Problem $2$: A heat exchanger cools a fluid with specific heat of $3500\frac{J}{k}g-K$ flowing at $2k\frac{g}{s}$ from $80C$ to $53C$ using chilled water at $15C$ flowing at $2\mathrm{.}5k\frac{g}{s}.$ The overall heat transfer coefficient is $2000\frac{W}{m}2K.$ Find the areas required for the following heat exchanger types:

$($a$)$ Parallel flow

$($b$)$ Counterflow

$($c$)$ Shell and tube $($water is tube side$)$

$($d$)$ Crossflow