This study is an extension of the Graetz problem to include the rarefaction effect, viscous dissipation term and axial conduction with constant-wall-heat-flux thermal boundary condition. The energy equation is solved analytically by using general eigenfunction expansion. The temperature distribution and the local Nusselt number are determined in terms of confluent hypergeometric functions. The effects of the rarefaction, axial conduction and viscous dissipation on the local Nusselt number are discussed in terms of dimensionless parameters such as the Knudsen number, Peclet number and Brinkman number. (C) 2009 Elsevier Masson SAS. All rights reserved.