In this study, steady laminar forced convection slip flow in a microtube subjected to an axially varying heat flux is investigated numerically using the finite volume method. The classical Graetz problem is considered, which can be named as micro-Graetz problem for the microscale condition. The viscous dissipation effect is included in the analysis. The problem studied can be also named as micro-Graetz-Brinkman problem. The slip flow regime is considered by incorporating the velocity slip and temperature jump conditions at wall. The effects of rarefaction, the viscous dissipation and the dimensionless amplitude of the axially varying or periodic heat flux on the local and mean Nusselt numbers as well as on the wall and bulk temperatures are obtained for some specific ranges of corresponding parameters. These effects are found to be interactive. It is disclosed that the mean Nusselt number decreases with an increase in the amplitude. (C) 2015 Elsevier Ltd. All rights reserved.