QUESTION $2(12$ MARKS$)$

For laminar flow in a pipe the convection heat transfer coefficient can be

calculated by:

$=3\mathrm{.}66+\frac{0\mathrm{.}668(\frac{D}{L})*Re*Pr*G{r}^{0\mathrm{.}3}}{1+0\mathrm{.}04(\frac{D}{L})}Re*Pr$

For turbulent flow the following expression is true:

$=0\mathrm{.}023R{e}^{0\mathrm{.}8}P{r}^{0\mathrm{.}3}G{r}^{0\mathrm{.}16}.$ If the $Re>2600,$ the flow is turbulent.

A pipe internal diameter $50$ mm is $10$ m long. It conveys air at a rate of

$0\mathrm{.}2\frac{m^3}{s}$ with the following properties:

$=0\mathrm{.}543\frac{(kg)}{m^3}$;$C_P=\frac{1029\mathrm{.}5(J)}{(kg)}*K$;$=2\mathrm{.}67{10}^{-5}\frac{(kg)}{(m)*(s)}$;$k=0\mathrm{.}0404\frac{(W)}{(m)*(K)}$

Calculate:

a$)$ Convection heat transfer coefficient if $=1\mathrm{.}25{10}^{-2}{K}^{-1}.$

b$)$ Heat loss by convection if the inside surface temperature of the pipe

is $350$ K and the air in the pipe is at $680$ K $.$