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There is a tubular heat exchanger with the outer tube radius of 4 cm, the inner tube radius of 2 cm, and the length of 15 m. Your goal is to process milk at a rate of 3 kg/s. The inlet temperatures of milk and hot water are 4 °C and 90 °C, respectively. The specific heat capacity of water is 4.19 kJ/(kg °C), and the specific heat capacity of the milk is 4.0 kJ/(kg °C). a. If you are using a con-current flow with a water flow rate of 6 kg/s, the outlet temperature of hot water is measured at 70.13 °C. What is the outlet temperature of the milk? Show your calculation steps and compare your result with that given by the virtual experiment. b. If you are using a counter-current flow, the outlet temperatures of hot water and milk are measured at 68.78 and 48.46 °C, respectively. What is the flow rate of water? Show your calculation steps. Try these conditions, and compare the temperatures with the result given by the virtual experiment. c. During this pasteurization process, what is the energy of water used? Sensible heat or latent heat?

There is a tubular heat exchanger with the outer tube radius of 4 cm, the inner tube radius of 2 cm, and the length of 15 m. Your goal is to process milk at a rate of 3 kg/s. The inlet temperatures of milk and hot water are 4 °C and 90 °C, respectively. The specific heat capacity of water is 4.19 kJ/(kg °C), and the specific heat capacity of the milk is 4.0 kJ/(kg °C). a. If you are using a con-current flow with a water flow rate of 6 kg/s, the outlet temperature of hot water is measured at 70.13 °C. What is the outlet temperature of the milk? Show your calculation steps and compare your result with that given by the virtual experiment. b. If you are using a counter-current flow, the outlet temperatures of hot water and milk are measured at 68.78 and 48.46 °C, respectively. What is the flow rate of water? Show your calculation steps. Try these conditions, and compare the temperatures with the result given by the virtual experiment. c. During this pasteurization process, what is the energy of water used? Sensible heat or latent heat?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Title: Heat Exchanger Analysis for Milk Pasteurization** **Introduction:** This study examines a tubular heat exchanger where milk is processed at a rate of 3 kg/s. The exchanger has an outer tube radius of 4 cm, an inner tube radius of 2 cm, and a length of 15 m. The inlet temperatures for milk and hot water are 4°C and 90°C, respectively. The specific heat capacities for water and milk are 4.19 kJ/(kg°C) and 4.0 kJ/(kg°C), respectively. **Tasks:** a. **Con-Current Flow Analysis:** - With a water flow rate of 6 kg/s, the outlet temperature of hot water is 70.13°C. - Determine the outlet temperature of the milk using calculation steps. - Compare the result with the virtual experiment. b. **Counter-Current Flow Analysis:** - Outlet temperatures are measured as 68.78°C for hot water and 48.46°C for milk. - Calculate the flow rate of water. - Evaluate the results against the virtual experiment. c. **Energy Analysis:** - Assess whether the energy of water used in the pasteurization process is sensible heat or latent heat. d. **Heat Transfer Rates:** - Determine the heat transfer rates for con-current and counter-current flow directions. - Identify which flow direction is more efficient. e. **Log Mean Temperature Difference (LMTD):** - Calculate the LMTD for both flow conditions. - Compare and identify which flow direction has a higher LMTD. **Conclusion:** This study offers a comprehensive understanding of the dynamics in a tubular heat exchanger during the milk pasteurization process. By comparing con-current and counter-current operations, efficiency can be maximized. The calculations reinforce theoretical learning with practical virtual experimental data.
Transcribed Image Text:**Title: Heat Exchanger Analysis for Milk Pasteurization** **Introduction:** This study examines a tubular heat exchanger where milk is processed at a rate of 3 kg/s. The exchanger has an outer tube radius of 4 cm, an inner tube radius of 2 cm, and a length of 15 m. The inlet temperatures for milk and hot water are 4°C and 90°C, respectively. The specific heat capacities for water and milk are 4.19 kJ/(kg°C) and 4.0 kJ/(kg°C), respectively. **Tasks:** a. **Con-Current Flow Analysis:** - With a water flow rate of 6 kg/s, the outlet temperature of hot water is 70.13°C. - Determine the outlet temperature of the milk using calculation steps. - Compare the result with the virtual experiment. b. **Counter-Current Flow Analysis:** - Outlet temperatures are measured as 68.78°C for hot water and 48.46°C for milk. - Calculate the flow rate of water. - Evaluate the results against the virtual experiment. c. **Energy Analysis:** - Assess whether the energy of water used in the pasteurization process is sensible heat or latent heat. d. **Heat Transfer Rates:** - Determine the heat transfer rates for con-current and counter-current flow directions. - Identify which flow direction is more efficient. e. **Log Mean Temperature Difference (LMTD):** - Calculate the LMTD for both flow conditions. - Compare and identify which flow direction has a higher LMTD. **Conclusion:** This study offers a comprehensive understanding of the dynamics in a tubular heat exchanger during the milk pasteurization process. By comparing con-current and counter-current operations, efficiency can be maximized. The calculations reinforce theoretical learning with practical virtual experimental data.
The image contains a series of questions related to heat transfer and heat exchangers, specifically focusing on the process of heating milk. The questions are as follows: f. Calculate the overall heat transfer coefficient (U) for two conditions. Are the two U values the same? g. From your calculated U and ΔTₘ, which one of the two parameters is influencing the heat exchanger efficiency? h. If you want to heat the milk from 4 to 60 °C, how can you change the heat exchanger (e.g., length) or the operation conditions (e.g., flow rate, temperatures, etc.) to achieve this goal? i. If you increase the length of the tube, will the overall heat transfer coefficient U change? Explain why. j. If you increase the flow rate of milk, will U change? Explain why. k. Are there any situations when a co-current flow option may be preferred instead of a counter-current flow heat exchanger? l. After a long time of use, the heat exchanger is fouled inside the pipe. How does the fouling influence your milk pasteurization, and what actions can you take to achieve your pasteurization goal? Explain from both the heat transfer and fluid flow aspects.
Transcribed Image Text:The image contains a series of questions related to heat transfer and heat exchangers, specifically focusing on the process of heating milk. The questions are as follows: f. Calculate the overall heat transfer coefficient (U) for two conditions. Are the two U values the same? g. From your calculated U and ΔTₘ, which one of the two parameters is influencing the heat exchanger efficiency? h. If you want to heat the milk from 4 to 60 °C, how can you change the heat exchanger (e.g., length) or the operation conditions (e.g., flow rate, temperatures, etc.) to achieve this goal? i. If you increase the length of the tube, will the overall heat transfer coefficient U change? Explain why. j. If you increase the flow rate of milk, will U change? Explain why. k. Are there any situations when a co-current flow option may be preferred instead of a counter-current flow heat exchanger? l. After a long time of use, the heat exchanger is fouled inside the pipe. How does the fouling influence your milk pasteurization, and what actions can you take to achieve your pasteurization goal? Explain from both the heat transfer and fluid flow aspects.
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