Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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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.
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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
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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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