Problem #$2$: Sizing and Rating a Shell$-$Tube Heat Exchanger

You are asked to size a shell$-$and$-$tube heat exchanger that can be used to heat up water of a flow rate $12,500lb\frac{m}{h}r$ from $68F$ to $185F$ with high$-$pressure $(380$ psi $)$ hot distilled water available at $360F.$ Some preliminary design considerations are given below. You are asked to size an appropriate heat exchanger by following the design method based on the economic flow velocity in tubes as introduced in this class.

Some preliminary considerations lead to the following decisions:

$(1)$ Fluid placement: High$-$pressure hot water is placed inside the tube since a high$-$pressure of $380$ psi is involved.

$(2)$ Shell and head type: The U$-$tube bundle will be used because of easy cleaning and allowing for differential thermal expansion due to the larger temperature difference between the two streams. Hence, a type of AEU exchanger is specified and there will be one shell pass but possible multiple tube passes $(N_p).$

$(3)$ Tubing: Following the design guidelines for a fouling fluid service, $1$ in$.,10$ BWG tubes are selected to sustain high$-$pressure.

$(4)$ Tube layout: Since cleaning of the tube exterior surfaces is required, square pitch is specified Following the general design guidelines, for $1-in.$ tubes a tube pitch of $\frac{11}{4}in.$ is specified.

You are asked to size an AEU type shell and tube heat exchanger of one shell pass by specifying the following:

$\backslash$table$[[$Inner diameter of shell:,$D_s$