Problem $3$:

Distilled water with a flow rate of $50k\frac{g}{s}$ enters a shell$-$and$-$tube heat exchanger at $32C$ and leaves at $25C.$ Heat will be transferred to $150k\frac{g}{s}$ of raw water coming from a supply at $20C.$ A single shell and single tube pass is preferable. The tube diameter is OD with $16mm$ ID$)$ and tubes are laid out on a $1$ in$.$ square pitch. Use the baffle spacing of $0\mathrm{.}5m.$ A maximum length of the heat exchanger of $8m$ is required because of space limitations$.$ The tube material is $0\mathrm{.}5$ Cr$-$alloy $)=(42\mathrm{.}3\frac{W}{m}*K.$ Assume a total fouling resistance of $0\mathrm{.}000176m^2*\frac{K}{W}.$ Note that over$-$surface should not exceed $30\%.$ The maximum flow velocity through the tube is also suggested to be $2\frac{m}{s}$ to prevent erosion. Perform a thermal design for the heat exchanger.