$7\mathrm{.}75$ An air$-$cooled steam condenser is operated with air in cross flow over a square, in$-$line array of $400$ tubes $($NL $=$ NT $=20),$ with an outside tube diameter of $20$ mm and longitudinal and transverse pitches of SL $=60$ mm and ST $=30$ mm$,$ respectively. Saturated steam at a pressure of $2\mathrm{.}455$ bars enters the tubes, and a uniform tube outer surface temperature of Ts $=390$ K may be assumed to be maintained as condensation occurs within the tubes.

$($a$)$ If the temperature and velocity of the air upstream of the array are Ti $=300$ K and V $=4($ m$)/($s$),$ what is the temperature To of the air that leaves the array? As a first approximation, evaluate the properties of air at $300$ K$.$

$($b$)$ If the tubes are $2$ m long, what is the total heat transfer rate for the array? What is the rate at which steam is condensed in k$($g$)/($s$)?$

$($c$)$ Assess the effect of increasing NL by a factor of $2,$ while reducing SL to $30$ mm$.$ For this configuration, explore the effect of changes in the air velocity.