Machine learning-based modeling of MHD Jeffrey nanofluid flow with activation energy and motile microorganisms in a stratified medium

Purpose This study aims to examine magnetohydrodynamic (MHD) Jeffrey nanofluid (NF) flow with activation energy (AE) and motile microorganisms in a stratified medium over a stretching porous vertical plate. The objective is to examine the combined influences of porous effects, nanoparticle transport, bioconvection and stratification on flow behavior, heat transfer and mass transport while assessing the predictive capability of an artificial neural network (ANN) framework. Design/methodology/approach The two-phase Buongiorno model has been adopted. The governing nonlinear partial differential equations describing momentum, thermal energy, concentration and microorganism density are transformed into a system of ordinary differential equations using similarity transformations under appropriate boundary conditions. The resulting boundary value problem is solved numerically using the MATLAB solver bvp4c. The numerical data sets are generated by bvp4c. This numerical data set is used to train, test and validate an ANN by minimizing the mean square error through a data division of 70% for training and 15% each for testing and validation. Moreover, regression analysis, error histograms and training state performance specify the model accuracy. Findings The results specify that increasing the values of the porosity parameter decreases the velocity field while enhancing the temperature distribution. Brownian motion intensifies thermal transport but decreases nanoparticle concentration. Increased Lewis and Peclet numbers inhibit motile microorganism density, whereas parameters of stratification favor bioconvection effects. Variations in skin friction coefficient, Nusselt number and Sherwood number are quantified for key physical parameters. ANN predictions show excellent agreement with numerical results, with the best validation errors ranging from. Originality/value Existing studies mainly addressed MHD Jeffery and NF flows over linearly stretching surfaces with simplified transport models, whereas the present work develops a reliable hybrid numerical ANN framework to investigate two-dimensional MHD Jeffery NF flow over an exponentially stretching sheet, incorporating viscous dissipation, internal heat generation, AE and complex NF bioconvection effects in stratified porous media.