### One-dimensional Transient Heat Transfer Analysis**Problem Description:**Consider a 60-mm long aluminum fin with a thickness of 1 mm. The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of \( T_f = 15^\circ \text{C} \) and a convective heat transfer coefficient of \( h = 50 \, \frac{W}{m^2K} \). The fin is used to remove heat from a surface whose temperature is \( T_b = 80^\circ \text{C} \).**Material Properties:**- Thermal Conductivity (\( k \)): \( 186 \, \frac{W}{mK} \)- Density (\( \rho \)): \( 2500 \, \frac{kg}{m^3} \)- Specific Heat Capacity (\( C_p \)): \( 900 \, \frac{J}{kgK} \)**Initial Conditions:**- The fin is initially at \( 25^\circ \text{C} \).- Node 1 is always maintained at \( 80^\circ \text{C} \) from \( t = 0 \) sec.**Task Instructions:**1. **Discretization and Numerical Analysis:** - **a.** Show the discretization for node 2. - **b.** Show the discretization for node 5. - **c.** Provide the set of linear equations to be solved for the transient analysis.2. **Computational Methods:** - **d.** Provide either the EES (Engineering Equation Solver) script or MATLAB script with detailed explanations.3. **Data Visualization:** - **e.** Create a plot of the temperature of nodes 3 and 5 versus time using Excel or MATLAB.**Diagram Explanation:**The diagram shows the fin's configuration with a base temperature of \( 80^\circ \text{C} \), and an ambient temperature of \( 15^\circ \text{C} \). It highlights five nodes along the fin, indicating positions for temperature analysis. The heat transfer coefficient is labeled as \( h = 50 \, \frac{W}{m^2K} \).

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One-dimensional transient - Consider a 60-mm long aluminum fin (k = 186) with thickness of 1 mm. W mK The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of T₁ = 15°C and convective heat transfer coefficient of h = 50- from a surface whose temperature is T = 80° C. T base = 80 C W m²K T15 C h = 50 W/m2K (1) 2 (2) 3 (3) 4 (4) The fin is utilized to remove heat Consider the problem above for transient analysis. Using either implicit or explicit method, obtain solution of temperatures until it reaches steady state. If you are using the explicit method, please select appropriate time step that ensures stability. If you are using implicit method, then any time step should be good. For this problem, consider p = 2500 kg and Cp = 900 Assume that initially, the fin is at 25°C, while the node 1 is always 80° C from t = 0 sec. kgK a. Show the discretization for node 2 b. Show the discretization for node 5 c. Show the set of linear equations to be solved d. Show either the EES script or Matlab script and its explanation e. Make a plot of T of nodes 3 and 5 vs time using Excel or Matlab

One-dimensional transient - Consider a 60-mm long aluminum fin (k = 186) with thickness of 1 mm. W mK The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of T₁ = 15°C and convective heat transfer coefficient of h = 50- from a surface whose temperature is T = 80° C. T base = 80 C W m²K T15 C h = 50 W/m2K (1) 2 (2) 3 (3) 4 (4) The fin is utilized to remove heat Consider the problem above for transient analysis. Using either implicit or explicit method, obtain solution of temperatures until it reaches steady state. If you are using the explicit method, please select appropriate time step that ensures stability. If you are using implicit method, then any time step should be good. For this problem, consider p = 2500 kg and Cp = 900 Assume that initially, the fin is at 25°C, while the node 1 is always 80° C from t = 0 sec. kgK a. Show the discretization for node 2 b. Show the discretization for node 5 c. Show the set of linear equations to be solved d. Show either the EES script or Matlab script and its explanation e. Make a plot of T of nodes 3 and 5 vs time using Excel or Matlab

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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Question

### One-dimensional Transient Heat Transfer Analysis

**Problem Description:**

Consider a 60-mm long aluminum fin with a thickness of 1 mm. The width (into the paper) is 5 mm. The aluminum is exposed to air with an ambient temperature of \( T_f = 15^\circ \text{C} \) and a convective heat transfer coefficient of \( h = 50 \, \frac{W}{m^2K} \). The fin is used to remove heat from a surface whose temperature is \( T_b = 80^\circ \text{C} \).

**Material Properties:**

- Thermal Conductivity (\( k \)): \( 186 \, \frac{W}{mK} \)
- Density (\( \rho \)): \( 2500 \, \frac{kg}{m^3} \)
- Specific Heat Capacity (\( C_p \)): \( 900 \, \frac{J}{kgK} \)

**Initial Conditions:**

- The fin is initially at \( 25^\circ \text{C} \).
- Node 1 is always maintained at \( 80^\circ \text{C} \) from \( t = 0 \) sec.

**Task Instructions:**

1. **Discretization and Numerical Analysis:**
- **a.** Show the discretization for node 2.
- **b.** Show the discretization for node 5.
- **c.** Provide the set of linear equations to be solved for the transient analysis.

2. **Computational Methods:**
- **d.** Provide either the EES (Engineering Equation Solver) script or MATLAB script with detailed explanations.

3. **Data Visualization:**
- **e.** Create a plot of the temperature of nodes 3 and 5 versus time using Excel or MATLAB.

**Diagram Explanation:**

The diagram shows the fin's configuration with a base temperature of \( 80^\circ \text{C} \), and an ambient temperature of \( 15^\circ \text{C} \). It highlights five nodes along the fin, indicating positions for temperature analysis. The heat transfer coefficient is labeled as \( h = 50 \, \frac{W}{m^2K} \).

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