please do not use chat gpt or ai$.$ write neatly and show your working, thank you. Determine the overall heat transfer coefficient and determine the percentage over$-$design or under$-$design.

Calculate the pressure drop on both the tube side and shell side of the heat exchanger and specify whether these are within the limits$.$

A process stream, with an inlet temperature of $110C$ is to be cooled to $48C.$ The process stream has a flowrate of $33000k\frac{g}{h}.$ Cooling water is available at $25C$ for cooling purposes. The cooling water outlet temperature should not exceed $36C.$

The physical properties of the process and cooling water stream are as follows:

$\backslash$table$[[,$Process stroam,Cooling water$],[$Density $($kg$*$m$^(-3)),732,992],[$Heat capacity $($J$*$kg$^(-1)*$K$^(-1)),3320,4190],[$Viscosity $($N$*$s$*$m$^(-2)),3\mathrm{.}7\backslash$times $10^(-4),8\mathrm{.}0\backslash$times $10^(-4)],[$Thermal conductivity $($W$*$m$^(-1)*$K$^(-1)),0\mathrm{.}136,0\mathrm{.}613],[$Fouling coefficient $($W$*$m$^(-2)*$K$^(-1)),6000,3000],[$Allowable prossure drop $($kPa$),60,60]]$

Tubes $(k=45(W)-m^{-1}*K^{-1})$ with an outside diameter $(OD)=19\mathrm{.}05mm,$ wall thickness of $2mm$ and length $=4\mathrm{.}88m,$ are available. A triangular pitch $1\mathrm{.}25OD$ has been selected.