Water is flowing through a tube having an inside diameter of $5$ mm at a velocity of $0\mathrm{.}0125$ m$/$s$.$ At the inlet of the pipe the water has an average temperature of $588\mathrm{.}8$ K and at the outlet of the pipe the water has an average temperature of $477\mathrm{.}6$K$.$ The inside wall temperature is held constant at $477\mathrm{.}6$K by steam condensing outside the tube wall. The pipe is $8$ cm in length. Calculate the heat transfer coefficient AND the heat flux.