Design of Distillation Column and Heat Exchanger

A mixture of $x$ and $Y$ containing $76$ mole $\%$ of $x$ is to be separated in

multiple steps. A distillation column with a reboiler and a condenser is to be

used to separate the flow into one holding $96$ mole $\%x$ and another

holding $84$ mole $\%$ of $Y.$ Reflux ratio value is $2\mathrm{.}1R_{\text{m}\text{i}\text{n}}.$

A shell$-$and tube heat exchanger is to be utilized with the distillation

column descripted above. The cold fluid will enter the exchanger on the shell

side at a flow rate of $78kg{s}^{-1}$ a $35C$ and $10$ bars, and the hot fluid will enter

on the tube side at $130C$ and $8$ bars. The tubes should be thin$-$walled with

an internal diameter of not less than $1\mathrm{.}95cm$ and outer diameter not less

than $2\mathrm{.}8cm.$ The maximum length of each tube pass in the heat exchanger

cannot be less than $2\mathrm{.}2m.$ The heat transfer coefficient is given, $h_{in}=98\mathrm{.}5$

$\frac{W}{m^2}.$ K$.$

Design appropriate shell and tube heat exchangers based on the aforementioned specifications,

ensuring they meet the necessary criteria. Provide a detailed discussion on the designed heat

exchangers, covering the following aspects:

Display a schematic of the shell and tube design, highlighting the underlying assumptions.

Present the calculations for heat exchanger effectiveness $(),log$ mean temperature difference

$),$ heat transfer coefficient $($ho$),$ overall heat transfer coefficient $($U$),$ total surface area $($A$),$ and

tube length $($L$).$ Ensure that all calculations are in SI units.

Include a comprehensive diagram with clearly labelled dimensions.

Clearly articulate all calculations within the report.