Question No$.02$:

A counter$-$flow heat exchanger is used to cool $5k\frac{g}{s}$ of water $($specific heat capacity, $C_p=4\mathrm{.}18k\frac{J}{k}gC)$ from $80C$ to $40C$ using a stream of oil $($specific heat capacity, $C_p=2\mathrm{.}1k\frac{J}{k}gC)$ with a mass flow rate at $3k\frac{g}{s}.$ The inlet temperature of the oil is $20C.$

LMTD Method:

$($a$)$ Calculate the required heat transfer rate $($Q$)$ in the heat exchanger.

$($b$)$ Use the LMTD method to calculate the Log Mean Temperature Difference $($LMTD$)$ for the heat exchanger.

$($c$)$ If the overall heat transfer coefficient $($U$)$ is $500\frac{W}{m^2}C,$ determine the required heat transfer area $($A$)$ of the heat exchanger.

Effectiveness$-$NTU Method:

$($a$)$ Calculate the heat capacity rates and $C_{\text{m}\text{a}\text{x}})$ and determine the heat capacity ratio $(C_r).$

$($b$)$ Calculate the effectiveness $()$ of the heat exchanger.

$($c$)$ Verify the heat transfer rate $($Q$)$ using the effectiveness$-$NTU method and compare it to the value obtained using the LMTD method.