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This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

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The importance of including an electromagnetic actuator as a moving boundary on the dissipative flows of weakly conducting fluids had led to many published facts. But, nothing is known on the generalized differential quadrature analysis of magnetohydrodynamics over a Riga plate with emphasis on the case of viscous dissipation and space-dependent heat source.After deriving the simplified boundary layer equation that models the transport phenomenon, appropriate variables were used to non-dimensionalize and parameterize the partial differential equations. Thereafter, the resulting set of ordinary differential equations was solved numerically by applying a powerful differential quadrature algorithm. Based on the outcome of the simulation, it can be concluded that the viscous frictional effect can be minimized at the Riga plate either by weakening the suction process or by heightening the magnetic parameter. Moreover, the Lorentz forces have a hastening effect on the fluid motion, in the case when those magnetic causes are directed in the same sense of the developed flow.