In this study, laminar forced convective heat transfer of a Newtonian fluid in a micropipe is analyzed by taking the viscous dissipation effect, the velocity slip and the temperature jump at the wall into account. Hydrodynamically and thermally fully developed flow case is examined. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Either wall heating (the fluid is heated) case or wall cooling (the fluid is cooled) case is examined. The Nusselt numbers are analytically determined as a function of the Brinkman number and the Knudsen number. Different definitions of the Brinkman number based on the definition of the dimensionless temperature are discussed. It is disclosed that for the cases studied here, singularities for the Brinkman number-dependence of the Nusselt number are observed and they are discussed in view of the energy balance. (c) 2005 Elsevier Ltd. All rights reserved.