In this study, an analysis of laminar forced convection in a pipe for a Newtonian fluid with constant properties is performed by taking the viscous dissipation into account. This part of the study, Part 1. examines both hydrodynamically and thermally fully developed flow. Two different thermal boundary conditions are considered: constant heat flux (CHF) and constant wall temperature (ONIT). Either wall heating (the fluid is heated) or wall cooling (the fluid is cooled) is considered. The temperature distribution and Nusselt numbers are analytically determined as a function of the Brinkman number. (C) 2004 Elsevier Ltd. All rights reserved.