Question $(3)$: $[15$ points$]$

Saturated process steam at $)=(2257\frac{kJ}{k}g$ is condensed in a shell$-$and$-$tube heat exchanger $($one shell, two tube passes$).$ Cooling water enters the tubes at $15C$ with an average velocity of $3\mathrm{.}5\frac{m}{s}.$ The tubes are thin walled and made of copper with a diameter of $14$ mm and length of $0\mathrm{.}5$ m $.$ The convective heat transfer coefficient for condensation on the outer surface of the tubes is $21,800\frac{W}{m^2}K.$ Take water properties at $20C$ t

$($a$)$ Find the number of tubes$/$pass required to condense $2\mathrm{.}3k\frac{g}{s}$ of steam.

$($b$)$ Find the outlet water temperature.

$($c$)$ Find the maximum possible condensation rate that could be achieved with this heat exchanger using the same water flow rate and inlet temperature.