The extensive usage of blood-based hybrid-nanoparticles in blood clotting, tissue engineering and also biomedical scenarios has made them essential in the area of blood motion. Both silver (Ag) and molybdenum disulfide (MoS2) nanoparticles can be considered safe and stable for human application. The objective of this examination is to figure out the dual solutions and stability examination of blood-based hybrid nanofluid movement on the top of the unsteady permeable curved stretching/shrinking surface, using \(\text{Ag}\) and \({\text{MoS}}_{2}\) nanoparticles dispersed in blood. The analysis also considers the effects of porous medium, magnetic flux, Joule heating, exponential external heat source/sink and also viscous dissipation components remain intended in the study. The influence of a medium of porous is captured by applying Darcy–Forchheimer model. Using the transformation of similarity variable, governing nonlinear partial differential equations will be converted into system of nonlinear differential equations. The converted nonlinear differential equations are solved numerically by bvp4c problem solver in MATLAB software. The properties of the amount of hybrid nanoparticles, fluid suction or injection, curvature, unsteadiness and stretching/shrinking constraints on skin friction and local Nusselt number as well as the outlines of velocity and temperature are given in this paper. Since the fluid flow has two kinds of solution, stability examination is performed to discovery a stable point, that is, a physically realizable solution. The discovery reveals stable region for first solution and unstable region for second solution. Moreover, the solution of upper region has a positive eigenvalue and the solution of lower region has a negative one.
