Heat conduction through plane wall

[gfd43tg]

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?

 

[Chestermiller]

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

 

[gfd43tg]

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.

 

[Chestermiller]

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.