through small hydraulic diameters. A constant heat flux boundary condition is assumed. The effect of channel dimensions, channel wall thickness, bottom thickness, and inlet velocity on the pressure drop, temperature difference, and maximum allowable heat flux are presented. The results indicate that a narrow and deep channel with thin bottom thickness and relatively thin channel wall thickness results in improved heat transfer performance with a relatively high but acceptable pressure drop. A nearly optimized structure of heat sink is found that can cool a chip with heat flux of $350W∕cm2$ at a pumping power of $0.314W$.