QUESTION TWO: $(30$ marks$)$

$0\mathrm{.}06k\frac{g}{s}$ of hot air flows through un $-$ insulated sheet metal duct of $180$ mm diameter. The air enters the duct at a temperature of $110C$ and after a distance of $4\mathrm{.}5$ m gets cooled to a temperature of $70C.$ The heat transfer coefficient between the outer surface of the duct and cold ambient air at $5C$ is $6\mathrm{.}5\frac{W}{m^2}C.$ Using illustrative sketches, calculate the following:

i$)$ The heat loss from the duct over its $4\mathrm{.}5$ m length.

$(14$ marks$)$

ii$)$ The heat flux and the duct surface temperature at the length of $4\mathrm{.}5$ m $.$

$(16$ marks$)$

Show all the workings.