Abstract: The current article aims to develop a theoretical model for electromagnetohydrodynamic flow over a stagnation point flow of hybrid nanofluid with nonlinear thermal radiation and non-uniform heat source/sink. This mathematical model is implemented to blood-based nanofluids for two different nanoparticles. The linear and nonlinear thermal radiations are chosen to be varying the purpose, to see the temperature modifications in this model. For simplifying the governing flow equations, appropriate conversions are taken into interpretation to switch appropriately the ensuing partial differential equations to ordinary differential equations. The rehabilitated mathematical formulations are solved numerically via an effective procedure based on RK 4th order via a shooting scheme. The consequences of sundry variables are established via pictorial representations. The attained outcomes of this model meticulously match with those existing in the literature for some limiting conditions. The outcomes of this study are of repute in the valuation of the effect of some important design parameters on heat transfer and therefore in the optimization of industrial processes. This theoretical model consists of the EMHD and thermal radiation cases through blood flow and it has a significant attitude on the magnetic delivery in blood, the therapeutic procedure of hyperthermia, magnetic endoscopy, understanding/regulating blood flow, transport of complex bio-waste fluids and heat transfer in capillaries, etc. Graphic abstract: Schematic diagram of the physical problem [Figure not available: see fulltext.]. © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.