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

For the missing data or datasheet make assumptions for it here is my assumption

$-$ The specific heat capacity of water is $4\mathrm{.}18$ kJ$/$kg$$K

$-$ The thermal conductivity of the tube material is $16$ W$/$m$$K $($assuming stainless steel$)$

$-$ The viscosity of water at the average temperature is $0\mathrm{.}000653$ kg$/$m$$s

$-$ The density of water at the average temperature is $995$ kg$/$m$^3$

$-$ The Prandtl number of water at the average temperature is $5\mathrm{.}83$

Given data:

$-$ Mass flow rate of condensed steam: $105$ kg$/$h

$-$ Inlet temperature of condensed steam: $90\backslash$deg C

$-$ Outlet temperature of condensed steam: $50\backslash$deg C

$-$ Inlet temperature of cooling water: $10\backslash$deg C

$-$ Maximum outlet temperature of cooling water: $40\backslash$deg C

$-$ Tube outer diameter: $3/2$ inch $(0\mathrm{.}0127$ m$)$

$-$ Tube thickness: $0\mathrm{.}083$ inch $(0\mathrm{.}00211$ m$)$

$-$ Tube length: $8$ feet $(2\mathrm{.}438$ m$)$

$-$ Tube pitch: triangular

Check if my assumptions suitable and solve according to that