The current procedure is to examine the effects of wall axial conduction on heat transfer for laminar flow in pipes. The procedure combines the analytical solution of the problem of the fluid region with a numerical approximation of conduction of the solid wall and has the capability of handling the step change in outer surface boundary condition and wall thermal conductivity. The pipe under investigation is divided into two sections: non-heated and heated ones, and the conductivities of the sections are assumed to be different. The obtained results show that the local heat transfer parameters such as wall and fluid temperatures, and Nusselt number are greatly influenced by the step change in wall conductivity and the partially heated wall arrangement. The results of the present study may have applications in the design of heat transfer devices.