You are required to solve some design problems for a one$-$shell two$-$passes shell$-$and$-$tube heat exchanger to cool down hot reaction products dissolved in water $($you can assume properties for water$).$ For that purpose,

Find empirical correlations and a method to calculate shell side convection heat transfer coefficient and overall heat transfer coefficient and answer the following questions

a$)$ How do the convection heat transfer coefficients depend on mass flow rate or $Re?$

b$)$ Why baffles are used in shell$-$and$-$tube type heat exchangers?

c$)$ What kinds of flow you have inside the shell with baffles?

$($Submit this part due ${21}^{st}$ of December $2023)$

In order to cool down the reaction effluents carried in water from $95C$ to $35C,$ it is supplied to the shell side of the shell$-$and$-$tube heat exchanger with a mass flow rate of $40k\frac{g}{s},$ where cold water at $5C$ is supplied from $100$ tubes at a total mass flow rate of $50k\frac{g}{s}.$ For the exchanger having properties as listed below,

Calculate convection coefficients for shell and tube side

Calculate the required length per pass to achieve this cooling.

Calculate the power required to pump cold water at a flow rate of $50k\frac{g}{s}.$

Assuming the same overall heat transfer coefficient with the first part, what would be the length per pass for a two$-$shell four$-$pass shell and tube heat exchanger to achieve the same outlet temperatures?

$\backslash$table$[[$Properties$,],[$Tube material,AISI $316$ stainless steel$],[$Tube O$.$D$.(mm),20],[$Tube thickness $(mm),1\mathrm{.}5],[$Number of tubes,$\frac{100}{?}$ pass$],[$Tube pitch $(mm),25],[$Baffle spacing $(mm),300],[$Baffle cut,$25\%$ Segmental$],[$Shell inner diameter $(mm),550]]$