Unsteady mixed convection of Jeffrey nanofluid with Cattaneo–Christov heat flux and activation energy: A comparative MATLAB-PINN study

Abstract

This study examines the unsteady flow and transport behavior of a Jeffrey nanofluid over a stretching surface in the presence of Stefan blowing/suction, Cattaneo–Christov heat flux, activation energy, mixed convection and nonlinear porous medium effects. The governing nonlinear boundary layer equations are transformed using similarity variables and solved numerically using a MATLAB-based BVP4c solver, with further validation performed through a physics-informed neural network approach. A comprehensive parametric analysis is conducted to investigate the influence of key physical parameters on the velocity, temperature, and concentration fields. The results indicate that unsteadiness and porous drag significantly suppress the velocity while enhancing temperature and concentration due to reduced convective transport. Thermal and solutal buoyancy parameters accelerate the flow but decrease thermal and concentration distributions. The thermal relaxation parameter reduces temperature, whereas chemical reaction and activation energy strongly influence species transport. Additionally, Brownian motion and thermophoresis exhibit competing effects on nanoparticle concentration. The reliability of the proposed physics-informed neural network approach is confirmed through excellent agreement with the MATLAB BVP4c solution, with L2 errors of 2.71 × 10 − 3 , 3.02 × 10 − 2 , and 6.76 × 10 − 2 for velocity, temperature, and concentration distributions respectively. The results are beneficial in understanding advanced thermal management systems, nanofluid-based cooling technologies, porous heat exchangers, energy conversion devices, and chemical processing systems where enhanced heat and mass transport of non-Newtonian nanofluids is needed.