Cross$-$flow heat exchanger

Hot process water $(95k\frac{g}{m}in)$ is used in a cross$-$flow heat exchanger to heat $70k\frac{g}{m}in$ of colder,

fresh water. The hot water enters the heat exchanger at $107C($the system is pressurized$),$ while the

colder water enters the heat exchanger at $5C.$ The heat transfer coefficient $($per shell$)$ is

$(UA{)}_1=2570\frac{W}{K}.$

The hot water on the tube side flows through a large number of U$-$tubes, each making four passes

through the cold water, which flows $($mixed$)$ through a containment bath.

$41C($a$)$ Apply the NTU method to estimate the cold$-$side outlet water temperature from a single such

cross$-$flow heat exchanger. Use the inlet temperatures to estimate properties, as required.

$($b$)$ Determine the $($integer$)$ number of such heat exchangers in series that would be required to ob$-$

tain an outlet water temperature of $95C($for this part, correct the heat capacity on the cold side

to account for this outlet temperature, by using the average cold$-$side temperature of $50C).$