MHD flow and heat transfer of Carreau nanofluid with slip effects, and modified Fourier–Fick’s law heat–mass fluxes over a paraboloid surface in porous medium

This study thoroughly analyzes the steady, three-dimensional boundary layer flow, heat transfer, and mass transfer of MHD Carreau nanofluid over a paraboloid surface embedded in a porous medium. It considers the integrated effects of Coriolis force, velocity slip, thermal radiation, Hall and ion slip, viscous dissipation, non-uniform heat source/sink, and chemical reactions on the flow. Main features of the analysis are the formulation of the Navier stokes equations, energy and concentration equations using the Cattaneo–Christov heat and mass flux models, rather than the classical Fourier’s law and Fick’s law, which is used to account for time relaxation effects. The governing nonlinear, coupled partial differential equations are converted into an ordinary differential system using similarity variables and then solved numerically using the finite element method. Sensitivity analysis using the response surface methodology exhibits the conditions for optimized heat transfer. The noteworthy findings are presented through graphical analyses of fluid flow parameters. The study reveals that the magnetic field slows fluid flow, while velocity increases with Hall and ion slip effects, mixed convection, concentration buoyancy parameters, and the Darcy number. Moreover, temperature increases with Brownian diffusion, the Eckert number, and radiation but decreases with a higher Prandtl number and thermal relaxation time. Moreover, as the Hall and ion slip parameters increase, the velocity profile also intensifies. The analysis reveals that the Prandtl number (Pr) is the dominant parameter, consistently exhibiting the highest Partial rank correlation coefficient(PRCC) value of 0.8650, emphasizing its crucial role in influencing the system’s behavior. Reliability is ensured through grid convergence analysis, and the numerical results were rigorously validated through detailed comparisons with previous studies and benchmark solutions. These findings are particularly relevant for energy systems, materials processing, and other industrial processes involving nanofluids in porous media, where precise control of thermal and fluid flow properties is crucial. Additionally, extending the study to other non-Newtonian fluids will broaden the applicability to a wider range of industrial applications.