A combined numerical and analytical solution procedure is proposed to examine the conjugate heat transfer for laminar flow in a pipe. This simple and rather general procedure has the capability of handling the constant temperature, the constant heat flux, and the convection heat transfer boundary conditions of the pipe outer surface without detailed program modification. The results of the present work and fully analytical solution are compared to test the proposed solution procedure. The general trend of predicted results is in agreement with the analytical solution, but the quantitative differences between them is considered to be acceptable from the numerical point of view. Variation in the local Nusselt number and in the the wall and local mean fluid temperature across the axial direction is strongly dependent on the pipe wall thermal conductivity and the boundary condition at the outer surface of the pipe wall. Two non-dimensional numbers, the thermal conductivity ratio k(s)/k(f) and the Blot number, are found to be controlling parameters for the effect of wall axial heat conduction on the heat transfer characteristics.