Water is flowing in a smooth pipe of diameter D. A section of this pipe having a length of L is…

Water is flowing in a smooth pipe of diameter D. A section
of this pipe having a length of L is heated. Water at the inlet to the heated
section has a temperature of Tf1. Water temperature at the exit of
the heated section is Tf2. The heated section of the pipe wall is
maintained at a constant heat flux so that a constant temperature difference of
_Ts = Ts – Tf exists between the wall
and the bulk water temperature. Show that for turbulent flow in the pipe and a
specified heated length and pipe diameter, water temperature at the exit of the
heated section is given by: