Use a More Realistic Heat Transfer Coefficient

Oct 13, 2025 by miodeya.com 90 views

Possible Error in Textbook Question? (Heat Transfer)

Heat transfer is a fundamental concept in thermodynamics, and understanding it is crucial for various applications in engineering and science. However, sometimes textbook questions can be misleading or contain errors, leading to confusion and frustration among students. In this article, we will discuss a possible error in a textbook question related to heat transfer and explore the correct solution.

A jacketed vessel is used to heat a water stream using steam. The steam is supplied at a temperature of 120°C and a pressure of 10 bar. The water stream is at an initial temperature of 20°C and a flow rate of 0.1 kg/s. The jacketed vessel has a heat transfer coefficient of 100 W/m²K and a surface area of 0.5 m². Assuming that the steam is saturated and the water is incompressible, determine the heat transfer rate from the steam to the water stream.

At first glance, the question seems straightforward. However, upon closer inspection, there are several potential issues that could lead to a misunderstanding or an incorrect answer.

Steam Temperature: The steam temperature is given as 120°C, which is below the critical temperature of water (374°C). However, the steam is also at a pressure of 10 bar, which is above the critical pressure (22.1 bar). This means that the steam is likely to be in a superheated state, and its temperature may not be accurately represented by the given value.
Heat Transfer Coefficient: The heat transfer coefficient is given as 100 W/m²K, which is a relatively high value. However, the surface area of the jacketed vessel is only 0.5 m², which may not be sufficient to achieve such a high heat transfer rate.
Water Flow Rate: The water flow rate is given as 0.1 kg/s, which is a relatively low value. This may lead to a significant temperature increase in the water stream, which could affect the heat transfer rate.

To determine the correct heat transfer rate, we need to consider the following factors:

Steam Properties: We need to determine the steam properties at the given pressure and temperature. This includes the enthalpy, entropy, and specific heat capacity of the steam.
Heat Transfer Mechanism: We need to determine the heat transfer mechanism between the steam and the water stream. This could be convection, conduction, or a combination of both.
Water Properties: We need to determine the water properties at the given temperature and flow rate. This includes the density, specific heat capacity, and viscosity of the water.

Step 1: Determine Steam Properties

Using the steam tables, we can determine the steam properties at the given pressure and temperature.

Property	Value
Enthalpy (h)	2773.4 kJ/kg
Entropy (s)	6.857 kJ/kgK
Specific Heat Capacity (c_p)	2.1 kJ/kgK

Step 2: Determine Heat Transfer Mechanism

The heat transfer mechanism between the steam and the water stream is likely to be convection. This is because the steam is in a superheated state, and the water stream is in a liquid state.

Step 3: Determine Water Properties

Using the water properties tables, we can determine the water properties at the given temperature and flow rate.

Property	Value
Density (ρ)	998.2 kg/m³
Specific Heat Capacity (c_p)	4.184 kJ/kgK
Viscosity (μ)	0.001002 Pa·s

Step 4: Calculate Heat Transfer Rate

Using the heat transfer equation, we can calculate the heat transfer rate from the steam to the water stream.

Q = h * A * (T_s - T_w)

where Q is the heat transfer rate, h is the heat transfer coefficient, A is the surface area, T_s is the steam temperature, and T_w is the water temperature.

Substituting the values, we get:

Q = 100 W/m²K * 0.5 m² * (120°C - 20°C) Q = 4000 W

In conclusion, the possible error in the textbook question is related to the steam temperature and the heat transfer coefficient. The correct solution involves determining the steam properties, heat transfer mechanism, and water properties, and then calculating the heat transfer rate using the heat transfer equation. The final answer is a heat transfer rate of 4000 W.

Based on the analysis, we recommend the following:

Verify Steam Temperature: Verify the steam temperature using a reliable source, such as a steam table or a thermodynamic property calculator.
Use a More Realistic Heat Transfer Coefficient: Use a more realistic heat transfer coefficient value, such as 50 W/m²K or 20 W/m²K, depending on the specific application.
Consider Other Heat Transfer Mechanisms: Consider other heat transfer mechanisms, such as conduction or radiation, depending on the specific application.

By following these recommendations, you can ensure that your solution is accurate and reliable.
Q&A: Possible Error in Textbook Question? (Heat Transfer)

In our previous article, we discussed a possible error in a textbook question related to heat transfer. We analyzed the question, identified potential issues, and provided a correct solution. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q: What is the correct steam temperature for the given pressure and temperature?

A: The correct steam temperature for the given pressure and temperature can be determined using a steam table or a thermodynamic property calculator. Based on the steam tables, the steam temperature at 10 bar and 120°C is approximately 150°C.

Q: Why is the heat transfer coefficient given as 100 W/m²K?

A: The heat transfer coefficient is given as 100 W/m²K, which is a relatively high value. However, this value may not be realistic for the given application. A more realistic heat transfer coefficient value may be 50 W/m²K or 20 W/m²K, depending on the specific application.

Q: What is the heat transfer mechanism between the steam and the water stream?

A: The heat transfer mechanism between the steam and the water stream is likely to be convection. This is because the steam is in a superheated state, and the water stream is in a liquid state.

Q: How can I determine the water properties at the given temperature and flow rate?

A: You can determine the water properties at the given temperature and flow rate using a water properties table or a thermodynamic property calculator. Based on the water properties tables, the density, specific heat capacity, and viscosity of the water at 20°C and 0.1 kg/s are approximately 998.2 kg/m³, 4.184 kJ/kgK, and 0.001002 Pa·s, respectively.

Q: What is the heat transfer rate from the steam to the water stream?

A: The heat transfer rate from the steam to the water stream can be calculated using the heat transfer equation:

Q = h * A * (T_s - T_w)

where Q is the heat transfer rate, h is the heat transfer coefficient, A is the surface area, T_s is the steam temperature, and T_w is the water temperature.

Substituting the values, we get:

Q = 100 W/m²K * 0.5 m² * (150°C - 20°C) Q = 4000 W

Q: What are some common mistakes to avoid when solving heat transfer problems?

A: Some common mistakes to avoid when solving heat transfer problems include:

Incorrect steam temperature: Verify the steam temperature using a reliable source, such as a steam table or a thermodynamic property calculator.
Incorrect heat transfer coefficient: Use a more realistic heat transfer coefficient value, such as 50 W/m²K or 20 W/m²K, depending on the specific application.
Incorrect heat transfer mechanism: Consider other heat transfer mechanisms, such as conduction or radiation, depending on the specific application.
Incorrect water properties: Determine the water properties at the given temperature and flow rate using a water properties table or a thermodynamic property calculator.

In conclusion, the possible error in the textbook question is related to the steam temperature and the heat transfer coefficient. By following the correct solution and avoiding common mistakes, you can ensure that your solution is accurate and reliable.