A double$-$pipe parallel$-$flow heat exchanger is to heat water $(c_p=4180\frac{J}{k}g*K)$ from $25C$ to $60C$ at a rate of $0\mathrm{.}2k\frac{g}{s}.$ The heating is to be accomplished by geothermal water $(c_p=4310\frac{J}{k}g*K)$ available at $140C$ at a mass flow rate of $0\mathrm{.}3k\frac{g}{s}.$ The inner tube is thin$-$walled and has a diameter of $0\mathrm{.}8$ cm $.$ If the outer tube with geothermal water has a diameter of $2\mathrm{.}5$ cm $.$ Determine the length of the tube required to achieve the desired heating.

Hint use $=1000k\frac{g}{m^3},v=1{10}^{-6}\frac{m^2}{sec},$ and Pr at Tavg$\_$cold$=40$C and T$=$avg$\_$hot$=130$C$,$ and $kf=\mathrm{.}6\frac{W}{m}C$ for both geothermal hot and cool side water.