Heat transmitted in convection from a pipe

In summary, the question is asking for the amount of heat delivered to the surrounding air by natural convection in 1 hour, given a vertical steam pipe with a constant temperature of 95°C and surrounded by air at atmospheric pressure and 20°C. The equations used to solve this problem are the heat convection current equation and the coefficient of natural convection in air for a vertical pipe. However, there may be difficulty in determining the heat transfer coefficient for both forced and free convection situations due to a large Reynold's number.
  • #1
Karol
1,380
22

Homework Statement


A vertical steam pipe of outside diameter 7.5 cm and height 4 m has its outer surface at the constant temperature of 950C. The surrounding air is at atmospheric pressure and at 200C.
How much heat is delivered to the air by natural convection in 1 hr?

Homework Equations


[tex]\mbox{The heat convection current H: }H=hA\,\Delta t[/tex]
[tex]\mbox{Coefficient of naural convection in air at atmospheric pressure for a vertical pipe (diameter D): }h=1.00\times10^{-4\left(\frac{\Delta t}{D}\right)^{1/4}}[/tex]

The Attempt at a Solution


[tex]h=1.00\times10^{-4\left(\frac{75}{7.5}\right)^{1/4}=0.00018[/tex]
[tex]H=0.00018\cdot\frac{\pi\cdot 7.5^2}{4}400\cdot 75=235.7\left[Cal/Sec\right]=848,469\left[Cal/hr\right][/tex]
The answer, according to the book, should be 454,000.
If this isn't the place for this subject, please guide me to another sight that deals with those kind of problems.
 
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  • #2
I see you have '400' in your final line. I don't think that belongs there, else you are essentially multiplying by volume and not cross-sectional area 'A'.
 
  • #3
I have a similar question. I'm trying to determine the heat loss in our steam pipes both outside exposed to the wind(forced convection) and inside our plant(free convection). I'm having some trouble in determining the heat transfer coefficient, h for both situations. When I calculate the Reynold's number for the wind blowing on the pipes, its so large that I can't use any of the normal equations to find the Nusselt number. The equations I'm using are
Nu = hl/k where h is heat transfer coefficient, l is a characteristic length (I'm using the diameter of the pipe and insulation), and k is the thermal conductivity of the insulation.
and
Nu = .023Re^.8 * Pr^.3 this range is valid for approx 100< Re < 50,000
My Re is 300,000+

Suggestions?
Thanks
 
  • #4
cmpersson said:
I have a similar question. I'm trying to determine the heat loss in our steam pipes both outside exposed to the wind(forced convection) and inside our plant(free convection). I'm having some trouble in determining the heat transfer coefficient, h for both situations. When I calculate the Reynold's number for the wind blowing on the pipes, its so large that I can't use any of the normal equations to find the Nusselt number. The equations I'm using are
Nu = hl/k where h is heat transfer coefficient, l is a characteristic length (I'm using the diameter of the pipe and insulation), and k is the thermal conductivity of the insulation.
and
Nu = .023Re^.8 * Pr^.3 this range is valid for approx 100< Re < 50,000
My Re is 300,000+

Suggestions?
Thanks

you should start your own thread, but your Re is outside the range for that equation, thus it cannot be used for your problem.
 
  • #5


I would like to point out that the equation used to calculate the coefficient of natural convection (h) is an empirical equation and may not accurately represent the heat transfer in this specific scenario. It is important to consider factors such as the geometry of the pipe, the properties of the fluid, and the flow conditions in order to accurately determine the heat transfer coefficient.

Additionally, the unit conversion for the final answer is incorrect. The correct unit for heat transfer rate is watts (W) or joules per second (J/s), not calories per second (Cal/sec). Therefore, the final answer should be approximately 848,469 watts or 848,469 joules per second.

It is also important to note that the given temperature of the pipe (950C) is extremely high and may affect the accuracy of the calculation. Further analysis and consideration of other factors may be necessary to accurately determine the heat transfer in this scenario.
 

1. What is convection?

Convection is the transfer of heat through the movement of a fluid, such as air or water. In this case, the fluid is heated by the pipe and then carries the heat away from the pipe, transferring it to its surroundings.

2. How does heat transfer in convection from a pipe?

In convection, heat is transferred through the movement of a fluid. As the fluid near the pipe is heated, it becomes less dense and rises, carrying the heat with it. This creates a continuous circulation of fluid, allowing the heat to be transferred away from the pipe.

3. What factors affect the rate of heat transfer in convection from a pipe?

The rate of heat transfer in convection is affected by several factors, including the temperature difference between the pipe and the surrounding fluid, the velocity of the fluid, and the properties of the fluid, such as its density and viscosity.

4. How does the shape of the pipe affect heat transfer in convection?

The shape of the pipe can affect heat transfer in convection. A pipe with a larger surface area will allow for more heat to be transferred, while a smaller surface area will result in less heat transfer. Additionally, the shape of the pipe can affect the flow of the fluid, which can also impact the rate of heat transfer.

5. What are some real-world examples of heat transfer in convection from a pipe?

Convection from a pipe is a common occurrence in everyday life. Examples include the heating of a room through a radiator, the cooling of a car engine through a radiator, and the transfer of heat in a pot of boiling water. It is also used in industrial processes, such as in cooling towers and heat exchangers.

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