A copper pipe $($k $=400$ W$$m$1$K$1)$

is used for carrying hot water entering at $58$C$.$ The

pipe diameter is $18$ mm and the wall thickness is $2$

mm$.$ The pipes are $8$ m long. The pipe is exposed

to the surrounding air at $5$C providing a natural

convection coeffcient of $3\mathrm{.}6$ W$$m$2$K$1.$ Estimate

the heat loss rate as well as water temperature at

the exit when the water flow rate is $10$ gpm $(1$ gal

$=3\mathrm{.}785$ L$).$ The relevant water properties at the esti$-$

mated average temperature of $32$C are: $996$ kg$$m$3$;

$4180$ J$$kg$1$K$1$; $0\mathrm{.}6184$ W$$m$1$K$1$; with a Pr $=$

$5\mathrm{.}18.$