3. (30 Pts) A hot water storage system is being designed in which a large thin-walled...

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3. (30 Pts) A hot water storage system is being designed in which a large thin-walled tank is warmed by a heat transfer fluid flowing through a jacket around the side walls of the tank. The system specifications are listed as follows: The hot water tank has outer radius Ro = 1m and length L = 3 m The hot water tank is initially filled with water at T20C The heat transfer fluid flows through the jacket at TH=80C and the convection heat transfer coefficient to the water tank h = 200 W m K- L Assume no flow processes occur inside the water itself, and the internal heat transfer process can be modeled as just conduction. Insulated Insulated Ro a. (6 Pts) The water in the tank will be heated with the hot fluid for 4 hrs. Determine the most appropriate method to model this transient heat transfer process (e.g., lumped capacitance, 1st term series solution, semi-infinite system model). Quantitatively justify your conclusion. b. (8 Pts) Plot qualitative temperature profiles through the water tank at different times during this 4 hr heating process. c. (8 Pts) Determine the total heat transferred to the water after 4 hours and the resulting increase in the average water temperature. Hint: If Bi 1 and Fo < 0.2, the surface temperature of the tank can be approximated as fixed at TH during the heating process. d. (8 Pts) Someone suggests an improvement to this heating process in which a mixing impeller is used to briefly stir the water after each hour of heating (i.e., at t = 1 hr, 2 hr.). This resets the temperature of the water in the tank to be uniform at the current average temperature. Determine the increase in average water temperature after four hours of heating with this process. Does this strategy significantly improve the overall heat transfer rate? BONUS! e. (5 Pts) What would the average temperature rise be in the tank if the mixing is performed continuously? 3. (30 Pts) A hot water storage system is being designed in which a large thin-walled tank is warmed by a heat transfer fluid flowing through a jacket around the side walls of the tank. The system specifications are listed as follows: The hot water tank has outer radius Ro = 1m and length L = 3 m The hot water tank is initially filled with water at T20C The heat transfer fluid flows through the jacket at TH=80C and the convection heat transfer coefficient to the water tank h = 200 W m K- L Assume no flow processes occur inside the water itself, and the internal heat transfer process can be modeled as just conduction. Insulated Insulated Ro a. (6 Pts) The water in the tank will be heated with the hot fluid for 4 hrs. Determine the most appropriate method to model this transient heat transfer process (e.g., lumped capacitance, 1st term series solution, semi-infinite system model). Quantitatively justify your conclusion. b. (8 Pts) Plot qualitative temperature profiles through the water tank at different times during this 4 hr heating process. c. (8 Pts) Determine the total heat transferred to the water after 4 hours and the resulting increase in the average water temperature. Hint: If Bi 1 and Fo < 0.2, the surface temperature of the tank can be approximated as fixed at TH during the heating process. d. (8 Pts) Someone suggests an improvement to this heating process in which a mixing impeller is used to briefly stir the water after each hour of heating (i.e., at t = 1 hr, 2 hr.). This resets the temperature of the water in the tank to be uniform at the current average temperature. Determine the increase in average water temperature after four hours of heating with this process. Does this strategy significantly improve the overall heat transfer rate? BONUS! e. (5 Pts) What would the average temperature rise be in the tank if the mixing is performed continuously?