The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k(sf), and when k(sf) <= 25 the increasing tube thickness and the decreasing k(sf) could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux. (C) 2010 Elsevier Ltd. All rights reserved.