Intelligent framework for dual solutions of copper oxide nanoparticles suspension in thermally varied fluid reservoirs using the Koo–Kleinstreuer–Li (KKL) Model

This analysis examines the thermal and momentum physiognomies of copper oxide nanoparticle suspensions (nanofluids) past a permeable wall, including general magnetic effects. Understanding these dynamics is critical for enhancing heat transfer in numerous engineering applications, such as cooling and energy systems. The Koo–Kleinstreuer–Li (KKL) rheological model is used to develop a mathematical outline that incorporate for both static and Brownian thermal conductivities. Dual solutions for the velocity and temperature profiles are calculated under varying circumstances. An artificial neural network (ANN) method is applied to confirm the precision of the results, employing convergence plots of mean squared errors, histograms, and regression investigation. The outcomes disclose that the generalized magnetic effects along with permeability of surface meaningfully impact both the velocity and temperature distributions, with copper oxide nanoparticles enhancing thermal conductivity by up to 20 %. This effort extends existing models by integrating ANN-based optimization and providing more reliable predictions for nanofluid behavior in thermally variable environments. The results recommend that magnetic effects and thermal conductivity can be leveraged to enhance heat transfer processes in nanofluid-based systems.