Thanks in advance.Heat Transfer Modeling: Get Insight for Physical Intuition

[JordanD]

Hello everyone,

I was hoping to get some insight on a model I am trying to create. Quick background in case it is important, I am now working at a new internship I landed for the summer doing some modeling and what not on areas of physics I have never worked on before. It has also been a few years since I have had a proper thermodynamics course so I am rusty.

I can't get into great detail, NDAs and what not, but I was hoping to glean some insight so I can begin to understand what is happening.

Here is my problem. There is a strip of Al (10" x 2.25" x 15um sorry for not converting units) being joule heated, i.e. one end at some positive potential and the other ground. I moreorless understand that part. Provided enough time the strip will be at a constant temp, but how do I gain some kind of timing info from this notion. I mean when I flip the switch it isn't instantly X degrees, its a heating rate, right?

Now to take this notion further imagine I now apply some kind of room temp air stream from say a hose (circular in case it matters) to the center of the strip. With this convective air flow cooling the strip how does that propagate through the rest of the strip? So now there is some kind of cooling rate that is being applied to the strip, so what implications does that bare?

I could just go ahead an pop this into comsol like I plan on doing, but I would really like to gain some sort of physical intuition first.

 

[Chestermiller]

What does potential have to do with heat transfer?

 

[JordanD]

Well that is how joule heating works. You have some potential and some current that creates some power dissipation over the object in question.

 

[Chestermiller]

Well that is how joule heating works. You have some potential and some current that creates some power dissipation over the object in question.

As a guy with tons of heat transfer experience, I have never heard anything described this way. Are you referring to electrical potential and current?

If that is the case, then, what is your piece of material in physical contact with? Is it levitated in the air, or is it actually touching something that it can exchange heat with?

 

[bigfooted]

From wikipedia:

Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.
Joule's first law, also known as the Joule–Lenz law,[1] states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current:

so it is describing for instance the heating of the wire of a light bulb. Suppose you have a very long and thin wire. The temperature of the wire can be described by the one-dimensional heat equation (when there is no flow around the wire). So: how can the heat equation be modified to take into account the heating due to current, with the information given above?

 

[Chestermiller]

From wikipedia:

Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.
Joule's first law, also known as the Joule–Lenz law,[1] states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current:

so it is describing for instance the heating of the wire of a light bulb. Suppose you have a very long and thin wire. The temperature of the wire can be described by the one-dimensional heat equation (when there is no flow around the wire). So: how can the heat equation be modified to take into account the heating due to current, with the information given above?

That is not what I interpret the OP to be asking. He seems to be asking about the temperature that the sample attains when the current is flowing and the sample equilibrates with the surrounding air (or other surroundings). Because the sample is so thin, this will be dominated by natural convective heat transfer outside the sample.

 

[bigfooted]

Yes, you are right, the convection is an important part of the problem description.

I see two ways of approaching the problem. The first method is by analyzing the 1D heat equation. The convective cooling will be a sink term in the equation, and the Joule heating will be a source term. You can find analytic solutions when the source, sink and boundary conditions stay relatively simple. From the solution you can then determine the characteristic heating time (they are the eigenvalues of the problem)

The other approach is the lumped analysis: https://en.wikipedia.org/wiki/Lumped_element_model
This method is used a lot for the analysis of electric circuits, but it can be used as well for the analysis of heat transfer. You then have to find the rate of heat transfer and the thermal resistance terms of Joule heating. This is more the mechanical engineering approach, whereas the first method is more the mathematical physics approach. Depending on your background you might prefer one over the other.

 

[Nidum]

With the meagre information given about the problem I think making a blind guess would be just as accurate .

This is just a bit of cooking foil waving about in the air as far as we know so far . Most likely result of putting any significant current through it is going to be a melt down .

Even if the current could be regulated sufficiently well to just heat the foil without melting it the local temperatures on the foil surface would be all over the place and constantly varying .

@JordanD - can you tell us any more details about the actual set up and the purpose of the experiment ? I'm sure we'd all like to help you with this problem but we really need a lot more information about it first .

 

[Chestermiller]

Yes, you are right, the convection is an important part of the problem description.

I see two ways of approaching the problem. The first method is by analyzing the 1D heat equation. The convective cooling will be a sink term in the equation, and the Joule heating will be a source term. You can find analytic solutions when the source, sink and boundary conditions stay relatively simple. From the solution you can then determine the characteristic heating time (they are the eigenvalues of the problem)

The other approach is the lumped analysis: https://en.wikipedia.org/wiki/Lumped_element_model
This method is used a lot for the analysis of electric circuits, but it can be used as well for the analysis of heat transfer. You then have to find the rate of heat transfer and the thermal resistance terms of Joule heating. This is more the mechanical engineering approach, whereas the first method is more the mathematical physics approach. Depending on your background you might prefer one over the other.

The heat transfer is going to be dominated by the convective heat transfer, and there is no need to consider conduction because the sample is so thin.

 

[JordanD]

Sure I can offer a bit more info. The Al strip is definitely not melting. It is part of a proprietary process that is being used daily. It works very well, but my boss would like to gain a much better understanding of the physics going on so we can know if the process is fully optimized or not.

The strip is just held at two ends, so a current can pass through and heat the strip. So in this scheme I have grown to understand that this is kind of a stationary state equation, i.e. the strip is uniformly heated at all times. I understand this is a good approximation, but I am really just trying to understand where maybe that breaks down. I am also trying to figure out how the radiative and convective cooling comes in, and how those effect the heat of the strip especially when there is a localized stream of air in contact with the strip.

I would also imagine that the speed of the air flow has to come into play in some way, but I am not quite sure how to bring that in.

 

[Chestermiller]

Sure I can offer a bit more info. The Al strip is definitely not melting. It is part of a proprietary process that is being used daily. It works very well, but my boss would like to gain a much better understanding of the physics going on so we can know if the process is fully optimized or not.

The strip is just held at two ends, so a current can pass through and heat the strip. So in this scheme I have grown to understand that this is kind of a stationary state equation, i.e. the strip is uniformly heated at all times. I understand this is a good approximation, but I am really just trying to understand where maybe that breaks down. I am also trying to figure out how the radiative and convective cooling comes in, and how those effect the heat of the strip especially when there is a localized stream of air in contact with the strip.

I would also imagine that the speed of the air flow has to come into play in some way, but I am not quite sure how to bring that in.

Get yourself a copy of Transport Phenomena by Bird, Stewart, and Lightfoot. They discuss the fundamentals of natural- and forced convection heat transfer, and present experimental correlations for determining the heat transfer coefficient. They also discuss radiative heat transfer, and show how to calculate it. Finally, they even include a table of typical ranges of values for natural and forced convection heat transfer coefficients to get a quick estimate of what you are dealing with in a given system (say, in your case, a very quick estimate of the sample temperature).