Outside air ( v =15.89 x 106 m2/s, p= 1.16 kg/m3, Pr=D0.707, k=0.0263 W/mK) with temperature of T=-12 °C flows over a flat glass window (kglass=1.05W/mK) with L=0.5m lengt the air velocity is measured as U=1.25 m/s and the glass thickness is t= 50 mm, calculate: 1. Reynolds number at the glass edge (i.e. point A)-Is the flow laminar or turbulent? 2. Average shear stress on outer surface of the glass 3. Velocity boundary layer thickness at the glass edge (point A) 4. Average convective heat transfer coefficient on outer surface of the glass
Outside air ( v =15.89 x 106 m2/s, p= 1.16 kg/m3, Pr=D0.707, k=0.0263 W/mK) with temperature of T=-12 °C flows over a flat glass window (kglass=1.05W/mK) with L=0.5m lengt the air velocity is measured as U=1.25 m/s and the glass thickness is t= 50 mm, calculate: 1. Reynolds number at the glass edge (i.e. point A)-Is the flow laminar or turbulent? 2. Average shear stress on outer surface of the glass 3. Velocity boundary layer thickness at the glass edge (point A) 4. Average convective heat transfer coefficient on outer surface of the glass
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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![### Educational Resource: Convection Heat Transfer Correlations
#### Hint:
\[ C_{f,x} = \frac{\tau_{s,x}}{\left( \frac{1}{2} \rho (u_{\infty})^2 \right)} \]
#### Table 7.7: Summary of convection heat transfer correlations for external flow
(This table appears on pages 484 and 485 of the 7th edition; pages 354 and 355 of the 8th edition.)
### Table 7.7
| Correlation | Geometry | Conditions |
|-------------|-----------|-------------|
| \(\delta = 5x \text{Re}_x^{-1/2}\) (7.19) | Flat plate | Laminar, \( T_s \) |
| \(\overline{C}_{f,x} = 0.664 \text{Re}_x^{-1/2}\) (7.20) | Flat plate | Laminar, local, \( T_s \) |
| \(\overline{Nu}_x = 0.332 \text{Re}_x^{1/2} Pr^{1/3}\) (7.23) | Flat plate | Laminar, local, \( T_s \), \( Pr \ge 0.6 \) |
| \(\delta_t = 8 \text{Pr}^{-1/3}\) (7.24) | Flat plate | Laminar, \( T_s \) |
| \(\overline{C}_f = 1.328 \text{Re}_L^{-1/2}\) (7.29) | Flat plate | Laminar, average, \( T_s \) |
| \(\overline{Nu}_L = 0.664 \text{Re}_L^{1/2} Pr^{1/3}\) (7.30) | Flat plate | Laminar, average, \( T_s \), \( Pr \ge 0.6 \) |
| \(\overline{Nu}_x = 0.564 \text{Re}_x^{1/2} Pr^{1/3}\) (7.32) | Flat plate | Laminar, local, \( T_s \), \( Pr \le 0.05 \), \( Pe_x \ge 100 \) |
| \(\overline{C}_{f,x} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e9db50a-4d56-435a-a058-414853800bca%2F2fb0ab02-e844-4146-8e7a-99f9f5ef0728%2Fgkzibjj_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Convection Heat Transfer Correlations
#### Hint:
\[ C_{f,x} = \frac{\tau_{s,x}}{\left( \frac{1}{2} \rho (u_{\infty})^2 \right)} \]
#### Table 7.7: Summary of convection heat transfer correlations for external flow
(This table appears on pages 484 and 485 of the 7th edition; pages 354 and 355 of the 8th edition.)
### Table 7.7
| Correlation | Geometry | Conditions |
|-------------|-----------|-------------|
| \(\delta = 5x \text{Re}_x^{-1/2}\) (7.19) | Flat plate | Laminar, \( T_s \) |
| \(\overline{C}_{f,x} = 0.664 \text{Re}_x^{-1/2}\) (7.20) | Flat plate | Laminar, local, \( T_s \) |
| \(\overline{Nu}_x = 0.332 \text{Re}_x^{1/2} Pr^{1/3}\) (7.23) | Flat plate | Laminar, local, \( T_s \), \( Pr \ge 0.6 \) |
| \(\delta_t = 8 \text{Pr}^{-1/3}\) (7.24) | Flat plate | Laminar, \( T_s \) |
| \(\overline{C}_f = 1.328 \text{Re}_L^{-1/2}\) (7.29) | Flat plate | Laminar, average, \( T_s \) |
| \(\overline{Nu}_L = 0.664 \text{Re}_L^{1/2} Pr^{1/3}\) (7.30) | Flat plate | Laminar, average, \( T_s \), \( Pr \ge 0.6 \) |
| \(\overline{Nu}_x = 0.564 \text{Re}_x^{1/2} Pr^{1/3}\) (7.32) | Flat plate | Laminar, local, \( T_s \), \( Pr \le 0.05 \), \( Pe_x \ge 100 \) |
| \(\overline{C}_{f,x} =
![## Analytical Problem: Heat Transfer and Fluid Flow over a Flat Glass Window
### Problem Statement
Outside air (ν = 15.89 × 10^-6 m^2/s, ρ = 1.16 kg/m^3, Pr = 0.707, k = 0.0263 W/mK) with a temperature of T∞ = -12 °C flows over a flat glass window (k_glass = 1.05 W/mK) with a length (L) of 0.5m. The air velocity is measured as U∞ = 1.25 m/s and the glass thickness is t = 50 mm. Calculate:
1. The Reynolds number at the glass edge (i.e., point A). Determine whether the flow is laminar or turbulent.
2. The average shear stress on the outer surface of the glass.
3. The velocity boundary layer thickness at the glass edge (point A).
4. The average convective heat transfer coefficient on the outer surface of the glass.
### Diagram Description
A simple diagram is provided to visualize the problem. It shows a rectangular flat glass with a length of 0.5 m. The point A is at the edge where the air velocity is measured. An arrow indicates the direction of the air flow, moving horizontally over the surface of the glass.
---
### Breaking Down the Problem:
#### 1. Reynolds Number at the Glass Edge
The Reynolds number (Re) is calculated using the formula:
\[ Re = \frac{U∞ \times L}{ν} \]
- \( U∞ = 1.25 \, \text{m/s} \)
- \( L = 0.5 \, \text{m} \)
- \( ν = 15.89 \times 10^{-6} \, \text{m}^2/\text{s} \)
#### 2. Average Shear Stress on Outer Surface
Shear stress (τ) is calculated as:
\[ τ = μ \left( \frac{dU}{dy} \right) \]
where \( μ \) (dynamic viscosity) can be found using:
\[ μ = ν \times ρ \]
#### 3. Velocity Boundary Layer Thickness
Boundary layer thickness (δ) at the glass edge is given by:
\[ δ \approx \frac{5L}{\sqrt{Re_L}} \]
(This is a typical estimation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e9db50a-4d56-435a-a058-414853800bca%2F2fb0ab02-e844-4146-8e7a-99f9f5ef0728%2Fm767n1h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Analytical Problem: Heat Transfer and Fluid Flow over a Flat Glass Window
### Problem Statement
Outside air (ν = 15.89 × 10^-6 m^2/s, ρ = 1.16 kg/m^3, Pr = 0.707, k = 0.0263 W/mK) with a temperature of T∞ = -12 °C flows over a flat glass window (k_glass = 1.05 W/mK) with a length (L) of 0.5m. The air velocity is measured as U∞ = 1.25 m/s and the glass thickness is t = 50 mm. Calculate:
1. The Reynolds number at the glass edge (i.e., point A). Determine whether the flow is laminar or turbulent.
2. The average shear stress on the outer surface of the glass.
3. The velocity boundary layer thickness at the glass edge (point A).
4. The average convective heat transfer coefficient on the outer surface of the glass.
### Diagram Description
A simple diagram is provided to visualize the problem. It shows a rectangular flat glass with a length of 0.5 m. The point A is at the edge where the air velocity is measured. An arrow indicates the direction of the air flow, moving horizontally over the surface of the glass.
---
### Breaking Down the Problem:
#### 1. Reynolds Number at the Glass Edge
The Reynolds number (Re) is calculated using the formula:
\[ Re = \frac{U∞ \times L}{ν} \]
- \( U∞ = 1.25 \, \text{m/s} \)
- \( L = 0.5 \, \text{m} \)
- \( ν = 15.89 \times 10^{-6} \, \text{m}^2/\text{s} \)
#### 2. Average Shear Stress on Outer Surface
Shear stress (τ) is calculated as:
\[ τ = μ \left( \frac{dU}{dy} \right) \]
where \( μ \) (dynamic viscosity) can be found using:
\[ μ = ν \times ρ \]
#### 3. Velocity Boundary Layer Thickness
Boundary layer thickness (δ) at the glass edge is given by:
\[ δ \approx \frac{5L}{\sqrt{Re_L}} \]
(This is a typical estimation
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