What Is the Rate of Heat Transfer per Unit Length in a Plastic Pipe?

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Discussion Overview

The discussion revolves around calculating the rate of heat transfer per unit length in a plastic pipe, given specific thermal properties and temperature conditions. The problem is framed as a homework question involving the application of heat transfer equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem statement, including the thermal conductivity of the plastic pipe and the temperatures at the inner and outer surfaces.
  • Another participant clarifies that since the question asks for heat transfer per unit length, the total length of the pipe is not necessary for the calculation.
  • A participant questions whether it is reasonable to assume a length of 1 meter for the calculation, interpreting "unit length" as 1 meter.
  • Another participant confirms that "W/m" represents the amount of heat transfer per unit length, equating watts to joules per second.
  • A later reply indicates that after performing calculations, the participant arrived at a value of 78 W/m for the rate of heat transfer.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of "per unit length" and the meaning of the units involved. However, there is no consensus on the final calculated value, as it is presented as a personal result rather than a confirmed answer.

Contextual Notes

Participants discuss the need for assumptions regarding the length of the pipe, but the implications of these assumptions on the calculations are not fully resolved.

Who May Find This Useful

Students or individuals interested in heat transfer calculations, particularly in the context of homework or practical applications involving thermal conductivity in materials.

dzj633

Homework Statement


A plastic pipe (k=0.092 W/m.K) of inner and outer radius of 1 and 1.25 cm, respectively. If the inner and outer surfaces are at 60 °C and 30 °C, respectively. The rate of heat transfer per unit length is close to:
a) 98 W/m b) 89 W/m c) 78 W/m d) 168 W/m e) 112 W/m

Homework Equations


Qk = ( Ti - To )/( ln| ro / ri | / 2π * k * l )

The Attempt at a Solution


I set up all of my given values into the heat transfer equation above but i am not given a length of the pipe.. Am i missing key information to finish this problem, or do i not need the length to solve? Also, I converted temps to Kelvin and the radii to meters.[/B]
 
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The key phrase here is heat transfer per unit length. You do not need the total length of pipe because you are not looking for the total heat transferred.
 
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I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?
 
dzj633 said:
I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?
What do the units W/m mean to you?
 
W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]
 
dzj633 said:
W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]
With that being said, my thought of "a unit" would be 1 unit of length.
 
Yes, it's Watts per meter.
 
Correct, after my calculations I got 78 W/m.
 

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