Example $6$: Heating Water in a Counter$-$Flow

Faculty of Engineering and Techn

Heat Exchanger

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 $640\frac{W}{m^2}K,$ determine the length of the heat exchanger required to achieve the desired heating.. Calculate:

$($a$)$ the duty of the heat exchanger $($heat transfer load$)$

$($b$)$ the transfer area and length of heat exchanger required for this duty

Additional information:

Specific heat capacity of water $4\mathrm{.}18k\frac{J}{k}g$ K

Specific heat capacity of geothermal fluid $4\mathrm{.}31k\frac{J}{k}gK$