Heat conduction through plane wall

In summary: It is a wonderful book that had a new edition out about 12 years ago with lots of new developments and content.
  • #1
gfd43tg
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When you have energy going through a plane wall, I know that the heat flow rate should be constant, meaning what comes in should go out. But is this true even if it is transient, and a non-steady state process?

I think the energy content of the plane will not change for steady state, but for transient it will change, because there is an accumulation of energy term in the balance that is non-zero.

##\frac {dE}{dt} = \dot Q_{x} - \dot Q_{x+\Delta x} + \dot e_{gen}A \Delta x##

Maybe I should clarify. If the internal heat generation were zero, but ##\frac {dE}{dt}## was non-zero, would the energy content of the plane wall change?
 
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  • #2
Maylis said:
When you have energy going through a plane wall, I know that the heat flow rate should be constant, meaning what comes in should go out. But is this true even if it is transient, and a non-steady state process?

I think the energy content of the plane will not change for steady state, but for transient it will change, because there is an accumulation of energy term in the balance that is non-zero.

##\frac {dE}{dt} = \dot Q_{x} - \dot Q_{x+\Delta x} + \dot e_{gen}A \Delta x##

Maybe I should clarify. If the internal heat generation were zero, but ##\frac {dE}{dt}## was non-zero, would the energy content of the plane wall change?
Yes, you are certainly correct. Have you used Bird, Stewart, and Lightfoot's book Transport Phenomena in any of your courses. If so, check out Chapter 12, Temperature Distributions with More than One Independent Variable. Examples 12.1 and 12.2.

Chet
 
  • #3
No it was never the main textbook for any of my transport courses, my first one used Welty Rorrer And wicks and my second one uses cengel.

I know it's a classic chemical engineering book and I'll buy it when I see it on amazon at a price that's not too high.
 
  • #4
Maylis said:
No it was never the main textbook for any of my transport courses, my first one used Welty Rorrer And wicks and my second one uses cengel.

I know it's a classic chemical engineering book and I'll buy it when I see it on amazon at a price that's not too high.
It is a wonderful book that had a new edition out about 12 years ago with lots of new developments and content. During my 35 year chemical engineering career, I used this book more than all the other references put together.
 
  • #5


Yes, even if the internal heat generation is zero, the energy content of the plane wall would still change if ##\frac {dE}{dt}## is non-zero. This is because the heat flow rate is not constant in a non-steady state process. In a transient state, the heat flow rate can vary over time and the energy content of the wall will change accordingly. This is because heat conduction is a dynamic process and the rate of heat transfer is influenced by factors such as temperature gradient, thermal conductivity, and thermal diffusivity. Therefore, for a non-steady state process, the energy content of the plane wall will change over time.
 

What is heat conduction?

Heat conduction is the transfer of thermal energy from one material to another due to a difference in temperature between the two materials. This transfer occurs through direct contact between the materials, without any movement of the materials themselves.

How does heat conduction occur through a plane wall?

In a plane wall, heat conduction occurs through the transfer of thermal energy from one side of the wall to the other. This transfer of energy is caused by collisions between molecules in the wall, which causes the molecules to vibrate and transfer their energy to neighboring molecules.

What factors affect heat conduction through a plane wall?

The rate of heat conduction through a plane wall is affected by several factors, including the thickness and material of the wall, the temperature difference between the two sides of the wall, and the thermal conductivity of the material. Additionally, the surface area and boundary conditions of the wall can also impact the rate of heat conduction.

How is heat conduction through a plane wall calculated?

The rate of heat conduction through a plane wall can be calculated using Fourier's law, which states that the rate of heat transfer is directly proportional to the temperature difference and the thermal conductivity of the material, and inversely proportional to the thickness of the wall.

What are some real-life examples of heat conduction through a plane wall?

Heat conduction through a plane wall is a common occurrence in everyday life. Some examples include heat transfer through the walls of a building, the handle of a hot pan, or the walls of a thermos. It is also an important concept in engineering and materials science, as it is used to design and analyze the efficiency of various heat exchange systems.

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