Convection heat transfer is assessed for laminarly flowing liquid water through graphene nanochannels via molecular dynamics (MD) simulations. The use of MD simulations allows for direct assessment of the minute details and mechanisms influencing overall heat transfer behaviors within our study; despite the presence of unrealistic axial conduction from temperature resetting and periodic boundary conditions within MD, hydrodynamically and thermally fully-developed water flow conditions are observed. It is indicated that the physics of convective heat transfer deviate from traditional macroscale theory as the no-slip boundary condition is violated with dimensional sizes descending towards the nanoscale; investigation into hydrodynamic slip and thermal slip, termed microscopic mechanisms, is performed for their influence on nanoscale convective outcomes. The parameters of graphene-water interaction strength, channel height, water velocity, and wall temperature are manipulated to evaluate resultant convection behaviors while comparing the effects of differing magnitudes of microscopic mechanisms imposed under various test conditions. This study finds microscopic interfacial mechanisms to significantly augment momentum and thermal behaviors and thus the conduct of convective heat transfer. Hydrodynamic and thermal slip are strongly correlated in all test case scenarios with the exception of velocity manipulation; the influence of thermal slip is found to dominate over that of hydrodynamic slip as surface advection is insignificant in high heat flux environments. Convective performance correlation is suggested as the ratio of thermal slip length to system size.