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A test is performed to determine the overall heat transfer coefficient of a shell-and-tube oil-to- water heat exchanger with 24 tubes of internal diameter 0.012 m and length 2 m (this is not the total L and D) in a single shell. Cold water (cp=4.180 kJ/kg° C) enters the tubes at 20° C and exits at 55° C at a rate of 3 kg/s. Oil cools the shell from 120° C to 45° C (cp= 2.150 kJ/kg°C). Because the heat exchanger is well-insulated, heat loss to the surroundings is negligible. The kinetic and potential energies of a fluid stream change insignificantly. Correction factor: F = 0.7 a) Determine the overall heat transfer coefficient U (kW/m². °C) of this heat exchanger based on the inner surface area of the tubes (use LMTD method). IkJ/s=1kW b) What is the primary reason for using many tube passes?

A test is performed to determine the overall heat transfer coefficient of a shell-and-tube oil-to- water heat exchanger with 24 tubes of internal diameter 0.012 m and length 2 m (this is not the total L and D) in a single shell. Cold water (cp=4.180 kJ/kg° C) enters the tubes at 20° C and exits at 55° C at a rate of 3 kg/s. Oil cools the shell from 120° C to 45° C (cp= 2.150 kJ/kg°C). Because the heat exchanger is well-insulated, heat loss to the surroundings is negligible. The kinetic and potential energies of a fluid stream change insignificantly. Correction factor: F = 0.7 a) Determine the overall heat transfer coefficient U (kW/m². °C) of this heat exchanger based on the inner surface area of the tubes (use LMTD method). IkJ/s=1kW b) What is the primary reason for using many tube passes?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A test is performed to determine the overall heat transfer coefficient of a shell-and-tube oil-to-water heat exchanger with 24 tubes of internal diameter 0.012 m and length 2 m (this is not the total L and D) in a single shell. Cold water (\(c_p = 4.180 \, \text{kJ/kg}^\circ \text{C}\)) enters the tubes at 20°C and exits at 55°C at a rate of 3 kg/s. Oil cools the shell from 120°C to 45°C (\(c_p = 2.150 \, \text{kJ/kg}^\circ \text{C}\)). Because the heat exchanger is well-insulated, heat loss to the surroundings is negligible. The kinetic and potential energies of a fluid stream change insignificantly. Correction factor: F = 0.7 a) Determine the overall heat transfer coefficient \(U \, (\text{kW/m}^2\cdot \text{°C})\) of this heat exchanger based on the inner surface area of the tubes (use LMTD method). \[1 \, \text{kJ/s} = 1 \, \text{kW}\] b) What is the primary reason for using many tube passes?
Transcribed Image Text:A test is performed to determine the overall heat transfer coefficient of a shell-and-tube oil-to-water heat exchanger with 24 tubes of internal diameter 0.012 m and length 2 m (this is not the total L and D) in a single shell. Cold water (\(c_p = 4.180 \, \text{kJ/kg}^\circ \text{C}\)) enters the tubes at 20°C and exits at 55°C at a rate of 3 kg/s. Oil cools the shell from 120°C to 45°C (\(c_p = 2.150 \, \text{kJ/kg}^\circ \text{C}\)). Because the heat exchanger is well-insulated, heat loss to the surroundings is negligible. The kinetic and potential energies of a fluid stream change insignificantly. Correction factor: F = 0.7 a) Determine the overall heat transfer coefficient \(U \, (\text{kW/m}^2\cdot \text{°C})\) of this heat exchanger based on the inner surface area of the tubes (use LMTD method). \[1 \, \text{kJ/s} = 1 \, \text{kW}\] b) What is the primary reason for using many tube passes?
**Heat Exchanger Diagram** The image depicts a heat exchanger where oil and water are used as the working fluids. The setup consists of 24 tubes designed for optimal heat transfer between the fluids. - **Oil Flow:** - Inlet Temperature: 120°C - Outlet Temperature: 55°C - **Water Flow:** - Inlet Temperature: 20°C - Outlet Temperature: 45°C - Flow Rate: 3 kg/s **Explanation:** The diagram illustrates the flow process within the heat exchanger. The oil enters at a higher temperature of 120°C and exits at 55°C after transferring heat to the water. Conversely, the water enters at 20°C and absorbs heat, raising its temperature to 45°C, with a flow rate of 3 kg/s. The system is designed to efficiently balance the heat exchange, represented by the parallel arrangement of 24 tubes.
Transcribed Image Text:**Heat Exchanger Diagram** The image depicts a heat exchanger where oil and water are used as the working fluids. The setup consists of 24 tubes designed for optimal heat transfer between the fluids. - **Oil Flow:** - Inlet Temperature: 120°C - Outlet Temperature: 55°C - **Water Flow:** - Inlet Temperature: 20°C - Outlet Temperature: 45°C - Flow Rate: 3 kg/s **Explanation:** The diagram illustrates the flow process within the heat exchanger. The oil enters at a higher temperature of 120°C and exits at 55°C after transferring heat to the water. Conversely, the water enters at 20°C and absorbs heat, raising its temperature to 45°C, with a flow rate of 3 kg/s. The system is designed to efficiently balance the heat exchange, represented by the parallel arrangement of 24 tubes.
Expert Solution
Step 1

To Find : 

The overall heat transfer coefficient .

Given :

The internal diameter is di=0.012 m

The number of tubes is n=24

The lenght is L=2m

The specific heat of cold water  is cp=4.180 kJkg·°C

The inlet temperature is Tw,i=20 °C

The exit temperature is Tw,e=55 °C

The mass flow rate is m=3 kgs

The inlet temperature of oil is To,i=120°C

The exit temperature of oil is To,e=45°C

The specific heat of oil is cp,o=2.150 kJkg·°C

The correction factor is F=0.7

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