The flow and heat transfer characteristics of a tri-hybrid nanofluid in a porous medium are investigated under the influence of magnetohydrodynamics (MHD) and a ramped wall temperature. A Maxwell fluid is employed as the base fluid, in which three types of spherical nanoparticles, tungsten trioxide (WO₃), silver (Ag), and titanium dioxide (TiO₂), are suspended. The physical model is formulated using a system of partial differential equations subject to appropriate initial and boundary conditions. To enhance the novelty of the analysis, fractional derivatives are incorporated into the Maxwell fluid model along with porosity effects. Among the various definitions of fractional derivatives, the Caputo fractional derivative is preferred for its wide applicability in physical problems. The fractional-order derivatives are evaluated using the Caputo formulation, while the Crank–Nicolson numerical scheme is employed to discretize the time-dependent terms and solve the governing equations under ramped heating conditions. The proposed framework, which combines the Caputo fractional derivative with the Crank–Nicolson method to analyze tri-hybrid nanofluid flow, is a distinctive feature of this work. The Caputo derivative effectively captures memory-dependent behavior, allowing the model to account for the system’s dependence on its past states. This capability is particularly important for nanofluids exhibiting nonlocal and anomalous interactions, where classical integer-order models based on simple linear stress–strain relationships fail to accurately represent the complex rheological behavior. Overall, the adopted numerical approach provides improved accuracy and flexibility in modeling complex heat transfer processes, making the present study relevant to a wide range of biomedical and industrial applications.

The integration of nanofluids with porous media has become essential in modern engineering processes because of their ability to meet the ultra-high cooling demands of advanced industrial systems. Their exceptional thermal conductivity also makes nanofluids highly valuable in nanotechnology, electronic device fabrication, and biomedical applications. Motivated by these advantages, the present study investigates the heat and mass transfer behavior of a micropolar nanofluid flowing over a nonlinearly stretching/shrinking slanted surface. Appropriate similarity transformations are employed to reduce the governing system of micropolar nanofluid equations to a set of nonlinear ordinary differential equations, which are solved numerically using the MATLAB bvp4c solver. The analysis reveals a three-solution structure, prompting a stability assessment to determine the physically realizable branch. The results indicate that only the first solution branch is stable and physically meaningful. The findings further show that the microrotation boundary layer thickness increases across all three-solution regimes as the material parameter increases. In addition, an increase in the Grashof number significantly accelerates the fluid velocity. The concentration profile rises with increasing thermophoresis parameter, whereas it diminishes with increasing Brownian motion.