rroblem $1(15$ pts$)$

Water $($specific heat $=4000\frac{J}{k}gK)$ is to be heated by hot air $($specific heat $=1000\frac{J}{k}gK)$ in a double$-$pipe counter flow heat exchanger. Air enters the heat exchanger at $900$ degC at a rate of at $0\mathrm{.}10k\frac{g}{s}$ and leaves at $150$ degC $.$ Water enters at $20$ degC at a rate of $1k\frac{g}{s}.$ The overall heat transfer coefficient based on the inner side of the tube is $100\frac{W}{m}2K.$ Determine the length of the tube required for a tube diameter of $0\mathrm{.}025$ m $.$ Now, repeat the calculation for length if the heat exchanger is now a double$-$pipe counter flow.