Using ChemCAD in dynamic mode, simulate the temperature versus time for a hot water stream leaving the tube side of a $1\mathrm{.}19f{t}^2$ heat exchanger after being cooled using cooling water on the shell side and after a set point change from $40$ to $39C$ and then a second change back to $40C.$

The control valve trim is linear with a valve coefficient of $0\mathrm{.}24GP\frac{M}{({)}^{0\mathrm{.}5}},$ a rangeability of $8$ and an outlet pressure of $26$ psig when fully open. The hot water flow has a constant rate of $0\mathrm{.}2GPM$ and enters at $55C$ and $55g,$ while the cold water enters at $18C$ and $55g.$ The process time constant for a hot out temperature set point at $39C$ is $6$ seconds. The shell and tube heat exchanger has an overall heat transfer coefficient of $70Bt\frac{u}{h}{r}_{f-f{t}^2-F}.$

Adjust the Proportional Band, PB $($note that proportional gain is Kp$=100/$PB$)$ Integral time and Derivative time for an approximate quarter amplitude dampening temperature response to the set point changes. Save the simulation file and upload to Blackboard with a word document showing sample calculations, your temperature and setpoint vs time graph as a figure and your P$,$ PI or PID settings as PB$,$ Ti and Td values in the figure caption.