Question:a) We want to increase heat transfer by placing fans to provide forced convection to reduce the length of the pipe necessary (Note that the outside surface temperature of the pipe remains the same at 100oC). What is the rate of heat transfer from pipe to the air per meter length if the air speed over the pipe surface is 5m/s? What is the total length of the pipe necessary?Problem:Consider a rectangular warehouse with the dimensions of 40m long x 20m widex10m height. The overall heat transfer coefficient for all sidewalls is Uwall=0.3 W/m2K (Approx. R=20 hr.ft2.oF/Btu) and for the flat roof, it is Uroof= 0.20W/m2K. The floor can be assumed to be insulated and we can ignore the heat transfer through the doors, etc. We want to maintain the inside air temperature at 15oC while the outside temperature is 0oC by using a thin-walled, 5.0cm diameter copper pipe that carries steam. Steam enters the pipe as saturated vapor at 100oC. So, as it starts losing heat to the inside air, it starts to condense. The thin-walled pipe is made of, a highly conductive material such that the outside temperature of the pipe is at 100oC steam temperature over its entire surface. The average emissivity of the pipe is 0.8 and the only radiative exchange is with the air inside of the building at 15oC. We want to determine the length of the pipe necessary to keep the inside temperature at the desired level. **Transcription for Educational Website:**This section covers the dimensionless numbers used in fluid dynamics and heat transfer:1. **Rayleigh Number (RaD):**\[Ra_D = \frac{g \beta (T_s - T_\infty) D^3}{\alpha \nu}\]- **g**: Gravitational acceleration- **β**: Volumetric thermal expansion coefficient- **Ts**: Surface temperature- **T∞**: Ambient temperature- **D**: Characteristic length- **α**: Thermal diffusivity- **ν**: Kinematic viscosityThe Rayleigh number is used to characterize the type of flow in heat transfer problems involving natural convection.2. **Reynolds Number (ReD):**\[Re_D = \frac{Vel \cdot D}{\nu}\]- **Vel**: Flow velocity- **D**: Characteristic length- **ν**: Kinematic viscosityThe Reynolds number indicates whether the flow is laminar or turbulent. These equations are critical for analyzing and predicting fluid flow behavior in various engineering applications. **Description of Heat Transfer in a Cylindrical Pipe:**The image illustrates a cylindrical pipe exposed to different thermal conditions. Here's a detailed breakdown:1. **Pipe Material and Orientation:** - A long cylindrical pipe, potentially made of metal, as depicted by its copper-like appearance. 2. **Fluid and Temperature Conditions:** - **Inside the Pipe:** - Steam flows through the pipe at a temperature of \(100^\circ\text{C}\). - **Outside the Pipe:** - The surrounding air has a temperature of \(15^\circ\text{C}\).3. **Heat Transfer Mechanisms:** - The pipe's surface temperature (\(T_s\)) is maintained at \(100^\circ\text{C}\). - Heat transfer from the pipe to the surrounding air involves both convection and radiation, represented by \( \dot{Q}_{\text{conv}} + \dot{Q}_{\text{rad}} \).4. **Convection Details:** - The image suggests natural convection currents around the pipe in sections labeled as “Parts c & d: Natural convection.” - In “Part e,” forced convection is depicted with air moving at a velocity \(V = 5 \, \text{m/s}\).5. **Diagram Elements:** - Arrows indicate the direction of heat flow and convection currents. - The length of the pipe is denoted by \(L\).This setup models how heat transfers through a cylindrical pipe exposed to different layers of moving and stationary air, combining principles of conduction, convection, and radiation.

Answered: Image /qna-images/answer/edbe0c44-f6e5-4c21-b00b-6e42c0e9edba.jpg

Answered: We want to increase heat transfer by…

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

See similar textbooks

Related questions

Question

Question:

a) We want to increase heat transfer by placing fans to provide forced convection to reduce the length of the pipe necessary (Note that the outside surface temperature of the pipe remains the same at 100^oC). What is the rate of heat transfer from pipe to the air per meter length if the air speed over the pipe surface is 5m/s? What is the total length of the pipe necessary?

Problem:

Consider a rectangular warehouse with the dimensions of 40m long x 20m widex10m height. The overall heat transfer coefficient for all sidewalls is U_wall=0.3 W/m²K (Approx. R=20 hr.ft².^oF/Btu) and for the flat roof, it is U_roof= 0.20W/m²K. The floor can be assumed to be insulated and we can ignore the heat transfer through the doors, etc. We want to maintain the inside air temperature at 15^oC while the outside temperature is 0^oC by using a thin-walled, 5.0cm diameter copper pipe that carries steam. Steam enters the pipe as saturated vapor at 100^oC. So, as it starts losing heat to the inside air, it starts to condense. The thin-walled pipe is made of, a highly conductive material such that the outside temperature of the pipe is at 100^oC steam temperature over its entire surface. The average emissivity of the pipe is 0.8 and the only radiative exchange is with the air inside of the building at 15^oC. We want to determine the length of the pipe necessary to keep the inside temperature at the desired level.

**Transcription for Educational Website:**

This section covers the dimensionless numbers used in fluid dynamics and heat transfer:

1. **Rayleigh Number (RaD):**

\[
Ra_D = \frac{g \beta (T_s - T_\infty) D^3}{\alpha \nu}
\]

- **g**: Gravitational acceleration
- **β**: Volumetric thermal expansion coefficient
- **Ts**: Surface temperature
- **T∞**: Ambient temperature
- **D**: Characteristic length
- **α**: Thermal diffusivity
- **ν**: Kinematic viscosity

The Rayleigh number is used to characterize the type of flow in heat transfer problems involving natural convection.

2. **Reynolds Number (ReD):**

\[
Re_D = \frac{Vel \cdot D}{\nu}
\]

- **Vel**: Flow velocity
- **D**: Characteristic length
- **ν**: Kinematic viscosity

The Reynolds number indicates whether the flow is laminar or turbulent.

These equations are critical for analyzing and predicting fluid flow behavior in various engineering applications.

**Description of Heat Transfer in a Cylindrical Pipe:**

The image illustrates a cylindrical pipe exposed to different thermal conditions. Here's a detailed breakdown:

1. **Pipe Material and Orientation:**
- A long cylindrical pipe, potentially made of metal, as depicted by its copper-like appearance.

2. **Fluid and Temperature Conditions:**
- **Inside the Pipe:**
- Steam flows through the pipe at a temperature of \(100^\circ\text{C}\).
- **Outside the Pipe:**
- The surrounding air has a temperature of \(15^\circ\text{C}\).

3. **Heat Transfer Mechanisms:**
- The pipe's surface temperature (\(T_s\)) is maintained at \(100^\circ\text{C}\).
- Heat transfer from the pipe to the surrounding air involves both convection and radiation, represented by \( \dot{Q}_{\text{conv}} + \dot{Q}_{\text{rad}} \).

4. **Convection Details:**
- The image suggests natural convection currents around the pipe in sections labeled as “Parts c & d: Natural convection.”
- In “Part e,” forced convection is depicted with air moving at a velocity \(V = 5 \, \text{m/s}\).

5. **Diagram Elements:**
- Arrows indicate the direction of heat flow and convection currents.
- The length of the pipe is denoted by \(L\).

This setup models how heat transfers through a cylindrical pipe exposed to different layers of moving and stationary air, combining principles of conduction, convection, and radiation.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here