Fully developed heat flow in a pipe can be considered in the following situation. If the wall of the pipe is constantly heated or cooled so that the heat flux from the wall to the fluid via convection is a fixed value, then the bulk temperature of the fluid steadily increases or decreases respectively at a fixed rate along the flow direction.
An example can be a pipe entirely covered by an electrical heating pad with the flow being introduced after a uniform heat flux from the pad is achieved. At some distance away from the entrance of the fluid, fully developed heat flow is achieved when the heat transfer coefficient of the fluid becomes constant and the temperature profile has the same shape along the flow. This distance is defined as the thermal entrance length, which is important for engineers to design efficient heat transfer processes.