Cold water D₁ Do Hot R-134a Part b:Limestone layer a) Determine the overall heat transfer coefficient (W/m². °C) of this heat exchanger (assume no fouling). b) Determine the overall heat transfer coefficient (W/m². °C) of this heat exchanger, assume there is fouling. A 2-mm-thick layer of limestone (k = 1.3 W/m °C) forms on the outer surface of the inner tube. The limestone layer can be treated as a plain wall layer since its thickness is very small relative to its diameter.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Educational Website Transcription

**Title:** Double-Pipe Heat Exchanger for Refrigerant Condensation

**Introduction:**

A double-pipe heat exchanger is a device used to transfer heat between two fluids. This particular setup features a long, thin-walled exchanger with inner and outer shell diameters of 0.01 m and 0.025 m, respectively.

**System Description:**

- **Objective:** To condense refrigerant-134a using water at a temperature of 20°C.
- **Refrigerant Flow:** Moves through the tube with a convection heat transfer coefficient of \( h_i = 4100 \, \text{W/m}^2 \cdot \text{°C} \).
- **Water Flow:** Water traverses the shell at a rate of 0.3 kg/s.
- **Tube Material:** Assumed to be highly conductive with negligible thickness, leading to minimal thermal resistance.

Both the refrigerant and water flows are fully developed, and their properties are assumed constant during the process.

**Water Properties:**

- **Density (\( \rho \)):** 998 kg/m³
- **Kinematic Viscosity (\( \nu \)):** \( \mu/\rho = 1.004 \times 10^{-6} \, \text{m}^2/\text{s} \)
- **Thermal Conductivity (\( k \)):** 0.598 W/m·°C
- **Prandtl Number (\( \text{Pr} \)):** 7.01

**Diagram Explanation:**

- The diagram displays a transverse cross-section of the double-pipe heat exchanger.
- The larger circle represents the outer diameter (\( D_o \)) of the shell containing cold water.
- The smaller inner circle indicates the inner diameter (\( D_i \)) of the tube carrying the refrigerant.
- The arrows illustrate the flow direction of the cold water around the tube within the shell.

This simplified depiction assists in visualizing the heat exchange process wherein cold water absorbs heat from the refrigerant, causing it to condense.
Transcribed Image Text:### Educational Website Transcription **Title:** Double-Pipe Heat Exchanger for Refrigerant Condensation **Introduction:** A double-pipe heat exchanger is a device used to transfer heat between two fluids. This particular setup features a long, thin-walled exchanger with inner and outer shell diameters of 0.01 m and 0.025 m, respectively. **System Description:** - **Objective:** To condense refrigerant-134a using water at a temperature of 20°C. - **Refrigerant Flow:** Moves through the tube with a convection heat transfer coefficient of \( h_i = 4100 \, \text{W/m}^2 \cdot \text{°C} \). - **Water Flow:** Water traverses the shell at a rate of 0.3 kg/s. - **Tube Material:** Assumed to be highly conductive with negligible thickness, leading to minimal thermal resistance. Both the refrigerant and water flows are fully developed, and their properties are assumed constant during the process. **Water Properties:** - **Density (\( \rho \)):** 998 kg/m³ - **Kinematic Viscosity (\( \nu \)):** \( \mu/\rho = 1.004 \times 10^{-6} \, \text{m}^2/\text{s} \) - **Thermal Conductivity (\( k \)):** 0.598 W/m·°C - **Prandtl Number (\( \text{Pr} \)):** 7.01 **Diagram Explanation:** - The diagram displays a transverse cross-section of the double-pipe heat exchanger. - The larger circle represents the outer diameter (\( D_o \)) of the shell containing cold water. - The smaller inner circle indicates the inner diameter (\( D_i \)) of the tube carrying the refrigerant. - The arrows illustrate the flow direction of the cold water around the tube within the shell. This simplified depiction assists in visualizing the heat exchange process wherein cold water absorbs heat from the refrigerant, causing it to condense.
**Heat Exchanger Analysis**

**Problem Statement:**

a) *Determine the overall heat transfer coefficient (W/m²·°C) of this heat exchanger (assume no fouling).*

b) *Determine the overall heat transfer coefficient (W/m²·°C) of this heat exchanger, assume there is fouling. A 2-mm-thick layer of limestone (\( k = 1.3 \) W/m·°C) forms on the outer surface of the inner tube. The limestone layer can be treated as a plain wall layer since its thickness is very small relative to its diameter.*

**Diagram Explanation:**

The diagram in the image depicts a cross-section of a heat exchanger with the following components:

- An inner tube represented by a circle with an internal diameter \( D_i \).
- An outer layer showing a thin layer of limestone labeled "Part b: Limestone layer."
- The surrounding area outside the inner tube is labeled "Cold water."
- Hot R-134a fluid is inside the inner tube.

The diagram highlights the dual function of the heat exchanger: transferring heat between the hot R-134a and the cold water while considering fouling effects represented by the limestone layer.

**Instructions:**

Click "Save and Submit" to save and submit. Click "Save All Answers" to save all answers.

This instructional task focuses on understanding and analyzing the heat transfer processes within a heat exchanger, both with and without the presence of fouling on the surface of the inner tube.
Transcribed Image Text:**Heat Exchanger Analysis** **Problem Statement:** a) *Determine the overall heat transfer coefficient (W/m²·°C) of this heat exchanger (assume no fouling).* b) *Determine the overall heat transfer coefficient (W/m²·°C) of this heat exchanger, assume there is fouling. A 2-mm-thick layer of limestone (\( k = 1.3 \) W/m·°C) forms on the outer surface of the inner tube. The limestone layer can be treated as a plain wall layer since its thickness is very small relative to its diameter.* **Diagram Explanation:** The diagram in the image depicts a cross-section of a heat exchanger with the following components: - An inner tube represented by a circle with an internal diameter \( D_i \). - An outer layer showing a thin layer of limestone labeled "Part b: Limestone layer." - The surrounding area outside the inner tube is labeled "Cold water." - Hot R-134a fluid is inside the inner tube. The diagram highlights the dual function of the heat exchanger: transferring heat between the hot R-134a and the cold water while considering fouling effects represented by the limestone layer. **Instructions:** Click "Save and Submit" to save and submit. Click "Save All Answers" to save all answers. This instructional task focuses on understanding and analyzing the heat transfer processes within a heat exchanger, both with and without the presence of fouling on the surface of the inner tube.
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