We wish to use the analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (j and f) of the Offset Strip-Fin (OSF) array. 1. Compare the predictions of the friction factor using equation 5.6 of the book to the measurements of Webb and Joshi (taken from "Prediction of the Friction Factor for the Offset Strip-Fin Matrix" and given in the last column of the table below) for surfaces 1 and 8 (see Table below) at Reph = 529 and 623, respectively. As shown in the table below, the experimental friction factors for surfaces, 1 and 8 are 0.0551 and 0.0434 respectively. Use CD= 0.8. Surface 1 8 α 0.123 0.224 t/l 0.016 0.064 h (mm) t (mm) Dh (mm) 38.1 0.406 38.1 1.626 7.518 10.897 f 0.0551 0.0434 2. Use the Webb and Joshi model given in the notes to make a plot of Nu versus the fin length (1) for 1 mm <5 mm. You should use 0.5 mm increments of 1 or smaller. Use a= 0.184, t = 0.102 mm, h = 4.98 mm, and Reph = 500. Explain why the Nu behaves as it does with respect to 1. Assume that the fin efficiency is equal to 1. 3. Convert the Nu data that you generated in Problem 2 above into j-factors by assuming that Pr=0.7. Next calculate the friction factor for the same values of 1, the same Reph, and for the same geometric parameters as Problem 2. Plot flj versus the fin length (1) for 1 mm </<5 mm. Does your plot verify the Reynolds analogy for this case? Explain why this should be expected.
We wish to use the analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (j and f) of the Offset Strip-Fin (OSF) array. 1. Compare the predictions of the friction factor using equation 5.6 of the book to the measurements of Webb and Joshi (taken from "Prediction of the Friction Factor for the Offset Strip-Fin Matrix" and given in the last column of the table below) for surfaces 1 and 8 (see Table below) at Reph = 529 and 623, respectively. As shown in the table below, the experimental friction factors for surfaces, 1 and 8 are 0.0551 and 0.0434 respectively. Use CD= 0.8. Surface 1 8 α 0.123 0.224 t/l 0.016 0.064 h (mm) t (mm) Dh (mm) 38.1 0.406 38.1 1.626 7.518 10.897 f 0.0551 0.0434 2. Use the Webb and Joshi model given in the notes to make a plot of Nu versus the fin length (1) for 1 mm <5 mm. You should use 0.5 mm increments of 1 or smaller. Use a= 0.184, t = 0.102 mm, h = 4.98 mm, and Reph = 500. Explain why the Nu behaves as it does with respect to 1. Assume that the fin efficiency is equal to 1. 3. Convert the Nu data that you generated in Problem 2 above into j-factors by assuming that Pr=0.7. Next calculate the friction factor for the same values of 1, the same Reph, and for the same geometric parameters as Problem 2. Plot flj versus the fin length (1) for 1 mm </<5 mm. Does your plot verify the Reynolds analogy for this case? Explain why this should be expected.
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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![The given mathematical expression is:
\[ f = \frac{1 - \gamma}{(1 + \gamma)(1 + \alpha + \delta)} \left( f_p + \alpha f_t + \frac{C D_t}{2 L_p} \right) \]
This equation likely represents a physical or engineering concept, where the variables and constants have specific meanings within the context of the formula. Here is an explanation of the terms used in the equation:
- \( \gamma \), \( \alpha \), and \( \delta \) are parameters or constants that need to be defined based on the specific application of the formula.
- \( f \) represents the function or value that is being computed.
- \( f_p \) and \( f_t \) could be component values or functions that contribute to the overall computation of \( f \).
- \( C \), \( D_t \), and \( L_p \) are additional parameters or measurements that play a role in the equation, possibly representing physical dimensions or coefficients.
To fully understand this equation, it's crucial to know the application context and the specific definitions of each parameter and variable. This could be part of a more extensive study on a topic such as fluid dynamics, structural mechanics, or another field in engineering or physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0e69105-edad-4e40-a986-7d2af8f1b9bd%2F884e5075-9f13-46c8-8f72-0b89978007ee%2Fqf153mk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given mathematical expression is:
\[ f = \frac{1 - \gamma}{(1 + \gamma)(1 + \alpha + \delta)} \left( f_p + \alpha f_t + \frac{C D_t}{2 L_p} \right) \]
This equation likely represents a physical or engineering concept, where the variables and constants have specific meanings within the context of the formula. Here is an explanation of the terms used in the equation:
- \( \gamma \), \( \alpha \), and \( \delta \) are parameters or constants that need to be defined based on the specific application of the formula.
- \( f \) represents the function or value that is being computed.
- \( f_p \) and \( f_t \) could be component values or functions that contribute to the overall computation of \( f \).
- \( C \), \( D_t \), and \( L_p \) are additional parameters or measurements that play a role in the equation, possibly representing physical dimensions or coefficients.
To fully understand this equation, it's crucial to know the application context and the specific definitions of each parameter and variable. This could be part of a more extensive study on a topic such as fluid dynamics, structural mechanics, or another field in engineering or physics.
![### Heat Transfer and Friction Characteristics Prediction Using Analytical Models
#### Objectives:
The goal is to use an analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (\(j\) and \(f\)) of the Offset Strip-Fin (OSF) array.
1. **Comparison with Experimental Data:**
- Utilize the friction factor prediction model (equation 5.6 from the reference book) and compare the results with experimental measurements by Webb and Joshi.
- The experimental data and friction factors for surfaces 1 and 8 are presented at Reynolds numbers (Re)\<sub>Dh</sub> = 529 and 623 respectively.
- Experimental Friction Factors:
- Surface 1: \( f = 0.0551 \)
- Surface 8: \( f = 0.0434 \)
- Use \( C_D = 0.8 \)
**Table 1**: Geometric Parameters for Surfaces 1 and 8:
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Surface} & \alpha & \frac{t}{l} & h \text{ (mm)} & t \text{ (mm)} & D_h \text{ (mm)} & f \\
\hline
1 & 0.123 & 0.016 & 38.1 & 0.406 & 7.518 & 0.0551 \\
8 & 0.224 & 0.064 & 38.1 & 1.626 & 10.897 & 0.0434 \\
\hline
\end{array}
\]
2. **Nu vs. Fin Length Plot:**
- Use the Webb and Joshi model to create a plot of the Nusselt number (Nu) against fin length (l) for \( 1 \text{ mm} < l < 5 \text{ mm} \).
- Use 0.5 mm increments of \( l \) or smaller.
- Parameters: \( \alpha = 0.184 \), \( t = 0.102 \) mm, \( h = 4.98 \) mm, Re_Dh = 500.
- Discuss](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0e69105-edad-4e40-a986-7d2af8f1b9bd%2F884e5075-9f13-46c8-8f72-0b89978007ee%2F2k7764q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Heat Transfer and Friction Characteristics Prediction Using Analytical Models
#### Objectives:
The goal is to use an analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (\(j\) and \(f\)) of the Offset Strip-Fin (OSF) array.
1. **Comparison with Experimental Data:**
- Utilize the friction factor prediction model (equation 5.6 from the reference book) and compare the results with experimental measurements by Webb and Joshi.
- The experimental data and friction factors for surfaces 1 and 8 are presented at Reynolds numbers (Re)\<sub>Dh</sub> = 529 and 623 respectively.
- Experimental Friction Factors:
- Surface 1: \( f = 0.0551 \)
- Surface 8: \( f = 0.0434 \)
- Use \( C_D = 0.8 \)
**Table 1**: Geometric Parameters for Surfaces 1 and 8:
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Surface} & \alpha & \frac{t}{l} & h \text{ (mm)} & t \text{ (mm)} & D_h \text{ (mm)} & f \\
\hline
1 & 0.123 & 0.016 & 38.1 & 0.406 & 7.518 & 0.0551 \\
8 & 0.224 & 0.064 & 38.1 & 1.626 & 10.897 & 0.0434 \\
\hline
\end{array}
\]
2. **Nu vs. Fin Length Plot:**
- Use the Webb and Joshi model to create a plot of the Nusselt number (Nu) against fin length (l) for \( 1 \text{ mm} < l < 5 \text{ mm} \).
- Use 0.5 mm increments of \( l \) or smaller.
- Parameters: \( \alpha = 0.184 \), \( t = 0.102 \) mm, \( h = 4.98 \) mm, Re_Dh = 500.
- Discuss
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