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.

To enhance the productivity of heat exchangers, a new type of heat transfer fluid called hybrid nanofluid was characterized. An abundance of industrial and technological processes depends on heat transfer through these fluid flows, whether in laminar or turbulent conditions. The thermal resistance of the fluid based on a heat transfer system might be increased to improve a significant number of applications. Therefore, the present investigation, establishing a framework for differential equations to examine the influence of thermal radiation and heat source/sink on magnetohydrodynamics (MHD) Marangoni convection flow of hybrid nanofluid (HNF) in a Saturated Porous medium. By introducing new similarity variables, the problem of Marangoni convection is simplified to account for the effects of radiation and porous medium. This study’s originality is the combined impact of the heat source and porous material. The governing nonlinear partial differential equations for momentum and energy are transformed into ordinary differential equations by applying the required similarity adjustment. The shooting strategy is used to achieve numerical solutions for certain modeled ordinary differential equations. Excellent agreement with the shooting technique in the MATLAB (bvp4c) code is demonstrated by a comprehensive numerical comparison conducted for a variety of variables. Investigations are conducted into specific physical characteristics related to temperature and velocity profiles. For several factors, the results are tabulated and graphically analyzed. The velocity plots are increasing with the rise in the Stretching parameter, and volume quantity of copper, while for large values of marangoni parameter, porosity parameter, and Magnetic parameter the opposite trend shows. Larger volume concentrations of copper, larger values of heat source parameter, thermal radiation, and stretching parameter features all increase the temperature pattern, while opposite trends shows for porosity components, magnetic, and marangoni parameter. The graph of streamlines and isotherms are also plotted. The numerical results were compared with previous published work.