Problem $3(30$ points$)$: A coolant $(c_p=1035\frac{J}{k}g*K,=75\mathrm{.}5{10}^{-4}k\frac{g}{s}*m,k=0\mathrm{.}06\frac{W}{m}*K$ and $Pr=15)$ is flowing through tubes in a single shell and two tube passes heat exchanger at a rate of $4\mathrm{.}80k\frac{g}{s}.$ Inlet and outlet temperatures of the coolant are $25C$ and $15C$ respectively. The heat exchanger consists of $65$ brass tubes $(k=137\frac{W}{m}*K)$ of $15$ mm outside diameter and $12\mathrm{.}4$ mm inside diameter. The coolant is cooled by the chilled water flow at a rate of $2\mathrm{.}45k\frac{g}{s}$ and an inlet temperature of $3C$ in the shell. The water has average specific heat of water is $4180\frac{J}{k}g*K$ and provides average heat convection coefficient of $9950\frac{W}{m^2}K$ over the outer surface of the tubes. Determine the required tube length per pass.