QUESTION $1$

$[$Total $50$ Marks$]$

Water, flowing at a rate of $0\mathrm{.}9\frac{l}{m}in$ is to be heated from $10C$ to $80C$ by passing it through a circular tube with an isoflux electrically resistive heater mounted around the external surface of the tube. There are two possible tubes available for the heating process, one with a $1$ mm internal diameter, and another with a $10$ mm internal diameter. Both tubes are $20$ m long and made from a material with negligible surface roughness. The flow may be assumed to be thermally and hydraulically fully developed in both cases.

$($i$)$ For both tube options calculate the frictional pressure drop and the pumping power.

$[20$ marks$]$

$($ii$)$ For both tube Toptions calculate the surface temperature of the tube at the flow outlet.

$[20$ marks$]$

$($iii$)$ List the advantages and disadvantages of both tube options.

$[10$ marks$]$

The following properties may be used for water: $=1000k\frac{g}{m^3}$;$=0\mathrm{.}001$ Pa s; $k=0\mathrm{.}61\frac{W}{m}K$;$c_p=4180\frac{J}{k}gK.$