Solve the below problem:
Q: In open heart surgery under hypothermic conditions, the patient's blood is cooled before the surgery and re-warmed afterward. It is proposed that a concentric tube, counter flow heat exchanger of length 0.5 m be used for this purpose, with the thin-walled inner tube having a diameter of 55 mm. The specific heat of the blood is 3500 J/kg · K.
(a) If water at Th,i = 60°C and mh = 0.10 kg/s is used to heat blood entering the exchanger at Tc,i = 18°C and mc = 0.05 kg/s, what is the temperature of the blood leaving the exchanger? The overall heat transfer coefficient is 500 W/m2 · K.
(b) The surgeon may wish to control the heat rate q and the outlet temperature Tc,o of the blood by altering the flow rate and/or inlet temperature of the water during the re-warming process. To assist in the development of an appropriate controller for the prescribed values of mc and Tc,i, compute and plot q and Tc,o as a function of mh for 0.05 < mh="">< 0.20="" kg/s="" and="" values="" of="" th,i="50," 60,="" and="" 70?c.="" since="" the="" dominant="" influence="" on="" the="" overall="" heat="" transfer="" coefficient="" is="" associated="" with="" the="" blood="" flow="" conditions,="" the="" value="" of="" u="" may="" be="" assumed="" to="" remain="" at="" 500="" w/m2="" ·="" k.="" should="" certain="" operating="" conditions="" be="" excluded?="">