A double$-$pipe parallel$-$flow heat exchanger is to heat water $(cp=4180\frac{J}{k}g*K)$ from $25C$ to $60C$ at a rate of $0\mathrm{.}2k\frac{g}{s}.$ The heating is to be accomplished by geothermal water $(cp=4310\frac{J}{k}g*K$ 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 overall heat transfer coefficient of the heat exchanger is $550\frac{W}{m}2*K,$ determine the length of the tube required to achieve the desired heating.

Hot water flowing at a rate of $2\mathrm{.}5k\frac{g}{s}$ is to be cooled from $100C$ to $35C$ by using a source of cold water $(cp=4178\frac{J}{k}g*K)$ flowing at $5k\frac{g}{s}$ and $15C$ through a $20-mm-$diameter tube of negligible wall thickness. The overall heat transfer coefficient of the heat exchanger is estimated to be $500\frac{W}{m}2*K.$ If the specific heat of the hot water is $4188\frac{J}{k}g*K$ and assuming that the capacity ratio and effectiveness remain the same, determine the heat exchanger surface area for the following four heat exchangers using effectiveness$-$NTU method: $($a$)$ parallel flow, $($b$)$ counter flow, $($c$)$ shell$-$and$-$tube heat exchanger with $2-$shell passes and $40-$tube passes $($the effectiveness is for $2$ shell passes ${}_2),$ and $($d$)$ cross$-$flow heat exchanger with one fluid $($hot$)$mixed and other fluid $($cold$)$ unmixed.