In this numerical study, steady laminar conjugate heat transfer of in a tube subjected to an axially varying heat flux at the outer wall is investigated using the finite volume method. The effects of the thermal conductivity ratio, the diameter ratio and the dimensionless amplitude of the axially varying or periodic heat flux on the local and mean Nusselt numbers as well as on the temperature and the interface heat flux distribution are determined for a range of corresponding parameters. Results obtained for some limiting cases are found to be in a good harmony with those given in the literature. (C) 2014 Elsevier Ltd. All rights reserved.