A $1-2$ shell$-$and$-$tube heat exchanger is used to cool condensed steam at a rate of $105$ kg$/$h from $108$C to $68$C using cooling water available at $28$C$.$ The operating conditions do not permit exit temperatures of cooling water exceeding $40\backslash$deg C$.$ Select a counter flow heat exchanger with $$ 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