Neural network modeling of non-Newtonian NEPCMs suspension in a non-Darcy porous medium under LTNE conditions

Background: Analyzing buoyancy-driven convection in porous media has numerous applications in chemical processing and geothermal energy extraction. The complication of heat transfer (HT) in porous media, especially under Local Thermal Non-Equilibrium (LTNE) conditions, may need sophisticated examination to precisely predict system behavior. In addition, when it comes to using nanomaterials with the aim of enhancing heat transfer efficiency of thermal systems, nano-encapsulated phase change materials (NEPCMs) would offer a promising solution. NEPCMs merge the high latent heat storage capacity of phase change materials (PCMs) with nanoparticles' improved thermal conductivity, making them ideal for energy storage, electronic cooling, and thermal and solar energy applications. In this regard, this study examines the coupled natural convection and entropy generation of a non-Newtonian NEPCM suspension within a fluid-saturated porous hexagonal enclosure. The Forchheimer-Brinkman-extended Darcy (FBED) model is established to characterize the interaction between the porous medium and the NEPCM suspension flow. The thermal interaction between the suspension and the solid is analyzed using LTNE assumptions, where both NEPCMs suspension and solid matrix temperatures exhibit local fluctuations. Methods: Governing equations of the system are solved using the finite element method (FEM) and the average Nusselt numbers for both phases are assessed through an artificial neural network (ANN)-based multi-layer perceptron (MLP) algorithm. This algorithm is further employed to conduct regression analysis, evaluate the mean square error, and analyze the error histogram of the neural network. Significant Findings: The results indicate that while the same parameters influence heat transfer in both phases, the suspension phase is more sensitive to variations in Ra, Da, and n. In contrast, the solid phase exhibits a relatively stronger dependence on λ and H, with Ste having the least impact on heat transfer in both phases. Furthermore, the regression coefficients are identified as R = 0.99987 for Nu_ave,nf and R = 0.99971 for Nu_ave,s indicating a strong correlation between the predicted values of the ANN model and the actual values.