$20$ points $-$ A thin$-$walled double$-$pipe heat exchanger is to be used to cool oil $(c_p=2500\frac{J}{k}g*K)$ from $150C$ to $70C$ at a rate of $2k\frac{g}{s}$ by water $(c_p=4180\frac{J}{k}g*K)$ that enters at $20C$ at a rate of $3k\frac{g}{s}.$ The diameter of the tube is $2\mathrm{.}5cm.$ The overall heat transfer coefficient $($ U $)$ of this heat exchanger is estimated to be $24k\frac{W}{m}2C.$ Use LMTD method to determine the required length for

a$.$ A parallel$-$flow heat exchanger

b$.$ A counter$-$flow heat exchanger

c$.2-$shell passed and $4-$tube passes

Parallel flow

Counter flow