A double$-$pipe heat exchanger must be designed to evaporate $2\mathrm{.}5k\frac{g}{s}$ of water at $120C.$ The heating is to be accomplished by passing hot oil, available at $180C,$ through the inner pipe of the heat exchanger. The convective heat transfer coefficient on the evaporation side $($in the annulus$)$ is $h_0={10}^{5}W{m}^{-2}{K}^{-1}.$ The inner pipe is a $5-cm$ thin$-$walled.

$($a$)$ Compute the oil flow rate if the oil leaves the exchanger at $140C.(2$ points$)$

$($b$)$ Calculate the required area of heat transfer. $(5$ points$)$

Suppose that after a long operating time, the fouling factor is ${10}^{-4}K\frac{m^2}{W}.$ Given the same design flowrate of oil calculated in $($a$)$ and oil inlet temperature $(180C),$

$($c$)$ Evaluate the new oil leaving temperature. $(3$ point$)$

Please use the following thermo$-$physical properties:

For the oil, at $160C,=806kg{m}^{-3},lo{n}_p=2\mathrm{.}471kJk{g}^{-1}{K}^{-1},=2\mathrm{.}4{10}^{-4}$Pas,$k=0\mathrm{.}132W{m}^{-1}{K}^{-1},$ and $Pr=4$:$5.$

For water$/$steam$,$ the latent heat of vaporisation at $120C$ is $2203k\frac{J}{k}g$

End of Questions