A $30cm-OD$ and $100cm$ long horizontal steam pipe has an outer surface temperature of $500K$ and is in still air at $300K.$ Calculate the average heat transfer coefficient and the convective heat loss from the pipe. The air properties at the mean fluid temperature $\frac{500+300}{2}=400K$ are as follows.

$k=0\mathrm{.}0331\frac{W}{m}-K,v=25\mathrm{.}5{10}^{-6}\frac{m^2}{s},Pr=0\mathrm{.}69.$ Assume air to be an ideal gas. Use a suitable correlation for your calculation.

$\frac{?}{\text{b}\text{a}\text{r}}(N)u_D=0\mathrm{.}36+\frac{0\mathrm{.}518R{a}_D^{\frac{1}{4}}}{[1+(\frac{0\mathrm{.}559}{P}r{)}^{\frac{9}{6}}{]}^{\frac{4}{9}}}$; for ${10}^{-6}{10}^9$

Repeat your calculation for the same cylinder kept in vertical condition, keeping all other given parameters the same. Use a suitable correlation, as given below, for your calculation.

$\frac{D}{L}\frac{35}{G{r}_L^{\frac{1}{4}}}\frac{?}{\text{b}\text{a}\text{r}}(N)u_L=0\mathrm{.}59R{a}_L^{\frac{1}{4}}$ for ${10}^4$

Comment $on$ heat transfer rates and convective heat transfer coefficients obtained $in$ horizontal and vertical cases.

The above two correlations for vertical cases are actually valid for vertical flat plates. These correlations also apply $to$ vertical cylinder provided the following condition $is$ satisfied. Check the validity.

$\frac{D}{L}\frac{35}{G{r}_L^{\frac{1}{4}}}$