# Heat transfer: Plane wall criterium

• -Brick-
In summary, the conversation is about describing the heat storage in a sanitation pipe when hot water flows through it. The approach is simplified by assuming a sudden change in temperature from 20°C to 60°C. The mentioned example in the book uses a half plane wall approach and has certain assumptions, including an adiabatic outer surface and the use of Bessel functions. The use of EES is mentioned and the poster is looking for direction in their research on heat transfer. There is also a discussion about the use of 'criterion' vs 'criterium' in the forum post.
-Brick-
Hello fellow scientists,

I'm working on describing the heat that's being stored in a sanitation pipe when hot water starts flowing through the pipe. I'm starting off with a simplified approach by assuming that the water in the pipe suddenly changes from 20°C to 60°C.

I found a good start by making 'Example 5.4 of Incropera' where a pipe is suddenly exposed to hot oil internally.

My question: In the mentioned example they make a simplification by approaching the pipe as a half plane wall. The pipe of the example is 1m in diameter and 4cm in thickness. Is there a criterion which makes that the (half) plane wall approach can be followed? Would there be another way?
I would be working with standard copper and PE-X sanitation pipes with an internal diamter ranging from 10mm (1mm thick for copper, 2mm for PEX) to 50mm (1,5mm thick copper, 4mm PEX).

The example in the book has the following order:
a) Pipe approached as a half plane wall. The midsection coincides with the outer surface.
b) Pipe's outer surface is adiabatic so δT/δx|x=0=0

Analysis:
1) Bi and Fo for Plane wall at a certain time
2) θ_0= C*exp(-ζ² Fo)
Get C and ζ from Table.
3) Use ζ to calculate the other temperatures.

Once I have the values of C and ζ, I plot the graph using EESI have started my research into heat transfer just recently and made some exercises on steady state heat transfer and the lumped capacitance model. I'm working with EES to make my exercises. I remade some bookexamples and had a fast look into Bessel functions. I know this subject is a work of long effort, but I would be grateful if someone could give me a clear direction where to go now.

-Brick-

Last edited:
'Criterium' is a race or competition of some sort. 'Criterion', plural 'criteria', a standard on which a judgment or decision is based, is the word to use in the OP.

On this forum I found a post on a different problem.

" With such a thin pipe wall compared to the radius, you can assume the pipe wall to act like a plane wall (the error in replacing 1/ln(ro/ri) with (ro+ri)/2(ro−ri) is about 0.1%), which let's you get rid of those logarithms. "

The assumptions should be justified. I would expect a comparison between the inner and outer perimeter, and make a comparison between a rectangle and trapezoid...

-Brick-

## 1. What is the definition of heat transfer?

Heat transfer is the movement of thermal energy from one object or system to another due to a difference in temperature.

## 2. How does heat transfer occur in a plane wall?

In a plane wall, heat transfer occurs through conduction, which is the transfer of thermal energy through a material without any physical movement of the material itself.

## 3. What is the plane wall criterium?

The plane wall criterium is a mathematical equation used to determine the heat transfer rate through a plane wall. It takes into account the thermal conductivity, thickness, and temperature difference of the wall.

## 4. How is the plane wall criterium calculated?

The plane wall criterium is calculated by dividing the thermal conductivity of the wall by the thickness and multiplying it by the temperature difference between the two sides of the wall. This gives the heat transfer rate per unit area of the wall.

## 5. What factors affect the heat transfer rate in a plane wall?

The heat transfer rate in a plane wall is affected by the thermal conductivity of the material, the thickness of the wall, and the temperature difference between the two sides of the wall. Other factors such as the surface area and boundary conditions may also play a role.

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