A counter$-$flow double$-$pipe heat exchanger is to heat water from $20C$ to $80C$ at a rate of $1\mathrm{.}2k\frac{g}{s}.$

The heating is to be accomplished by geothermal water available at $160C$ at a mass flow rate of $2k\frac{g}{s}.$

The inner tube is thin$-$walled and has a diameter of $1\mathrm{.}5$ cm $.$ If the overall heat transfer coefficient of the heat exchanger is $640\frac{W}{m^2}C,$

Use a heat transfer formula to determine the length of the heat exchanger required to achieve the desired heating.