In this study, we analyzed the time-dependent, 2D, inclined magnetohydrodynamics mixed convection stagnating point flow of nanoparticle toward a permeable stretchable surface with radiative heat effect. Four different types of water-based nanomaterials, namely titanium dioxide T i O 2 , copper C u , aluminum oxide A l 2 O 3 , and copper oxide C u O are analyzed in this investigation. Numerous engineering disciplines, including energy systems, material processing, thermal management, and environmental engineering, can benefit greatly from research in mixed convection, MHD, and nanofluids. The boundary layer representations of the dominating partial differential equations PDEs are converted into strong nonlinear ordinary differential equations ODEs utilizing similarities approach. The ODEs are computed numerically employing 4th order Runge–Kutta methodology-based shooting scheme. Few special situations, a remarkable alignment is determined between the present study and the outcomes obtained in the existing research. The impact of numerous pertinent variables on the prominent quantities such as velocity, temperature and concentration distributions, drag friction coefficient and heat transport are demonstrated graphically. It is noticed that the velocity and thermal curve decrease as the nanoparticle volume friction factor increases. Moreover, it is analyzed that higher values of nanoparticle concentration diminishes the velocity and temperature distributions.

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.