Investigation to evaluate axial wall heat conduction has been conducted for heat transfer in a laminar flow circular tube with two classical thermal boundary conditions at the outside wall. The tube ends are either adiabatic or with heat losses. The simulation is three-dimensional with various wall materials, wall thicknesses and tube lengths. A wide range of Peclet number from 7 to 14,000 is considered. Three evaluation criterion parameters including the axial conduction number, the modified axial conduction number, and the temperature gradient number are comprehensively studied to quantify the influence of axial wall heat conduction. Under the constant outside wall temperature boundary condition, the temperature gradient number is presented to assess the relevance of the axial wall heat conduction. The approximate range of the effect of axial wall heat conduction on the local Nusselt number for the fully developed flow is also obtained. (C) 2015 Elsevier Ltd. All rights reserved.