(15 pts) During the beer brewing process, wort solution in a pot is cooled with a...

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(15 pts) During the beer brewing process, wort solution in a pot is cooled with a submerged stainless steel tube coil that has cold water flowing on the inside. Assume the tube has inner diameter D = 10 mm, outer diameter Do = 12 mm, length L = 10 m, and thermal conductivity k = 15 W m K. The inside of the tube is cooled with a high flow rate of water (HTC;= 1000 W m K, Tw=20C). The outside of the tube has an average convection heat transfer coefficient to the wort of HTC. = 100 W m K. The pot has 15 kg of wort solution (cp = 4200 J kg K-) that is initially at Tw,0 = 80C. Assume that the wort is well mixed (i.e., at a uniform temperature at any given time). (6 pts) Draw a thermal resistance network representing the heat transfer processes between the wort and the cooling water. Neglect any heat transfer from the pot to the surrounding environment. Calculate the overall thermal resistance between the two streams. Find the initial rate of cooling heat transfer. (6 pts) Use a transient energy balance to solve for the time required to cool the wort solution to 25C. (3 pts) An impatient friend says that stainless steel has low thermal conductivity, and that you should speed up this step by using a copper cooling coil (keu = 390 W m K-) instead. Would this speed up the cooling process significantly? If not, suggest some other changes that could reduce the cooling time. (15 pts) During the beer brewing process, wort solution in a pot is cooled with a submerged stainless steel tube coil that has cold water flowing on the inside. Assume the tube has inner diameter D = 10 mm, outer diameter Do = 12 mm, length L = 10 m, and thermal conductivity k = 15 W m K. The inside of the tube is cooled with a high flow rate of water (HTC;= 1000 W m K, Tw=20C). The outside of the tube has an average convection heat transfer coefficient to the wort of HTC. = 100 W m K. The pot has 15 kg of wort solution (cp = 4200 J kg K-) that is initially at Tw,0 = 80C. Assume that the wort is well mixed (i.e., at a uniform temperature at any given time). (6 pts) Draw a thermal resistance network representing the heat transfer processes between the wort and the cooling water. Neglect any heat transfer from the pot to the surrounding environment. Calculate the overall thermal resistance between the two streams. Find the initial rate of cooling heat transfer. (6 pts) Use a transient energy balance to solve for the time required to cool the wort solution to 25C. (3 pts) An impatient friend says that stainless steel has low thermal conductivity, and that you should speed up this step by using a copper cooling coil (keu = 390 W m K-) instead. Would this speed up the cooling process significantly? If not, suggest some other changes that could reduce the cooling time.