Q$3.$ A shell$-$and$-$tube heat exchanger with $1-$shell pass and $14-$tube passes is used to heat water in the tubes with geothermal steam condensing at $k\frac{J}{k}g)$ on the shell side. The tubes are thin$-$walled and have a diameter of $2\mathrm{.}4$ cm and length of $3\mathrm{.}2$ m per pass. Water $)=(4180\frac{J}{k}g.C$ enters the tubes at $22C$ at a rate of $3\mathrm{.}9k\frac{g}{s}.$ If the temperature difference between the two fluids at the exit is $46C,$ determine $($a$)$ the rate of heat transfer, $($b$)$ the rate of condensation of steam, and $($c$)$ the overall heat transfer coefficient.