This is a theoretical exploration of the magnetohydrodynamic Carreau fluid in a suspension of dust and graphene nanoparticles. Graphene is a two-dimensional singe-atom thick carbon nanosheet. Due to its high thermal conductivity, electron mobility, large surface area and stability it has remarkable material, electrical, optical, physical and chemical properties, in this study a simulation is performed by mixing of Graphene+water and Graphene+Ethylene glycol into dusty non-Newtonian fluids. Dispersion of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation etc. Graphene+water and Graphene+Ethylene glycol mixtures are significant in optimizing the heat transport phenomena. Initially arising set of physical governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) with the assistance of similarity transformations. Consequential highly nonlinear ODEs are solved numerically through Runge-Kutta Fehlberg Scheme (RKFS). The computational results for Non-dimensional temperature, velocity, profiles are presented through graphs. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameter obtained. We also validated the present results with previous published study and found to be highly satisfactory. The formulated model in this study reveals that heat transfer rate and wall friction is higher in mixture of graphene +Ethylene glycol when compared to graphene +water.
**TOPICS:**
Fluids, Dust, Nanoparticles, Graphene, Unsteady flow, Heat flux, Heat transfer, Friction, Heat, Temperature, Stability, Magnetohydrodynamics, Simulation, Electron mobility, Thermal conductivity, Chemical properties, Non-Newtonian fluids, Carbon, Differential equations, Transport phenomena, Biosensors, Cancer, Atoms, Partial differential equations, Stem cells, Imaging, Biocompatibility