$[$E$5\mathrm{.}4$ Katoh $2$nd $(2015)]$ Sizing a double$-$pipe heat exchanger. Milk, flowing at $2,000$ L$/$h

through the stainless steel inner tube $(40$ mm i$.$d$.,2$ mm thick$)$ of a double tube$-$type heater, I

to be heated from $10$ to $85\backslash$deg C by saturated steam condensing at $120\backslash$deg C on the outer surface

of the inner tube. Calculate the total length of the heating tube required.

Additional data.

$$ Milk properties: $=0\mathrm{.}949$ kcal$/$kg$\backslash$deg C; $=1,030$ kg$/$m$3$; $=0\mathrm{.}457$ kcal$/$h$$m$\backslash$deg C; $=$

$0\mathrm{.}0112$ g$/$cm$$s

$$ Steam$-$side coefficient: $=10,000$ kcal$/$h$$m$2\backslash$deg C

$$ Stainless steel: $=15$ W$/$m$$K