$(30$ points$)$ To support a power station cooling system set up after a hurricane, ethylene glycol must be chilled to $307$ K or less in a counterflow heat exchanger. Seawater is available at $284$ K and at a flow rate of $17$ liters per minute $[$l$/$min$].$ The ethylene glycol passes through the pipe annulus with a convection heat transfer coefficient of $2100\frac{W}{m^2}*K$ and a flow rate of $9\frac{1}{m}in.$ For the seawater, use properties for water at $300$ K $.$ For the ethylene glycol, use properties at $370$ K $.$ Assume that all heat transfer goes from the ethylene glycol to the seawater.

$T_{c,i}=28$

a$.$ Use the Eftectiveness$-$Number ot I ranster Units $(-$NIU$)$ method to determine the overall heat transfer coefficient or UA $[$W$/$K$]$ of the counterflow heat exchanger required for this chilling process.

b$.$ Based on an applicable correlation from Table $8\mathrm{.}4,$ what is the convection heat transfer coefficient $\frac{W}{m^2}*(K)$ of the water flowing through the inside of the pipe? Assume fully developed flow and smooth pipe walls, and neglect fouling of the seawater.

c$.$ Based on the total resistance, determine the length $[$m$]$ of pipe needed for this counterflow heat exchanger. Assume that the pipe wall separating the two fluids is thin.

d$.$ What is the outlet temperature $[$K$]$ of the water?

e$.$ Present an engineering estimate for Size $m^3,$ Weight $[$kg$],$ and Power $[$kW$]($SWaP$)$ as well as a cost estimate $[$$$]$ for the ethylene glycol pump and the driving motor. Indicate the type of pump recommended for this application. Account for the major losses $($smooth pipe$)$ and minor losses $($one well rounded entrance, four $90$ flanged elbows, one well rounded exit$).$

f$.$ Present an engineering estimate for Size $[$m$^3],$ Weight $[$kg$],$ and Power $[$kW$]($SWaP$)$ as well as a cost estimate $[$$$]$ for the seawater pump and the driving motor. Indicate the type of pump recommended for this application. Account for major losses $($smooth pipe$)$ as well as a $25$ m elevation change required to move seawater from the waterline of the ship to the deck level.

Hint: For e$.$ and f$.,$ refer to the Mechanical Energy Form $($Head$)$ of Conservation of Energy for a Steady, One$-$Inlet, One$-$Exit Control Volume. Use the hydraulic diameter of the ethylene glycol tube. Online references for SWaP are encouraged, e$.$g$..$ find a Commercial Off The Shelf $($COTS$)$ item.