The development of the temperature profile in the flow is driven by heat transfer determined conditions on the inside surface of the pipe and the fluid. Heat transfer may be a result of a constant heat flux or constant surface temperature. Constant heat flux may be caused by joule heating from a heat source, like heat tape, wrapped around the pipe. Constant temperature conditions may be produced by a phase transition, such as condensation of saturated steam on a pipe surface.
Newtons law of cooling describes convection, the main form of heat transport between the fluid and the pipe:
where
*  is the heat flux into the fluid,
*  is the convection coefficient,
*  is the surface temperature, and
*  is the mean stream temperature.
Constant surface heat flux result in  becoming a constant as the flow develops and constant surface temperature results in  approaching zero.