Whey from cherese mamnfacturing has a composition of $3\frac{w}{?}\%$ solids and $97\frac{w}{w}\%$

water. Filtration is noed to conceatrate the solid fraction of whey by removing the walter. A

fred tank is filled with an initial mass of $200kg$ of whey and this whey is fed into the filtration

system at a flowrate of $30$kgmin. The filtration system removes only the water at a flow rate

of $8kgmi{n}^{-1}$ and recycles the concentrated whey back to the feed tank. Duning the filtration

process the concentrated whey heats up$.$ Therefore, before the concentrated whey is recycled

back to the feed tank, it is cooled from $35C$ to $25C$ in a heat exchanger using an inlet cooling

water temperature of $15C.$

$($a$)$ Sketch the process and label all the equipment, stream compositions and flowrates.

$($b$)$ Write the equation for the mass of whey in the feed tank as a function of time.

$($c$)$ For the membrane filtration system:

$($i$)$ Write the overall material balance for the process.

$($ii$)$ Write the material balance for water and solids, comment on the mass fraction used.

$($d$)$ Write the equation describing the change in the composition of water and solids in the tank

as a function of time.

$($e$)$ Calculate the heat load of the heat exchanger, give you ancwer in $kW.$

$($f$)$ If the temperature of the cooling water leaning the heat exchanger cannot exceed $25C.$

what condition does thas upose on the flownate of cooling water and what flowrate of

cooling water would you reconmend"

Table I: Specific heat capacine: in I kg $K$ for water and wher, Acrume for whey, the cpecific

heat capacine: only ray wnth temperanue and wot wath somposinon.