A $1-2$ shell$-$and$-$tube heat exchanger is used to cool condensed steam at a rate of $105$ kg$/$h from $90$ c$\backslash$deg to $50$ c$\backslash$deg using cooling water available at $10$ c$\backslash$deg The operating conditions do not permit exit temperatures of cooling water exceeding $40^\{\backslash$circ$\}$C$.$ Select a counter flow heat exchanger with $32$ inch OD tube, $16$ BWG$,$ triangular pitch and $8$ feet long tube arrangement with a tube thickness of $0\mathrm{.}083$ inch. By referring to the data sheet and with suitable assumptions, Evaluate the following:

$($i$)$ Mass flow rate of water;

$($ii$)$ Corrected LMTD

$($iii$)$ Total number of tubes;

$($iv$)$ Tube side Reynolds number;

$($v$)$ Inside heat transfer coefficient;

$($vi$)$ Shell side Reynolds number

$($vii$)$ Shell side heat transfer coefficient;

$($viii$)$ Overall heat transfer coefficient;

$($ix$)$ Inside heat transfer area

$($x$)$ Actual heat transfer area

$($xi$)$ Actual design overall heat transfer coefficient