Fractional modeling of MHD Jeffrey fluid flow with Rabotnov memory kernel: Heat and mass transfer analysis and artificial neural network prediction

This paper deals with the numerical implementation of viscoelastic fluids, which have potential applications in the polymer industry, lubrication, and various other important transport devices for heat and mass transfer. Here, the fractional Jeffrey fluid model in a porous medium is proposed, employing the Yang-Abdel-Cattani (YAC) operator with a Rabotnov exponential kernel to characterize memory-dependent impacts. The model that is being emphasized under concentration and temperature involves a heat source/sink, magnetohydrodynamic effects, resistance due to the porous medium, and a first-order chemical reaction. The analytical solution for the coupling of velocity, temperature, and concentration equations is presented in terms of Mittag-Leffler(ML) functions via the application of the Laplace transform(LT) technique. It is observed that the concentration field reduces with growth in the Schmidt number, while the temperature field reduces with an increase in the Prandtl number. The velocity field becomes weaker with the growth in the magnetic field and strengthens with the increase in the fractional order. We further, employ neural networks (ANNs) for independently confirming the obtained analytical solutions. The numerical simulations through ANNs brought out excellent predictive results with a reduction of about 93.41% of the MSE for the temperature solution and about 94.26% of the MSE for the concentration solution when compared with the MSE of the velocity solution, while the corresponding RMSE reductions are estimated as 74.33% and 76.03%, respectively. The corresponding MAE suffers reductions of 74.03% and 73.48%, respectively, while the R 2 values are found close to one for the temperature and concentration solutions, respectively. The numerical accuracy for the ANN predictions is exceptional, which substantiates the reliability of the NN models. The introduced model encapsulates a promising basis for further studies of various fractional viscoelastic transport systems and their engineering applications.