A system for heating water from an inlet temperature of Tm$,$i $=20\backslash$deg C to an outlet temperature of Tm$,$o $=60\backslash$deg C involves passing the water through a thick$-$walled tube having inner and outer diameters of $20$ and $40$ mm$.$ The outer surface of the tube is well insulated, and electrical heating within the wall provides for a uniform generation rate of q $10$ W$/$m $63=.1.$ For a water mass flow rate of m $=0\mathrm{.}1$ kg$/$s$,$ how long must the tube be to achieve the desired outlet temperature? $2.$ If the inner surface temperature of the tube is Ts $=70\backslash$deg C at the outlet, what is the local convection heat transfer coefficient at the outlet?