Abstract
The manuscript's goal is to examine how magneto-hydrodynamic slip flow affects a non-linear stretching cylinder while producing heat and radiation in presence of free stream velocity. Non-linear behavior produces a flow along with Brownian motion and thermophoresis. The shooting technique model was employed to solve moulded equations numerically following the advent of the Runga Kutta Fehlberg approach in MATLAB programming. The attractive pattern combined thermophoresis with a study of the effects of Brownian motion are also discussed. The effects of important fluid characteristics, such as outer velocity, heat radiation, and velocity of slip, thermophoresis, and Brownian motion are studied and represented via graphs and tables. It is revealed that, heat transfer rate falls down by 71.31% with increment in free stream velocity whereas heat transfer rate rises up by 34.43% with rise in Brownian motion parameter. Moreover, skin friction coefficient intensifies with increment in free stream velocity parameter. Current research has major applications in the production of glass fibers, biotechnological field, encompassing power plants, manufacturing of tetra packs, refrigeration systems, medical science, micro-electro-mechanical Systems and in wide variety of industries.