To analyze the fluid flow and thermal characteristics in a nanoscale system the planar Poiseuille flow of a Lennard-Jones liquid through parallel plates formed by fixed atoms is studied using nonequilibrium molecular dynamics simulations. The roles of important simulation parameters, such as the channel width, the magnitude of external field, the temperatures of the top and bottom plates, and the interaction potential parameter between fluid and wall atoms, which affect flow patterns and heat transfer rate inside the channel are investigated. Using the mesoscopic method, the integration of the Navier-Stokes equations and the energy conservation equation, hydrodynamic profiles are obtained. Linear constitutive relations give the basic transport coefficients such as viscosity and thermal conductivity from the number density, the velocity, and the temperature profiles. Under the various simulation conditions, interesting phenomena deviated from the continuum predictions have found. When the channel width is in the order of a few molecular diameters, the velocity profile shows oscillating shape, but the no-slip condition is still satisfied. As the magnitude of external field increases, the streaming velocity profiles exhibit large slip length near the walls. The strength of wall-fluid interaction, however, enhances or restrains the velocity slip. The temperature profiles always show large discontinuities near the walls meaning poor wall-fluid thermal interaction. This has not changed with the different wall temperature. Calculated Nusselt number is mostly lower than the continuum solution. However, the use of classical behavior for fitting the simulation data gives the values of Nusselt number very close to the continuum solution.