A hardworking PhD student fabricated a concentric parallel flow heat exchanger test rig to perform the preliminary experimentation based on the following data. $T_{Ci}=40C,T_{hi}=150C,C_C=20000\frac{W}{}C,C_h=10000\frac{W}{}C,$ Area $=30m^2,U=500\frac{W}{m^{2\text{@}}}C$

Part $($a$)$ For his weekly meeting he was required to find the following results. Find the following.

i$.$ What is the effectiveness of the heat exchanger?

ii$.$ What is the heat transfer rate $q$ for the heat exchanger?

iii. What are the exit temperatures of cold and hot fluid?

iv$.$ Draw the resistance network of the heat exchanger showing all the thermal resistances and the overall heat transfer coefficient based on inner tube diameter $($Hint: you don't need to calculate U$)$

Part $($b$)$ His supervisor asked him to disregard the area used in part $($a$).$ The area is now an unspecified design variable. He was required to calculate the area that will bring the hot flow out at $90C.$ Please find the new area.

Part $($c$)$ His professor was not happy with the outcome of the parallel flow heat exchanger. The student revisited MECH$4406$ notes and decided to flip the orientation of the concentric parallel heat exchanger to make it a counter flow heat exchanger and doubled the mass flow rate of the hot side fluid. He kept all other parameters the same as given in the problem statement. What will be the effect of the increase in mass flow rate of hot side on the following. $($Hint: you don't need to perform any calculation; counter flow temperature profile is given below for your reference$)$

i$.$ Hot temperature profile

ii$.$ Is hot fluid a condensing vapor or a fluid in evaporator

iii. Hot side exit temperature $T_{ho}$

iv$.$ Cold side exit temperature $T_{Co}$