The present study emphases on the three-dimensional (3D) Casson nanofluid flow across a slendering sheet in porous layers by considering the thermophoresis and Brownian motion effect. The proposed mathematical model has a tendency to characterise the effect of the non-uniform heat source/sink. In the present simulation, the graphene–water-based nanoparticles have been used at two different temperatures namely 10 and 50 °C. The nonlinear ordinary differential equations are solved using the Runge–Kutta Feldberg integration method. The characteristics of velocity, temperature and concentration boundary layers in the presence of graphene–water nanoparticles are presented for different physical parameters such as heat source/sink parameter, thermophoresis parameter, Brownian motion parameter, Casson fluid parameter, porosity parameter, volume fraction and velocity power index parameter. Moreover, the friction factor coefficients, Nusselt number and Sherwood number are also estimated and discussed for aforesaid physical parameters. It is found that there is a significant increase in the thermal and concentration boundary layer thickness when the strength of the thermophoresis parameter is increased. In contrast, thermal boundary layer increases with the rise in the Brownian motion parameter, while the reverse trend holds true for concentration field. In addition, the rate of heat and mass transfer rate are higher in case of graphene–water nanoparticle at 50 °C compared to 10 °C temperature. © 2018, The Natural Computing Applications Forum.