The development of nanotechnologies has motivated the study of flows with suspended nanoparticles to enhance the base fluid’s heat transfer coefficient. This innovative technique has been extensively used during the last decade. In this work, laminar, unsteady and developed flow with heat transfer using water-Cu nanofluid between two parallel plates was studied numerically by applying the statistical numerical Lattice Boltzmann method with Bhatnagar Gross Krook (BGK) approximation. The flow close to the thermodynamic equilibrium in the presence of a hydrophobic surface was considered. Velocity slip and temperature jump on the walls were estimated by Maxwell’s first order boundary conditions. The thermal conductivity and the dynamic viscosity of the nanofluid were calculated based on experimental correlations where the Brownian motions effect and the diameter of the nanoparticles can be taken into consideration. The local and average Nusselt number variation were investigated and the influence of the velocity slip and the temperature jump coefficients, the nanoparticle volume fractions, the diameter of the nanoparticles and the Reynolds number were considered.