In the present era of Industry 4.0, automation, and nanotechnology, many industrial applications require the simultaneous control of heat and fluid flow for better efficiency of machines. The polymeric excursion process, manufacturing of plastic films, glass, metallic equipment, all need control over friction forces and heat flow rates. Considering the importance of the subject, the present study deals with the stagnation point flow and heat transfer of water-based nanofluid over a stretching/shrinking sheet with a non-aligned axis of symmetry. The permeable sheet is considered in the presence of a uniform magnetic field. The non-linear partial differential equations governing the flow and heat transfer are converted into non-linear coupled ordinary differential equations using similarity transformations. The resultant equations are solved using “Particle Swarm Optimization” and Runge-Kutta method based hybrid shooting technique. Considering the nanoparticle size, concentration and shape-dependence on physical and thermal properties of nanofluid more realistic aggregation based mathematical models are used for both viscosity and thermal conductivity. Numerical results for the velocity profile, non-alignment function, temperature distribution and local skin friction are discussed with respect to the physical parameters like nanoparticle concentration, nanoparticle size, magnetic field, suction, and stretching/shrinking velocity. The existence of dual solutions are observed for the shrinking velocity parameter , and the practically realizable and stable solutions are filtered out by computing the eigenvalues for the formulated perturbed Eigen problem. The results for the stable solutions unveiled that, by changing the stretching velocity parameter λ < -1 from 0 to 0.5, there is approximately 38% enhancement in heat transfer rate and 42% decrement in skin friction coefficient. Moreover, in the case of shrinking velocity parameter λ = -1.25, with an increase in nanoparticle concentration from 0 to 5%, the skin friction coefficient reduces by 53%, whereas the change in nanoparticle size from 10 nm to 50 nm has a skin friction reduction of only 10%