Radial Heat Conduction through a Cylindrical Pipe

In summary, the problem involves calculating the heat transfer rate through a PVC pipe and the resulting decrease in temperature after one minute. Using Fourier's Law of Conduction and the surface area of a cylinder, the formula Q = [k2πL(Ti - To)] / [In(r2/r1)] is derived and substituted with given values to obtain a result of 27.428 (3dp). However, the unit for Q is not specified and can be determined by treating the units in the expression as algebraic variables and cancelling appropriately. More information is needed to calculate the decrease in inner temperature, such as the contents of the pipe.
  • #1
Thisbe Schwer
2
0

Homework Statement


A 1.75m long PVC pipe with a thermal conductivity of 0.19 W/mK has an internal diameter of 3mm and an external diameter of 5.5mm. Inner temperature is 298K and outer temperature is 273K. Calculate the heat transfer rate through the pipe and thus the decrease in the inner temperature after one minute.

Homework Equations


Fourier's Law of Conduction: Q = -kA(dT/dr)
Surface area of cylinder: A = 2πrL

The Attempt at a Solution


I've got the formula Q = [k2πL(Ti - To)] / [In(r2/r1)] and substituted in the values:
Q = [0.19W/mK * 2π * 1.75m * 25K] / [In(1.8333)]
Q = 16.625/0.6061...
Q = 27.428 (3dp)
But I'm a complete newbie to this kind of calculation, and I'm not sure what the unit for Q is? So I'm kind of stuck at this part of the question and not sure where to go from here.
Sorry for the silly question, but any help would really be appreciated![/B]
 
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  • #2
Thisbe Schwer said:
not sure what the unit for Q is
You can deduce it by treating the units in your expression (K, m, W) as algebraic variables and cancelling as appropriate.
Thisbe Schwer said:
thus the decrease in the inner temperature after one minute.
You need more information to compute this, such as what is in the pipe.
 
  • #3
So would the units for Q be W/m?
 
  • #4
Thisbe Schwer said:
So would the units for Q be W/m?
You had
Thisbe Schwer said:
0.19W/mK * 2π * 1.75m * 25K
Leaving out everything except the units:
(W/mK) * m * K. What does that reduce to?
 

FAQ: Radial Heat Conduction through a Cylindrical Pipe

What is radial heat conduction?

Radial heat conduction is the transfer of heat through a medium, such as a cylindrical pipe, from the inner surface to the outer surface. This type of heat transfer occurs when there is a temperature difference between the inner and outer surfaces of the pipe.

How does heat transfer occur in a cylindrical pipe?

In a cylindrical pipe, heat transfer occurs through a combination of conduction and convection. Conduction is the transfer of heat through the material of the pipe, while convection is the transfer of heat through the movement of fluid within the pipe.

What factors affect the rate of heat conduction in a cylindrical pipe?

The rate of heat conduction in a cylindrical pipe is affected by several factors, including the material of the pipe, the temperature difference between the inner and outer surfaces, the length of the pipe, and any insulating materials present.

How can the rate of heat conduction be calculated for a cylindrical pipe?

The rate of heat conduction through a cylindrical pipe can be calculated using the Fourier's law of heat conduction, which takes into account the physical properties of the material, the temperature gradient, and the surface area of the pipe.

What are some applications of radial heat conduction through a cylindrical pipe?

Radial heat conduction through a cylindrical pipe is commonly used in various industrial processes, such as heating and cooling systems, chemical reactions, and food processing. It is also an important concept in engineering and physics for understanding heat transfer in different systems.

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