In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, TiO2, and, Ag as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Homotopy Analysis Method (HAM) approach is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. A detailed research is also performed in order to investigate the influences of relevant constraints on the rates, momentum and heat transport for both TiO2 + Ag + Blood and TiO2 + Blood. One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in case of the hybrid nanofluid enhance the thermal conductivity from 5.8% to 11.947% and for the same value of the nanoparticle volume fraction in case of nanofluid enhance the thermal conductivity from 2.576% to 5.197%.