Constant heat flux or constant temperature

[Intoto]

Hey all, first time posting!

So I'm having trouble with understanding the differences between the constant heat flux and constant temperature condition when not in a textbook. Some research I have begun working on involves a strip of heat tape sandwiched between two aluminum plates which are allowed to reach steady state. When I think about this conceptually it seems like the plates would eventually reach a constant temperature condition, but at the same time it makes sense to me that it is a constant heat flux condition due to the constant heat transfer at the area in contact with the heat tape.

So my question is what am I missing conceptually to be able to easily determine what the conditions for this setup is? If it is constant heat flux then how would a constant temperature obtained instead? I would greatly appreciate any input that could help me clear this mental confliction.

 

[FactChecker]

If it is in a steady state condition, both the temperatures and the heat flux will be at their stable steady state values.

 

[Intoto]

Thanks for the reply! Ok so if the plates are vertical, I was told the temperature profile would show an increase in temperature as you go up it. Would this be just because of natural convection? I guess I'm asking why doesn't the constant heat flux result in a constant surface temperature. In my head it seems like since the heat tape should be at a uniform temperature, the plate should be heated to a uniform temperature as well.

 

[Chestermiller]

If the system is as you describe it, then the tape will not be at a constant temperature. The bottom part will be cooler than the top part because of the convective heat transfer. The constant heat flux would not result in a constant surface temperature.

 

[FactChecker]

We need to be careful of the terminology. I interpret "constant" as being constant in time at every point, but maybe different constants at different points. I would vote for the terms "uniform" or "equal" to mean that the temperatures are the same at all points.

 

[CWatters]

Thanks for the reply! Ok so if the plates are vertical, I was told the temperature profile would show an increase in temperature as you go up it. Would this be just because of natural convection?

You didn't really fully specify the system but if we assume you meant vertical, surrounded by air in a gravitational field then yes it could be due to convection.

I guess I'm asking why doesn't the constant heat flux result in a constant surface temperature. In my head it seems like since the heat tape should be at a uniform temperature, the plate should be heated to a uniform temperature as well.

The heat flux from tape to air isn't uniform. See diagram. Let's say the air in the room far from the plate is at 20C. If convection is set up the bottom of the plate looses heat into 20C air raising it's temperature causing it to rise. Let's say it's 25C by the time it gets to the top of the plate - so the top of the plate is loosing heat into 25C air. Heat flow/flux is proportional to the temperature gradient through the plate which is different at the top (15C) and the bottom (20C). eg The heat flux through each square inch/cm is greater at the bottom than the top.

Edit: As Chester said.. The temperature of the heat tape may end up hotter at the top than the bottom (if it's not the self regulating type). Heat escapes from it more easily at the bottom due to the different gradient.

 

[Intoto]

Ok I understand now! The surrounding fluid increases in temperature as it rises along the plate causing the heat loss at the top to be less! It seems so simple in hindsight.

Thank you all for the helpful replies!