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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. Surface 1 8 α 0.123 0.224 0.016 0.064 h (mm) 38.1 38.1 t (mm) 0.406 1.626 Dh (mm) 7.518 10.897 0.0551 0.0434

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. Surface 1 8 α 0.123 0.224 0.016 0.064 h (mm) 38.1 38.1 t (mm) 0.406 1.626 Dh (mm) 7.518 10.897 0.0551 0.0434

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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### Figure 5.7: Unit Cell for Derived Analytical Model The figure illustrates a unit cell that is utilized in deriving the analytical model by Joshi and Webb (1987) for the OSF (Orthogonally Stiffened Frame). #### Explanation: - **Unit Cell Structure:** The diagram shows a simplified representation of a unit cell. - **Arrows and Lines:** - Several arrows indicate forces or directions of stress/strain within the structure. - "S" denotes a specific parameter associated with the unit cell's structure. - "Lp" represents another parameter, possibly related to the length or another geometric aspect of the unit cell. ### Detailed Description: - The unit cell consists of rectangular blocks with arrows suggesting the directions of forces or connections within the framework. - The outer rectangles are connected with dashed lines, likely indicating the boundary or the limits of the unit cell. - The parameter "S" and "Lp" are key variables in the model being derived. **Purpose:** This visual representation helps in understanding how the analytical model quantifies the behavior of the OSF by breaking it down into manageable units. **Reference:** Derived from the work of Joshi and Webb from their 1987 analytical model, the unit cell serves as a foundational element for studying and modeling structural behaviors in orthogonally stiffened frames. For more in-depth learning, refer to Joshi and Webb's original studies and subsequent elaborative content on analytical models for architectural and engineering frameworks.
Transcribed Image Text:### Figure 5.7: Unit Cell for Derived Analytical Model The figure illustrates a unit cell that is utilized in deriving the analytical model by Joshi and Webb (1987) for the OSF (Orthogonally Stiffened Frame). #### Explanation: - **Unit Cell Structure:** The diagram shows a simplified representation of a unit cell. - **Arrows and Lines:** - Several arrows indicate forces or directions of stress/strain within the structure. - "S" denotes a specific parameter associated with the unit cell's structure. - "Lp" represents another parameter, possibly related to the length or another geometric aspect of the unit cell. ### Detailed Description: - The unit cell consists of rectangular blocks with arrows suggesting the directions of forces or connections within the framework. - The outer rectangles are connected with dashed lines, likely indicating the boundary or the limits of the unit cell. - The parameter "S" and "Lp" are key variables in the model being derived. **Purpose:** This visual representation helps in understanding how the analytical model quantifies the behavior of the OSF by breaking it down into manageable units. **Reference:** Derived from the work of Joshi and Webb from their 1987 analytical model, the unit cell serves as a foundational element for studying and modeling structural behaviors in orthogonally stiffened frames. For more in-depth learning, refer to Joshi and Webb's original studies and subsequent elaborative content on analytical models for architectural and engineering frameworks.
### Application of Analytical Model for Heat Transfer and Friction Characteristics in OSF Arrays #### Overview We aim to implement the analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (denoted as **j** and **f**, respectively) of the Offset Strip-Fin (OSF) array. #### Table 1: Surface Characteristics Data The following table provides key parameters for two specific surface types used in the study. | **Surface** | **α** | **t/l** | **h (mm)** | **t (mm)** | **D_h (mm)** | **f** | |-------------|----------|---------|------------|------------|--------------|-----------| | 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 | #### Instructions 1. **Plotting Nu vs fin length (l):** Use the Webb and Joshi model as specified in the course notes to create a plot of Nusselt number (Nu) versus the fin length (l) in the range of 1 mm to 5 mm, in 0.5 mm increments or smaller. For these calculations, utilize the following parameters: - α = 0.184 - t = 0.102 mm - h = 4.98 mm - \(Re_{D_h}\) = 500 While plotting, explain the behavior of the Nusselt number (Nu) in relation to different lengths (l). Assume the fin efficiency to be 1. 2. **Conversion to j-factors:** Convert the Nusselt number data from Problem 2 into j-factors, assuming \(Pr = 0.7\). Next, calculate the friction factor for the same values of fin length (l), \(Re_{D_h}\), and the geometric parameters. Plot the ratio \(f/j\) versus the fin length (l) for the range 1 mm < l < 5 mm. Evaluate the plot to verify the Reynolds analogy and discuss why the observed trends should be expected. ### Detailed Graphs and
Transcribed Image Text:### Application of Analytical Model for Heat Transfer and Friction Characteristics in OSF Arrays #### Overview We aim to implement the analytical model developed by Joshi and Webb to predict the heat transfer and friction characteristics (denoted as **j** and **f**, respectively) of the Offset Strip-Fin (OSF) array. #### Table 1: Surface Characteristics Data The following table provides key parameters for two specific surface types used in the study. | **Surface** | **α** | **t/l** | **h (mm)** | **t (mm)** | **D_h (mm)** | **f** | |-------------|----------|---------|------------|------------|--------------|-----------| | 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 | #### Instructions 1. **Plotting Nu vs fin length (l):** Use the Webb and Joshi model as specified in the course notes to create a plot of Nusselt number (Nu) versus the fin length (l) in the range of 1 mm to 5 mm, in 0.5 mm increments or smaller. For these calculations, utilize the following parameters: - α = 0.184 - t = 0.102 mm - h = 4.98 mm - \(Re_{D_h}\) = 500 While plotting, explain the behavior of the Nusselt number (Nu) in relation to different lengths (l). Assume the fin efficiency to be 1. 2. **Conversion to j-factors:** Convert the Nusselt number data from Problem 2 into j-factors, assuming \(Pr = 0.7\). Next, calculate the friction factor for the same values of fin length (l), \(Re_{D_h}\), and the geometric parameters. Plot the ratio \(f/j\) versus the fin length (l) for the range 1 mm < l < 5 mm. Evaluate the plot to verify the Reynolds analogy and discuss why the observed trends should be expected. ### Detailed Graphs and
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