$5$A$\mathrm{.}1)$ Water at flows through a $10$ cm ID pipe at a mass flow rate of $1k\frac{g}{s}.$ The pipe has a wall heater with a uniform flux of $100k\frac{W}{m^2}.$ The internal convection coefficient, $h=100\frac{W}{m^2}K.$ At a particular station, the water has a mean temperature of $40C.$

a$)$ How long is the pipe length required to heat the water to a mean temperature of $80C?$

b$)$ What is the wall temperature at the exit?