Physics-Informed Deep Learning Modeling of MHD Casson–Maxwell Nanofluid Flow with Variable Viscosity, Thermal Slip, and Viscous Dissipation Within a Porous Medium

This work focuses on studying the magnetohydrodynamic flow and heat transfer mechanism of a Casson–Maxwell nanofluid due to a stretching surface through a porous medium, using a physics-informed neural network (PINNs) approach as the main tool for the solution of the physical problem. The mathematical model describes the phenomena of viscosity variation with temperature, viscous dissipation, thermal slip, Brownian motion, thermophoresis, and drag force due to a porous medium, which give a realistic physical scenario of the coupled transport phenomena of momentum, heat, and nanoparticles. First, the nonlinear partial differential equations are converted into a dimensionless boundary layer model using similarity transformations. Then, the yielded system is solved via the PINNs approach, which integrates physical law within the optimization procedure. The proposed technique does not require a significant number of labeled datasets and provides accurate and stable predictions of the strongly nonlinear flow. A comprehensive parametric analysis was performed to explore the impact of the dimensionless controlling factors on the velocity, temperature, and nanoparticle concentration distributions. It is found that the interaction of magnetic field effects, porous media resistivity, thermal and concentration slip, viscosity variation, and viscous heating significantly modifies the transport features for the studied model of the Casson–Maxwell nanofluid, which can be used effectively to control the rate of heat and mass transfer. This study proves the efficiency of the PINN technique in solving this type of model, and it also provides useful insights for designing thermal systems, energy conversion devices, and electrically conducting viscoelastic nanofluid transport problems. The close concordance between the present findings and established data from the literature validates the precision and dependability of the developed PINN-based framework.