A $1-2($one shell pass, two tube pass$)$ shell and tube heat exchanger $($STHE$)$ contains $86$ tubes, $1$ in Outer Diameter $($OD$)16$ BWG $($British Wire Gauge$)$ stainless steel tubes arranged in staggered pitch with longitudinal and transverse pitches of $S_L=S_T=1\mathrm{.}25$ inches. This heat exchanger will be used to heat $4\mathrm{.}2k\frac{g}{s}$ of liquid water from $52C$ to $80C.$ Heating will be accomplished by steam having a gauge pressure of $97\mathrm{.}2$ kPa and condensing in the shell side. The heat transfer coefficient for the shell side will be assumed to be equal to $12000\frac{W}{m^2}.K..(1in=2\mathrm{.}54cm$;$P_{\text{a}\text{t}\text{m}}=101\mathrm{.}325$kPa $)(50$ points$)$

a$)$ Find the required steam mass flow rate for this process

B$)$ If the proposed length of the STHE is $5$ m $,$ is this SHTE satisfactory for your requirement? Your reply should be based on calculations.

How we can calculate the U