A hybrid atomistic-continuum method devoted to the study of multi-scale problems is presented. The simulation domain is decomposed into three regions: the bulk where the continuous Navier-Stokes and energy equations are solved, the neighbourhood of the wall simulated by the Molecular Dynamics and the overlap region which connects the macroscopic variables (velocity and temperature) between the former two regions. For the simulation of long micro/nano-channels, we adopt multiple molecular blocks along the flow direction, what enables the accurate capture of the velocity and temperature variations from the inlet to the outlet. The validity of the hybrid method is shown by comparisons with both analytical solutions and Finite Volume simulations. This method is then applied successfully to the study the hydrodynamic and thermal development of a liquid flow in a long micro/nano-channel.