$($a$)$ A shell$-$and$-$tube heat exchanger with $2-$shell passes and $12-$tube passes is used to

heat water $(C_p=4180\frac{J}{k}g*C)$ with ethylene glycol $(C_p=2680\frac{J}{k}g*C).$ Water

enters the tubes at $22C$ at a rate of $0\mathrm{.}8k\frac{g}{s}$ and leaves at $70C.$ Ethylene glycol

enters the shell at $110C$ and leaves at $60C.$ If the overall heat transfer coefficient

based on the tube side is $280\frac{W}{m^{2.C}},$ determine:

$($i$)$ the rate of heat transfer.

$[5$ Marks$]$

$($ii$)$ the heat transfer surface area on the tube side.

$[10$ Marks$]$