Laminar forced-convection heat transfer in a concentric annular pipe for a Newtonian fluid with constant properties was analysed by taking the viscous dissipation term into account at constant equal and non-equal heat flux boundary conditions. It can be said that viscous dissipation changes the temperature distributions and plays a very important role in heat transfer characteristics of a concentric annular pipe. The flow in this study was considered to be both thermally and hydrodynamically developed. Temperature distributions and Nusselt numbers were obtained for flows having different aspect ratios and Brinkman numbers. Depending on the boundary conditions, there is considerable effect of the viscous dissipation term on the thermal characteristics of the concentric annular flow. Viscous dissipation has higher effect on the heat transfer characteristic for the case where there is constant and equal heat flow from both walls.