▎ 摘　　要

Nowadays graphene is emerging as one of the most exciting nanomaterial due to its continuous 29 electrically conducting behavior even at zero carrier concentration. With this initiation, we investigate the flow of magnetohydrodynamic (MHD) water, water-30%EG, water-50%EG, graphene nanofluid over a stretched surface with thermal convection, and zero mass flux conditions and velocity slips comprising motile microorganisms and nanoparticles. Thermal radiation and Arrhenius activation energy are also be under consideration. The governing fluid equations are solved by Homotopy analysis method (HAM) and computed numerically with shooting technique after employing appropriate transformations. The consequence of numerous physical parameters on velocity, concentration, temperature, and density of motile microorganisms graphs as well as table are used for ethylene glycol based and water-based graphene nanoparticles. Additionally, numerically analyze the designed skin friction, Nusselt number, Sherwood number, and density of motile microorganisms. It is observed that due to heat generation and temperature the improvement of the nonlinear convection variable improves the wall friction. It is also originate that increasing the volume fraction of nanoparticles effectively boosting the thermal conductivity of water-50%EG when compared with water-30%EG and water nanofluids. Ethylene glycol based graphene nanofluids take less time for process as compared to water based nanofluids.