This research engages a non-similarity analysis to investigate the effects of ternary hybrid-nanoparticles in magnetohydrodynamics (MHD) Darcy-Forchheimer fluid stream stimulated by a porous stretching sheet. The ternary nanoparticles under study are copper, titanium and carbon nanotubes, whereas water is taken as a base fluid. In addition, the heat equation is modelled with the various pertinent factors such as thermal radiation, viscous dissipation, non-uniform, heat flux, and Joule heating. Following the mathematical formulations, the differential equations are non-dimensionless through a non-similarity conversion. Additionally, the local non-similarity approach is utilized to transform non-similar partial differential equations (PDEs) into ordinary differential equations (ODEs). The resulting set of reduced ordinary differential equations are solved numerically using the bvp4c MATLAB tool. To enhance the understanding of emerging physical model, key factors are comprehensively illustrated graphically and in tabular form. Moreover, the pertinent engineering parameters, namely skin friction and Nusselt number, are systematically portrayed in tabular form concerning the significant factors.

Hybrid nanofluids are recognized as advanced nanofluids due to their superior thermal properties and the potential advantages they offer in boosting heat transfer rates. Keeping the potential properties of hybrid nanofluid, this study aims to discuss the numerical solution for the the micro-rotating tangent hybrid nanofluid induced porous stretchable surface. Additionally, the consequences of suction/injection phenomena is also incorporated at the stretching plate in the presence of inclined MHD. In order to compute the micro-rotation effects of the tangent hyperbolic fluid the nonlinear micro-polar differential equation is introduced in the governed model. Moreover, the heat transfer equation is equipped with the several body forces like; Joule heating, heat source/sink and thermal slip factor. The above model is mathematically formulated. The mathematical formulation yields a set of interconnected non-linear partial differential equations. To derive a similarity solution, we introduce similarity variables. The numerical solution to the system of differential equation is achieved by engaging the Runge-Kutta-Fehlberg 45 (RKF-45) method, in conjunction with the shooting method. Graphical representations are employed to demonstrate the physical significance of relevant parameters. The investigation presents and discusses the impact of various parameters on linear velocity, angular velocity and temperature profiles. It is anticipated that a rise in both permeability and the magnetic parameter will lead to a significant decrease in the skin friction coefficient. Furthermore, as the Eckert number and heat source parameter reach substantial values, an increase in the heat transfer rate is foreseen.