It is necessary to preheat $150,000k\frac{g}{h}$ crude oil from $25C$ to $57C,$ with the bottom product from a distillation column. The product at $129,000k\frac{g}{h}$ is to be cooled from $146$ to $107C.$ There is available a tubular exchanger with steel tubes with an inside swell diameter of $23\frac{1}{4}in.,$ having one pass on the shell side and two passes on the tube side. It has $324$ tubes, $\frac{3}{4}in.$ OD$,$ BWG $14,12ft$ long arranged on a $1-$in$-$square pitch and supported by baffles with a $25$ percent cut, spaced at $9$in$.$ intervals. Would this exchanger be suitable; that is$,$ what is the allowable fouling factor? The average properties are shown in the following table.

Make appropriate conclusions with sufficient validation.

$\backslash$table$[[$Property$,$Product, outside tubes,Crude, inside tubes$],[$c$\_($p$)($J$/$g$*\backslash$deg C$),2\mathrm{.}20,1\mathrm{.}99],[\backslash$mu $($cp$),5\mathrm{.}2,2\mathrm{.}9],[$k$($W$/$m$*\backslash$deg C$),0\mathrm{.}119,0\mathrm{.}137],[\backslash$rho $($kg$/$m$^(3)),867,825]]$