Question $3(10$ marks$)$

$k=0\mathrm{.}03$

The pipeline transports heated crude oil at a mean bulk temperature of $45C$ and an average velocity of $1\mathrm{.}5\frac{m}{s}.$ The pipeline has a radius of $2\mathrm{.}5$ m $.$ The metallic pipe wall is very thin and its thermal resistance can be neglected. The pipe is insulated with a rubber shell that has a thermal conductivity k of $0\mathrm{.}03\frac{W}{m}.K$ and a thickness of $2\mathrm{.}5$ cm A mild breeze blows cold air across the pipeline, which has a temperature of $T_{\text{a}\text{i}\text{r}}=0C$ and a velocity of $u_{\text{a}\text{i}\text{r}}=5\frac{m}{s}.$

The diagram below illustrates a segment of the pipeline.

$\backslash$table$[[$Properties Crude Oil @ $45C,$Properties of Air @ $0C$